# Publications

2020
[1]
A. Abboud, K. Censor-Hillel, S. Khoury, and C. Lenzen, “Fooling Views: A New Lower Bound Technique for Distributed Computations under Congestion,” Distributed Computing, 2020.
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@article{Abboud2020, TITLE = {Fooling Views: A New Lower Bound Technique for Distributed Computations under Congestion}, AUTHOR = {Abboud, Amir and Censor-Hillel, Keren and Khoury, Seri and Lenzen, Christoph}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-020-00373-4}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2020}, JOURNAL = {Distributed Computing}, }
Endnote
%0 Journal Article %A Abboud, Amir %A Censor-Hillel, Keren %A Khoury, Seri %A Lenzen, Christoph %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fooling Views: A New Lower Bound Technique for Distributed Computations under Congestion : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F28E-9 %R 10.1007/s00446-020-00373-4 %7 2020 %D 2020 %J Distributed Computing %I Springer %C New York, NY %@ false
[2]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “Scheduling Lower Bounds via AND Subset Sum,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Abboud_ICALP2020, TITLE = {Scheduling Lower Bounds via AND Subset Sum}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124119}, DOI = {10.4230/LIPIcs.ICALP.2020.4}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {4}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Scheduling Lower Bounds via AND Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2826-2 %R 10.4230/LIPIcs.ICALP.2020.4 %U urn:nbn:de:0030-drops-124119 %D 2020 %B 47th International Colloquium on Automata, Languages, and Programming %Z date of event: 2020-07-08 - 2020-07-11 %C Saarbr&#252;cken, Germany (Virtual Conference) %B 47th International Colloquium on Automata, Languages, and Programming %E Czumaj, Artur; Dawa, Anuj; Merelli, Emanuela %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12411/https://creativecommons.org/licenses/by/3.0/legalcode
[3]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “Scheduling Lower Bounds via AND Subset Sum,” 2020. [Online]. Available: https://arxiv.org/abs/2003.07113. (arXiv: 2003.07113)
Abstract
Given $N$ instances $(X_1,t_1),\ldots,(X_N,t_N)$ of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers $X_i$ has a subset that sums up to the target integer $t_i$. We prove that this problem cannot be solved in time $\tilde{O}((N \cdot t_{max})^{1-\epsilon})$, for $t_{max}=\max_i t_i$ and any $\epsilon > 0$, assuming the $\forall \exists$ Strong Exponential Time Hypothesis ($\forall \exists$-SETH). We then use this result to exclude $\tilde{O}(n+P_{max} \cdot n^{1-\epsilon})$-time algorithms for several scheduling problems on $n$ jobs with maximum processing time $P_{max}$, based on $\forall \exists$-SETH. These include classical problems such as $1||\sum w_jU_j$, the problem of minimizing the total weight of tardy jobs on a single machine, and $P_2||\sum U_j$, the problem of minimizing the number of tardy jobs on two identical parallel machines.
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@online{Abboud_arXIv2003.07113, TITLE = {Scheduling Lower Bounds via {AND} Subset Sum}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.07113}, EPRINT = {2003.07113}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Given $N$ instances $(X_1,t_1),\ldots,(X_N,t_N)$ of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers $X_i$ has a subset that sums up to the target integer $t_i$. We prove that this problem cannot be solved in time $\tilde{O}((N \cdot t_{max})^{1-\epsilon})$, for $t_{max}=\max_i t_i$ and any $\epsilon > 0$, assuming the $\forall \exists$ Strong Exponential Time Hypothesis ($\forall \exists$-SETH). We then use this result to exclude $\tilde{O}(n+P_{max} \cdot n^{1-\epsilon})$-time algorithms for several scheduling problems on $n$ jobs with maximum processing time $P_{max}$, based on $\forall \exists$-SETH. These include classical problems such as $1||\sum w_jU_j$, the problem of minimizing the total weight of tardy jobs on a single machine, and $P_2||\sum U_j$, the problem of minimizing the number of tardy jobs on two identical parallel machines.}, }
Endnote
%0 Report %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Scheduling Lower Bounds via AND Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2A52-E %U https://arxiv.org/abs/2003.07113 %D 2020 %X Given $N$ instances $(X_1,t_1),\ldots,(X_N,t_N)$ of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers $X_i$ has a subset that sums up to the target integer $t_i$. We prove that this problem cannot be solved in time $\tilde{O}((N \cdot t_{max})^{1-\epsilon})$, for $t_{max}=\max_i t_i$ and any $\epsilon > 0$, assuming the $\forall \exists$ Strong Exponential Time Hypothesis ($\forall \exists$-SETH). We then use this result to exclude $\tilde{O}(n+P_{max} \cdot n^{1-\epsilon})$-time algorithms for several scheduling problems on $n$ jobs with maximum processing time $P_{max}$, based on $\forall \exists$-SETH. These include classical problems such as $1||\sum w_jU_j$, the problem of minimizing the total weight of tardy jobs on a single machine, and $P_2||\sum U_j$, the problem of minimizing the number of tardy jobs on two identical parallel machines. %K Computer Science, Data Structures and Algorithms, cs.DS
[4]
A. Agrawal, D. Lokshtanov, P. Misra, S. Saurabh, and M. Zehavi, “Polylogarithmic Approximation Algorithms for Weighted-F-deletion,” ACM Transactions on Algorithms, vol. 16, no. 4, 2020.
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@article{Agrawal2020, TITLE = {Polylogarithmic Approximation Algorithms for Weighted-F-deletion}, AUTHOR = {Agrawal, Akanksha and Lokshtanov, Daniel and Misra, Pranabendu and Saurabh, Saket and Zehavi, Meirav}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3389338}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2020}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {16}, NUMBER = {4}, EID = {51}, }
Endnote
%0 Journal Article %A Agrawal, Akanksha %A Lokshtanov, Daniel %A Misra, Pranabendu %A Saurabh, Saket %A Zehavi, Meirav %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Polylogarithmic Approximation Algorithms for Weighted-F-deletion : %G eng %U http://hdl.handle.net/21.11116/0000-0007-4903-4 %R 10.1145/3389338 %7 2020 %D 2020 %J ACM Transactions on Algorithms %V 16 %N 4 %Z sequence number: 51 %I ACM %C New York, NY %@ false
[5]
G. Amanatidis and P. Kleer, “Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences,” Random Structures and Algorithms, vol. 57, no. 3, 2020.
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@article{Amanatidis2020, TITLE = {Rapid mixing of the switch {M}arkov chain for strongly stable degree sequences}, AUTHOR = {Amanatidis, Georgios and Kleer, Pieter}, LANGUAGE = {eng}, ISSN = {1042-9832}, DOI = {10.1002/rsa.20949}, PUBLISHER = {Wiley}, ADDRESS = {New York, N.Y.}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Random Structures and Algorithms}, VOLUME = {57}, NUMBER = {3}, PAGES = {637--657}, }
Endnote
%0 Journal Article %A Amanatidis, Georgios %A Kleer, Pieter %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences : %G eng %U http://hdl.handle.net/21.11116/0000-0006-DC7A-A %R 10.1002/rsa.20949 %7 2020 %D 2020 %J Random Structures and Algorithms %V 57 %N 3 %& 637 %P 637 - 657 %I Wiley %C New York, N.Y. %@ false
[6]
A. Antoniadis, N. Garg, G. Kumar, and N. Kumar, “Parallel Machine Scheduling to Minimize Energy Consumption,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.
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@inproceedings{Antoniadis_SODA20, TITLE = {Parallel Machine Scheduling to Minimize Energy Consumption}, AUTHOR = {Antoniadis, Antonios and Garg, Naveen and Kumar, Gunjan and Kumar, Nikhil}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.5555/3381089.3381257}, PUBLISHER = {SIAM}, YEAR = {2020}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {2758--2769}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Garg, Naveen %A Kumar, Gunjan %A Kumar, Nikhil %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Parallel Machine Scheduling to Minimize Energy Consumption : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F26A-2 %R 10.5555/3381089.3381257 %D 2020 %B 31st Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2020-01-05 - 2020-01-08 %C Salt Lake City, UT, USA %B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms %E Chawla, Shuchi %P 2758 - 2769 %I SIAM %@ 978-1-61197-599-4
[7]
S. Arunachalam, S. Chakraborty, M. Koucký, N. Saurabh, and R. de Wolf, “Improved Bounds on Fourier Entropy and Min-entropy,” in 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020), Montpellier, France, 2020.
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@inproceedings{Arunachalam_STACS2020, TITLE = {Improved Bounds on {Fourier} Entropy and Min-entropy}, AUTHOR = {Arunachalam, Srinivasan and Chakraborty, Sourav and Kouck{\'y}, Michal and Saurabh, Nitin and de Wolf, Ronald}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-140-5}, URL = {urn:nbn:de:0030-drops-119062}, DOI = {10.4230/LIPIcs.STACS.2020.45}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)}, EDITOR = {Paul, Christophe and Bl{\"a}ser, Markus}, PAGES = {1--19}, EID = {45}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {154}, ADDRESS = {Montpellier, France}, }
Endnote
%0 Conference Proceedings %A Arunachalam, Srinivasan %A Chakraborty, Sourav %A Kouck&#253;, Michal %A Saurabh, Nitin %A de Wolf, Ronald %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Improved Bounds on Fourier Entropy and Min-entropy : %G eng %U http://hdl.handle.net/21.11116/0000-0006-97AB-F %R 10.4230/LIPIcs.STACS.2020.45 %U urn:nbn:de:0030-drops-119062 %D 2020 %B 37th International Symposium on Theoretical Aspects of Computer Science %Z date of event: 2020-03-10 - 2020-03-13 %C Montpellier, France %B 37th International Symposium on Theoretical Aspects of Computer Science %E Paul, Christophe; Bl&#228;ser, Markus %P 1 - 19 %Z sequence number: 45 %I Schloss Dagstuhl %@ 978-3-95977-140-5 %B Leibniz International Proceedings in Informatics %N 154 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/11906/
[8]
K. Axiotis, A. Backurs, K. Bringmann, C. Jin, V. Nakos, C. Tzamos, and H. Wu, “Fast and Simple Modular Subset Sum,” 2020. [Online]. Available: https://arxiv.org/abs/2008.10577. (arXiv: 2008.10577)
Abstract
We revisit the Subset Sum problem over the finite cyclic group $\mathbb{Z}_m$ for some given integer $m$. A series of recent works has provided asymptotically optimal algorithms for this problem under the Strong Exponential Time Hypothesis. Koiliaris and Xu (SODA'17, TALG'19) gave a deterministic algorithm running in time $\tilde{O}(m^{5/4})$, which was later improved to $O(m \log^7 m)$ randomized time by Axiotis et al. (SODA'19). In this work, we present two simple algorithms for the Modular Subset Sum problem running in near-linear time in $m$, both efficiently implementing Bellman's iteration over $\mathbb{Z}_m$. The first one is a randomized algorithm running in time $O(m\log^2 m)$, that is based solely on rolling hash and an elementary data-structure for prefix sums; to illustrate its simplicity we provide a short and efficient implementation of the algorithm in Python. Our second solution is a deterministic algorithm running in time $O(m\ \mathrm{polylog}\ m)$, that uses dynamic data structures for string manipulation. We further show that the techniques developed in this work can also lead to simple algorithms for the All Pairs Non-Decreasing Paths Problem (APNP) on undirected graphs, matching the asymptotically optimal running time of $\tilde{O}(n^2)$ provided in the recent work of Duan et al. (ICALP'19).
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@online{Axiotis_arXiv2008.10577, TITLE = {Fast and Simple Modular Subset Sum}, AUTHOR = {Axiotis, Kyriakos and Backurs, Arturs and Bringmann, Karl and Jin, Ce and Nakos, Vasileios and Tzamos, Christos and Wu, Hongxun}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2008.10577}, EPRINT = {2008.10577}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {We revisit the Subset Sum problem over the finite cyclic group $\mathbb{Z}_m$ for some given integer $m$. A series of recent works has provided asymptotically optimal algorithms for this problem under the Strong Exponential Time Hypothesis. Koiliaris and Xu (SODA'17, TALG'19) gave a deterministic algorithm running in time $\tilde{O}(m^{5/4})$, which was later improved to $O(m \log^7 m)$ randomized time by Axiotis et al. (SODA'19). In this work, we present two simple algorithms for the Modular Subset Sum problem running in near-linear time in $m$, both efficiently implementing Bellman's iteration over $\mathbb{Z}_m$. The first one is a randomized algorithm running in time $O(m\log^2 m)$, that is based solely on rolling hash and an elementary data-structure for prefix sums; to illustrate its simplicity we provide a short and efficient implementation of the algorithm in Python. Our second solution is a deterministic algorithm running in time $O(m\ \mathrm{polylog}\ m)$, that uses dynamic data structures for string manipulation. We further show that the techniques developed in this work can also lead to simple algorithms for the All Pairs Non-Decreasing Paths Problem (APNP) on undirected graphs, matching the asymptotically optimal running time of $\tilde{O}(n^2)$ provided in the recent work of Duan et al. (ICALP'19).}, }
Endnote
%0 Report %A Axiotis, Kyriakos %A Backurs, Arturs %A Bringmann, Karl %A Jin, Ce %A Nakos, Vasileios %A Tzamos, Christos %A Wu, Hongxun %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Fast and Simple Modular Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2A5B-5 %U https://arxiv.org/abs/2008.10577 %D 2020 %X We revisit the Subset Sum problem over the finite cyclic group $\mathbb{Z}_m$ for some given integer $m$. A series of recent works has provided asymptotically optimal algorithms for this problem under the Strong Exponential Time Hypothesis. Koiliaris and Xu (SODA'17, TALG'19) gave a deterministic algorithm running in time $\tilde{O}(m^{5/4})$, which was later improved to $O(m \log^7 m)$ randomized time by Axiotis et al. (SODA'19). In this work, we present two simple algorithms for the Modular Subset Sum problem running in near-linear time in $m$, both efficiently implementing Bellman's iteration over $\mathbb{Z}_m$. The first one is a randomized algorithm running in time $O(m\log^2 m)$, that is based solely on rolling hash and an elementary data-structure for prefix sums; to illustrate its simplicity we provide a short and efficient implementation of the algorithm in Python. Our second solution is a deterministic algorithm running in time $O(m\ \mathrm{polylog}\ m)$, that uses dynamic data structures for string manipulation. We further show that the techniques developed in this work can also lead to simple algorithms for the All Pairs Non-Decreasing Paths Problem (APNP) on undirected graphs, matching the asymptotically optimal running time of $\tilde{O}(n^2)$ provided in the recent work of Duan et al. (ICALP'19). %K Computer Science, Data Structures and Algorithms, cs.DS
[9]
R. Becker, Y. Emek, and C. Lenzen, “Low Diameter Graph Decompositions by Approximate Distance Computation,” in 11th Innovations in Theoretical Computer Science Conference (ITICS 2020), Seattle, WA, USA, 2020.
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@inproceedings{Becker_ITCS2020, TITLE = {Low Diameter Graph Decompositions by Approximate Distance Computation}, AUTHOR = {Becker, Ruben and Emek, Yuval and Lenzen, Christoph}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-134-4}, URL = {urn:nbn:de:0030-drops-117355}, DOI = {10.4230/LIPIcs.ITCS.2020.50}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {11th Innovations in Theoretical Computer Science Conference (ITICS 2020)}, EDITOR = {Vidick, Thomas}, EID = {50}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {151}, ADDRESS = {Seattle, WA, USA}, }
Endnote
%0 Conference Proceedings %A Becker, Ruben %A Emek, Yuval %A Lenzen, Christoph %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Low Diameter Graph Decompositions by Approximate Distance Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-A7A7-2 %R 10.4230/LIPIcs.ITCS.2020.50 %U urn:nbn:de:0030-drops-117355 %D 2020 %B 11th Innovations in Theoretical Computer Science Conference %Z date of event: 2020-01-12 - 2020-01-14 %C Seattle, WA, USA %B 11th Innovations in Theoretical Computer Science Conference %E Vidick, Thomas %Z sequence number: 50 %I Schloss Dagstuhl %@ 978-3-95977-134-4 %B Leibniz International Proceedings in Informatics %N 151 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/11735/https://drops.dagstuhl.de/doku/urheberrecht1.html
[10]
V. Bonifaci, E. Facca, F. Folz, A. Karrenbauer, P. Kolev, K. Mehlhorn, G. Morigi, G. Shahkarami, and Q. Vermande, “Physarum Multi-Commodity Flow Dynamics,” 2020. [Online]. Available: https://arxiv.org/abs/2009.01498. (arXiv: 2009.01498)
Abstract
In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks, see Figure \ref{Wet-Lab Experiments} for illustrations. Physarum polycephalum is a slime mold in the Mycetozoa group. For the shortest path problem, a mathematical model for the evolution of the slime was proposed in \cite{Tero-Kobayashi-Nakagaki} and its biological relevance was argued. The model was shown to solve shortest path problems, first in computer simulations and then by mathematical proof. It was later shown that the slime mold dynamics can solve more general linear programs and that many variants of the dynamics have similar convergence behavior. In this paper, we introduce a dynamics for the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterization of the optimum solution.
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@online{Bonifaci_arXiv2009.01498, TITLE = {Physarum Multi-Commodity Flow Dynamics}, AUTHOR = {Bonifaci, Vincenzo and Facca, Enrico and Folz, Frederic and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt and Morigi, Giovanna and Shahkarami, Golnoosh and Vermande, Quentin}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2009.01498}, EPRINT = {2009.01498}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks, see Figure \ref{Wet-Lab Experiments} for illustrations. Physarum polycephalum is a slime mold in the Mycetozoa group. For the shortest path problem, a mathematical model for the evolution of the slime was proposed in \cite{Tero-Kobayashi-Nakagaki} and its biological relevance was argued. The model was shown to solve shortest path problems, first in computer simulations and then by mathematical proof. It was later shown that the slime mold dynamics can solve more general linear programs and that many variants of the dynamics have similar convergence behavior. In this paper, we introduce a dynamics for the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterization of the optimum solution.}, }
Endnote
%0 Report %A Bonifaci, Vincenzo %A Facca, Enrico %A Folz, Frederic %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %A Morigi, Giovanna %A Shahkarami, Golnoosh %A Vermande, Quentin %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Physarum Multi-Commodity Flow Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2312-D %U https://arxiv.org/abs/2009.01498 %D 2020 %X In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks, see Figure \ref{Wet-Lab Experiments} for illustrations. Physarum polycephalum is a slime mold in the Mycetozoa group. For the shortest path problem, a mathematical model for the evolution of the slime was proposed in \cite{Tero-Kobayashi-Nakagaki} and its biological relevance was argued. The model was shown to solve shortest path problems, first in computer simulations and then by mathematical proof. It was later shown that the slime mold dynamics can solve more general linear programs and that many variants of the dynamics have similar convergence behavior. In this paper, we introduce a dynamics for the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterization of the optimum solution. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Neural and Evolutionary Computing, cs.NE
[11]
K. Bringmann, T. Husfeldt, and M. Magnusson, “Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth,” Algorithmica, vol. 82, no. 8, 2020.
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@article{Bringmann_2020a, TITLE = {Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth}, AUTHOR = {Bringmann, Karl and Husfeldt, Thore and Magnusson, M{\aa}ns}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-020-00680-z}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Algorithmica}, VOLUME = {82}, NUMBER = {8}, PAGES = {2292--2315}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Husfeldt, Thore %A Magnusson, M&#229;ns %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F289-E %R 10.1007/s00453-020-00680-z %7 2020 %D 2020 %J Algorithmica %V 82 %N 8 %& 2292 %P 2292 - 2315 %I Springer %C New York %@ false
[12]
K. Bringmann, P. Gawrychowski, S. Mozes, and O. Weimann, “Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can),” ACM Transactions on Algorithms, vol. 16, no. 4, 2020.
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@article{Bringmann_ToA2020, TITLE = {Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless {APSP} can)}, AUTHOR = {Bringmann, Karl and Gawrychowski, Pawe{\l} and Mozes, Shay and Weimann, Oren}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3381878}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2020}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {16}, NUMBER = {4}, EID = {48}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Gawrychowski, Pawe&#322; %A Mozes, Shay %A Weimann, Oren %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can) : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2502-D %R 10.1145/3381878 %7 2020 %D 2020 %J ACM Transactions on Algorithms %V 16 %N 4 %Z sequence number: 48 %I ACM %C New York, NY %@ false
[13]
K. Bringmann, M. Künnemann, and A. Nusser, “When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance Under Translation,” in 28th Annual European Symposium on Algorithms (ESA 2020), Pisa, Italy (Virtual Conference), 2020.
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@inproceedings{Bringmann_ESA2020, TITLE = {When {L}ipschitz Walks Your Dog: {A}lgorithm Engineering of the Discrete {F}r\'{e}chet Distance Under Translation}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-162-7}, URL = {urn:nbn:de:0030-drops-128912}, DOI = {10.4230/LIPIcs.ESA.2020.25}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {28th Annual European Symposium on Algorithms (ESA 2020)}, EDITOR = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, EID = {25}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {173}, ADDRESS = {Pisa, Italy (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fr&#233;chet Distance Under Translation : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2791-9 %R 10.4230/LIPIcs.ESA.2020.25 %U urn:nbn:de:0030-drops-128912 %D 2020 %B 28th Annual European Symposium on Algorithms %Z date of event: 2020-09-07 - 2020-09-09 %C Pisa, Italy (Virtual Conference) %B 28th Annual European Symposium on Algorithms %E Grandoni, Fabrizio; Herman, Grzegorz; Sanders, Peter %Z sequence number: 25 %I Schloss Dagstuhl %@ 978-3-95977-162-7 %B Leibniz International Proceedings in Informatics %N 173 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12891/https://creativecommons.org/licenses/by/3.0/legalcodehttps://gitlab.com/anusser/frechet_distance_under_translation
[14]
K. Bringmann, N. Fischer, D. Hermelin, D. Shabtay, and P. Wellnitz, “Faster Minimization of Tardy Processing Time on a Single Machine,” 2020. [Online]. Available: https://arxiv.org/abs/2003.07104. (arXiv: 2003.07104)
Abstract
This paper is concerned with the $1||\sum p_jU_j$ problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also a very important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The fastest known pseudo-polynomial time algorithm for the problem is the famous Lawler and Moore algorithm which runs in $O(P \cdot n)$ time, where $P$ is the total processing time of all $n$ jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date. In this paper we develop two new algorithms for $1||\sum p_jU_j$, each improving on Lawler and Moore's algorithm in a different scenario. Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, while for the first algorithm we define a new "skewed" version of $(\max,\min)$-convolution which is interesting in its own right.
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@online{Bringmann_arXiv2003.07104, TITLE = {Faster Minimization of Tardy Processing Time on a Single Machine}, AUTHOR = {Bringmann, Karl and Fischer, Nick and Hermelin, Danny and Shabtay, Dvir and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.07104}, EPRINT = {2003.07104}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {This paper is concerned with the $1||\sum p_jU_j$ problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also a very important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The fastest known pseudo-polynomial time algorithm for the problem is the famous Lawler and Moore algorithm which runs in $O(P \cdot n)$ time, where $P$ is the total processing time of all $n$ jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date. In this paper we develop two new algorithms for $1||\sum p_jU_j$, each improving on Lawler and Moore's algorithm in a different scenario. Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, while for the first algorithm we define a new "skewed" version of $(\max,\min)$-convolution which is interesting in its own right.}, }
Endnote
%0 Report %A Bringmann, Karl %A Fischer, Nick %A Hermelin, Danny %A Shabtay, Dvir %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Minimization of Tardy Processing Time on a Single Machine : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2A4E-4 %U https://arxiv.org/abs/2003.07104 %D 2020 %X This paper is concerned with the $1||\sum p_jU_j$ problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also a very important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The fastest known pseudo-polynomial time algorithm for the problem is the famous Lawler and Moore algorithm which runs in $O(P \cdot n)$ time, where $P$ is the total processing time of all $n$ jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date. In this paper we develop two new algorithms for $1||\sum p_jU_j$, each improving on Lawler and Moore's algorithm in a different scenario. Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, while for the first algorithm we define a new "skewed" version of $(\max,\min)$-convolution which is interesting in its own right. %K Computer Science, Data Structures and Algorithms, cs.DS
[15]
K. Bringmann, N. Fischer, D. Hermelin, D. Shabtay, and P. Wellnitz, “Faster Minimization of Tardy Processing Time on a Single Machine,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Bringmann_ICALP2020, TITLE = {Faster Minimization of Tardy Processing Time on a Single Machine}, AUTHOR = {Bringmann, Karl and Fischer, Nick and Hermelin, Danny and Shabtay, Dvir and Wellnitz, Philip}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124269}, DOI = {10.4230/LIPIcs.ICALP.2020.19}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {19}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Fischer, Nick %A Hermelin, Danny %A Shabtay, Dvir %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Minimization of Tardy Processing Time on a Single Machine : %G eng %U http://hdl.handle.net/21.11116/0000-0007-287E-0 %R 10.4230/LIPIcs.ICALP.2020.19 %U urn:nbn:de:0030-drops-124269 %D 2020 %B 47th International Colloquium on Automata, Languages, and Programming %Z date of event: 2020-07-08 - 2020-07-11 %C Saarbr&#252;cken, Germany (Virtual Conference) %B 47th International Colloquium on Automata, Languages, and Programming %E Czumaj, Artur; Dawa, Anuj; Merelli, Emanuela %Z sequence number: 19 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12426/https://creativecommons.org/licenses/by/3.0/legalcode
[16]
K. Bringmann and V. Nakos, “Top-k-convolution and the Quest for Near-linear Output-sensitive Subset Sum,” in STOC ’20, Chicago, IL, USA, 2020.
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@inproceedings{Bringmann_STOC2020, TITLE = {Top-$k$-convolution and the Quest for Near-linear Output-sensitive Subset Sum}, AUTHOR = {Bringmann, Karl and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {978-1-4503-6979-4}, DOI = {10.1145/3357713.3384308}, PUBLISHER = {ACM}, YEAR = {2020}, BOOKTITLE = {STOC '20}, EDITOR = {Makarychev, Konstantin and Makarychev, Yury and Tulsiani, Madhur and Kamath, Gautam and Chuzhoy, Julia}, PAGES = {982--995}, ADDRESS = {Chicago, IL, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Nakos, Vasileios %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Top-k-convolution and the Quest for Near-linear Output-sensitive Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-299D-B %R 10.1145/3357713.3384308 %D 2020 %B 52nd Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2020-06-22 - 2020-06-26 %C Chicago, IL, USA %B STOC '20 %E Makarychev, Konstantin; Makarychev, Yury; Tulsiani, Madhur; Kamath, Gautam; Chuzhoy, Julia %P 982 - 995 %I ACM %@ 978-1-4503-6979-4
[17]
K. Bringmann, M. Künnemann, and A. Nusser, “When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance under Translation,” 2020. [Online]. Available: https://arxiv.org/abs/2008.07510. (arXiv: 2008.07510)
Abstract
Consider the natural question of how to measure the similarity of curves in the plane by a quantity that is invariant under translations of the curves. Such a measure is justified whenever we aim to quantify the similarity of the curves' shapes rather than their positioning in the plane, e.g., to compare the similarity of handwritten characters. Perhaps the most natural such notion is the (discrete) Fr\'echet distance under translation. Unfortunately, the algorithmic literature on this problem yields a very pessimistic view: On polygonal curves with $n$ vertices, the fastest algorithm runs in time $O(n^{4.667})$ and cannot be improved below $n^{4-o(1)}$ unless the Strong Exponential Time Hypothesis fails. Can we still obtain an implementation that is efficient on realistic datasets? Spurred by the surprising performance of recent implementations for the Fr\'echet distance, we perform algorithm engineering for the Fr\'echet distance under translation. Our solution combines fast, but inexact tools from continuous optimization (specifically, branch-and-bound algorithms for global Lipschitz optimization) with exact, but expensive algorithms from computational geometry (specifically, problem-specific algorithms based on an arrangement construction). We combine these two ingredients to obtain an exact decision algorithm for the Fr\'echet distance under translation. For the related task of computing the distance value up to a desired precision, we engineer and compare different methods. On a benchmark set involving handwritten characters and route trajectories, our implementation answers a typical query for either task in the range of a few milliseconds up to a second on standard desktop hardware. We believe that our implementation will enable the use of the Fr\'echet distance under translation in applications, whereas previous approaches would have been computationally infeasible.
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@online{Bringmann_arXiv2008.07510, TITLE = {When {L}ipschitz Walks Your Dog: {A}lgorithm Engineering of the Discrete {F}r\'{e}chet Distance Under Translation}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2008.07510}, EPRINT = {2008.07510}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Consider the natural question of how to measure the similarity of curves in the plane by a quantity that is invariant under translations of the curves. Such a measure is justified whenever we aim to quantify the similarity of the curves' shapes rather than their positioning in the plane, e.g., to compare the similarity of handwritten characters. Perhaps the most natural such notion is the (discrete) Fr\'echet distance under translation. Unfortunately, the algorithmic literature on this problem yields a very pessimistic view: On polygonal curves with $n$ vertices, the fastest algorithm runs in time $O(n^{4.667})$ and cannot be improved below $n^{4-o(1)}$ unless the Strong Exponential Time Hypothesis fails. Can we still obtain an implementation that is efficient on realistic datasets? Spurred by the surprising performance of recent implementations for the Fr\'echet distance, we perform algorithm engineering for the Fr\'echet distance under translation. Our solution combines fast, but inexact tools from continuous optimization (specifically, branch-and-bound algorithms for global Lipschitz optimization) with exact, but expensive algorithms from computational geometry (specifically, problem-specific algorithms based on an arrangement construction). We combine these two ingredients to obtain an exact decision algorithm for the Fr\'echet distance under translation. For the related task of computing the distance value up to a desired precision, we engineer and compare different methods. On a benchmark set involving handwritten characters and route trajectories, our implementation answers a typical query for either task in the range of a few milliseconds up to a second on standard desktop hardware. We believe that our implementation will enable the use of the Fr\'echet distance under translation in applications, whereas previous approaches would have been computationally infeasible.}, }
Endnote
%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fr&#233;chet Distance under Translation : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2A56-A %U https://arxiv.org/abs/2008.07510 %D 2020 %X Consider the natural question of how to measure the similarity of curves in the plane by a quantity that is invariant under translations of the curves. Such a measure is justified whenever we aim to quantify the similarity of the curves' shapes rather than their positioning in the plane, e.g., to compare the similarity of handwritten characters. Perhaps the most natural such notion is the (discrete) Fr\'echet distance under translation. Unfortunately, the algorithmic literature on this problem yields a very pessimistic view: On polygonal curves with $n$ vertices, the fastest algorithm runs in time $O(n^{4.667})$ and cannot be improved below $n^{4-o(1)}$ unless the Strong Exponential Time Hypothesis fails. Can we still obtain an implementation that is efficient on realistic datasets? Spurred by the surprising performance of recent implementations for the Fr\'echet distance, we perform algorithm engineering for the Fr\'echet distance under translation. Our solution combines fast, but inexact tools from continuous optimization (specifically, branch-and-bound algorithms for global Lipschitz optimization) with exact, but expensive algorithms from computational geometry (specifically, problem-specific algorithms based on an arrangement construction). We combine these two ingredients to obtain an exact decision algorithm for the Fr\'echet distance under translation. For the related task of computing the distance value up to a desired precision, we engineer and compare different methods. On a benchmark set involving handwritten characters and route trajectories, our implementation answers a typical query for either task in the range of a few milliseconds up to a second on standard desktop hardware. We believe that our implementation will enable the use of the Fr\'echet distance under translation in applications, whereas previous approaches would have been computationally infeasible. %K Computer Science, Computational Geometry, cs.CG,Computer Science, Data Structures and Algorithms, cs.DS
[18]
J. Bund, C. Lenzen, and M. Medina, “Optimal Metastability-Containing Sorting via Parallel Prefix Computation,” IEEE Transactions on Computers, vol. 69, no. 2, 2020.
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@article{Bund_IEEETOC2020, TITLE = {Optimal Metastability-Containing Sorting via Parallel Prefix Computation}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, ISSN = {0018-9340}, DOI = {10.1109/TC.2019.2939818}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2020}, DATE = {2020}, JOURNAL = {IEEE Transactions on Computers}, VOLUME = {69}, NUMBER = {2}, PAGES = {198--211}, }
Endnote
%0 Journal Article %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-Containing Sorting via Parallel Prefix Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-9E7F-C %R 10.1109/TC.2019.2939818 %7 2020 %D 2020 %J IEEE Transactions on Computers %V 69 %N 2 %& 198 %P 198 - 211 %I IEEE %C Piscataway, NJ %@ false
[19]
J. Bund, M. Fugger, C. Lenzen, and M. Medina, “Synchronizer-Free Digital Link Controller,” IEEE Transactions on Circuits and Systems / I, Regular Papers, vol. 27, no. 10, 2020.
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@article{Bund2020, TITLE = {Synchronizer-Free Digital Link Controller}, AUTHOR = {Bund, Johannes and Fugger, Matthias and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, ISSN = {1057-7122}, DOI = {10.1109/TCSI.2020.2989552}, PUBLISHER = {Institute of Electrical and Electronics Engineers}, ADDRESS = {Piscataway, NJ}, YEAR = {2020}, DATE = {2020}, JOURNAL = {IEEE Transactions on Circuits and Systems / I, Regular Papers}, VOLUME = {27}, NUMBER = {10}, PAGES = {3562--3573}, }
Endnote
%0 Journal Article %A Bund, Johannes %A Fugger, Matthias %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Synchronizer-Free Digital Link Controller : %G eng %U http://hdl.handle.net/21.11116/0000-0007-35FE-0 %R 10.1109/TCSI.2020.2989552 %7 2020 %D 2020 %J IEEE Transactions on Circuits and Systems / I, Regular Papers %V 27 %N 10 %& 3562 %P 3562 - 3573 %I Institute of Electrical and Electronics Engineers %C Piscataway, NJ %@ false
[20]
J. Bund, M. Függer, C. Lenzen, M. Medina, and W. Rosenbaum, “PALS: Plesiochronous and Locally Synchronous Systems,” in 26th IEEE International Symposium on Asynchronous Circuits and Systems, Salt Lake City, UT, USA, 2020.
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@inproceedings{Bund_ASYNC2020, TITLE = {{PALS}: {P}lesiochronous and Locally Synchronous Systems}, AUTHOR = {Bund, Johannes and F{\"u}gger, Matthias and Lenzen, Christoph and Medina, Moti and Rosenbaum, Will}, LANGUAGE = {eng}, ISBN = {978-1-7281-5495-4}, DOI = {10.1109/ASYNC49171.2020.00013}, PUBLISHER = {IEEE}, YEAR = {2020}, BOOKTITLE = {26th IEEE International Symposium on Asynchronous Circuits and Systems}, PAGES = {36--43}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Bund, Johannes %A F&#252;gger, Matthias %A Lenzen, Christoph %A Medina, Moti %A Rosenbaum, Will %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T PALS: Plesiochronous and Locally Synchronous Systems : %G eng %U http://hdl.handle.net/21.11116/0000-0007-46B8-B %R 10.1109/ASYNC49171.2020.00013 %D 2020 %B 26th IEEE International Symposium on Asynchronous Circuits and Systems %Z date of event: 2020-05-17 - 2020-05-20 %C Salt Lake City, UT, USA %B 26th IEEE International Symposium on Asynchronous Circuits and Systems %P 36 - 43 %I IEEE %@ 978-1-7281-5495-4
[21]
J. Bund, M. Függer, C. Lenzen, M. Medina, and W. Rosenbaum, “PALS: Plesiochronous and Locally Synchronous Systems,” 2020. [Online]. Available: https://arxiv.org/abs/2003.05542. (arXiv: 2003.05542)
Abstract
Consider an arbitrary network of communicating modules on a chip, each requiring a local signal telling it when to execute a computational step. There are three common solutions to generating such a local clock signal: (i) by deriving it from a single, central clock source, (ii) by local, free-running oscillators, or (iii) by handshaking between neighboring modules. Conceptually, each of these solutions is the result of a perceived dichotomy in which (sub)systems are either clocked or fully asynchronous, suggesting that the designer's choice is limited to deciding where to draw the line between synchronous and asynchronous design. In contrast, we take the view that the better question to ask is how synchronous the system can and should be. Based on a distributed clock synchronization algorithm, we present a novel design providing modules with local clocks whose frequency bounds are almost as good as those of corresponding free-running oscillators, yet neighboring modules are guaranteed to have a phase offset substantially smaller than one clock cycle. Concretely, parameters obtained from a 15nm ASIC implementation running at 2GHz yield mathematical worst-case bounds of 30ps on phase offset for a 32x32 node grid network.
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@online{Bund_arXiv2003.05542, TITLE = {{PALS}: Plesiochronous and Locally Synchronous Systems}, AUTHOR = {Bund, Johannes and F{\"u}gger, Matthias and Lenzen, Christoph and Medina, Moti and Rosenbaum, Will}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.05542}, EPRINT = {2003.05542}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Consider an arbitrary network of communicating modules on a chip, each requiring a local signal telling it when to execute a computational step. There are three common solutions to generating such a local clock signal: (i) by deriving it from a single, central clock source, (ii) by local, free-running oscillators, or (iii) by handshaking between neighboring modules. Conceptually, each of these solutions is the result of a perceived dichotomy in which (sub)systems are either clocked or fully asynchronous, suggesting that the designer's choice is limited to deciding where to draw the line between synchronous and asynchronous design. In contrast, we take the view that the better question to ask is how synchronous the system can and should be. Based on a distributed clock synchronization algorithm, we present a novel design providing modules with local clocks whose frequency bounds are almost as good as those of corresponding free-running oscillators, yet neighboring modules are guaranteed to have a phase offset substantially smaller than one clock cycle. Concretely, parameters obtained from a 15nm ASIC implementation running at 2GHz yield mathematical worst-case bounds of 30ps on phase offset for a 32x32 node grid network.}, }
Endnote
%0 Report %A Bund, Johannes %A F&#252;gger, Matthias %A Lenzen, Christoph %A Medina, Moti %A Rosenbaum, Will %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T PALS: Plesiochronous and Locally Synchronous Systems : %G eng %U http://hdl.handle.net/21.11116/0000-0007-475C-3 %U https://arxiv.org/abs/2003.05542 %D 2020 %X Consider an arbitrary network of communicating modules on a chip, each requiring a local signal telling it when to execute a computational step. There are three common solutions to generating such a local clock signal: (i) by deriving it from a single, central clock source, (ii) by local, free-running oscillators, or (iii) by handshaking between neighboring modules. Conceptually, each of these solutions is the result of a perceived dichotomy in which (sub)systems are either clocked or fully asynchronous, suggesting that the designer's choice is limited to deciding where to draw the line between synchronous and asynchronous design. In contrast, we take the view that the better question to ask is how synchronous the system can and should be. Based on a distributed clock synchronization algorithm, we present a novel design providing modules with local clocks whose frequency bounds are almost as good as those of corresponding free-running oscillators, yet neighboring modules are guaranteed to have a phase offset substantially smaller than one clock cycle. Concretely, parameters obtained from a 15nm ASIC implementation running at 2GHz yield mathematical worst-case bounds of 30ps on phase offset for a 32x32 node grid network. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[22]
P. Chalermsook, M. Cygan, G. Kortsarz, B. Laekhanukit, P. Manurangsi, D. Nanongkai, and L. Trevisan, “From Gap-Exponential Time Hypothesis to Fixed Parameter Tractable Inapproximability: Clique, Dominating Set, and More,” SIAM Journal on Computing, vol. 49, no. 4, 2020.
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@article{Chalermsook2020, TITLE = {From Gap-Exponential Time Hypothesis to Fixed Parameter Tractable Inapproximability: {C}lique, Dominating Set, and More}, AUTHOR = {Chalermsook, Parinya and Cygan, Marek and Kortsarz, Guy and Laekhanukit, Bundit and Manurangsi, Pasin and Nanongkai, Danupon and Trevisan, Luca}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/18M1166869}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2020}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {49}, NUMBER = {4}, PAGES = {772--810}, }
Endnote
%0 Journal Article %A Chalermsook, Parinya %A Cygan, Marek %A Kortsarz, Guy %A Laekhanukit, Bundit %A Manurangsi, Pasin %A Nanongkai, Danupon %A Trevisan, Luca %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T From Gap-Exponential Time Hypothesis to Fixed Parameter Tractable Inapproximability: Clique, Dominating Set, and More : %G eng %U http://hdl.handle.net/21.11116/0000-0007-1D05-4 %R 10.1137/18M1166869 %7 2020 %D 2020 %J SIAM Journal on Computing %V 49 %N 4 %& 772 %P 772 - 810 %I SIAM %C Philadelphia, PA %@ false
[23]
R. H. Chitnis, A. E. Feldmann, M. HajiAghayi, and D. Marx, “Tight Bounds for Planar Strongly Connected Steiner Subgraph with Fixed Number of Terminals (and Extensions),” SIAM Journal on Computing, vol. 49, no. 2, 2020.
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@article{Chitnis2020, TITLE = {Tight Bounds for Planar Strongly Connected {Steiner} Subgraph with Fixed Number of Terminals (and Extensions)}, AUTHOR = {Chitnis, Rajesh H. and Feldmann, Andreas E. and HajiAghayi, MohammadTaghi and Marx, Daniel}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/18M122371X}, PUBLISHER = {Society for Industrial and Applied Mathematics.}, ADDRESS = {Philadelphia}, YEAR = {2020}, DATE = {2020}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {49}, NUMBER = {2}, PAGES = {318--364}, }
Endnote
%0 Journal Article %A Chitnis, Rajesh H. %A Feldmann, Andreas E. %A HajiAghayi, MohammadTaghi %A Marx, Daniel %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tight Bounds for Planar Strongly Connected Steiner Subgraph with Fixed Number of Terminals (and Extensions) : %G eng %U http://hdl.handle.net/21.11116/0000-0006-E002-A %R 10.1137/18M122371X %7 2020 %D 2020 %J SIAM Journal on Computing %V 49 %N 2 %& 318 %P 318 - 364 %I Society for Industrial and Applied Mathematics. %C Philadelphia %@ false
[24]
V. Cohen-Addad, P. N. Klein, and D. Marx, “On the Computational Tractability of a Geographic Clustering Problem Arising in Redistricting,” 2020. [Online]. Available: https://arxiv.org/abs/2009.00188. (arXiv: 2009.00188)
Abstract
Redistricting is the problem of dividing a state into a number $k$ of regions, called districts. Voters in each district elect a representative. The primary criteria are: each district is connected, district populations are equal (or nearly equal), and districts are "compact". There are multiple competing definitions of compactness, usually minimizing some quantity. One measure that has been recently promoted by Duchin and others is number of cut edges. In redistricting, one is given atomic regions out of which each district must be built. The populations of the atomic regions are given. Consider the graph with one vertex per atomic region (with weight equal to the region's population) and an edge between atomic regions that share a boundary. A districting plan is a partition of vertices into $k$ parts, each connnected, of nearly equal weight. The districts are considered compact to the extent that the plan minimizes the number of edges crossing between different parts. Consider two problems: find the most compact districting plan, and sample districting plans under a compactness constraint uniformly at random. Both problems are NP-hard so we restrict the input graph to have branchwidth at most $w$. (A planar graph's branchwidth is bounded by its diameter.) If both $k$ and $w$ are bounded by constants, the problems are solvable in polynomial time. Assume vertices have weight~1. One would like algorithms whose running times are of the form $O(f(k,w) n^c)$ for some constant $c$ independent of $k$ and $w$, in which case the problems are said to be fixed-parameter tractable with respect to $k$ and $w$). We show that, under a complexity-theoretic assumption, no such algorithms exist. However, we do give algorithms with running time $O(c^wn^{k+1})$. Thus if the diameter of the graph is moderately small and the number of districts is very small, our algorithm is useable.
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@online{Cohen-Addad_arXiv2009.00188, TITLE = {On the Computational Tractability of a Geographic Clustering Problem Arising in Redistricting}, AUTHOR = {Cohen-Addad, Vincent and Klein, Philip N. and Marx, D{\'a}niel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2009.00188}, EPRINT = {2009.00188}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Redistricting is the problem of dividing a state into a number $k$ of regions, called districts. Voters in each district elect a representative. The primary criteria are: each district is connected, district populations are equal (or nearly equal), and districts are "compact". There are multiple competing definitions of compactness, usually minimizing some quantity. One measure that has been recently promoted by Duchin and others is number of cut edges. In redistricting, one is given atomic regions out of which each district must be built. The populations of the atomic regions are given. Consider the graph with one vertex per atomic region (with weight equal to the region's population) and an edge between atomic regions that share a boundary. A districting plan is a partition of vertices into $k$ parts, each connnected, of nearly equal weight. The districts are considered compact to the extent that the plan minimizes the number of edges crossing between different parts. Consider two problems: find the most compact districting plan, and sample districting plans under a compactness constraint uniformly at random. Both problems are NP-hard so we restrict the input graph to have branchwidth at most $w$. (A planar graph's branchwidth is bounded by its diameter.) If both $k$ and $w$ are bounded by constants, the problems are solvable in polynomial time. Assume vertices have weight~1. One would like algorithms whose running times are of the form $O(f(k,w) n^c)$ for some constant $c$ independent of $k$ and $w$, in which case the problems are said to be fixed-parameter tractable with respect to $k$ and $w$). We show that, under a complexity-theoretic assumption, no such algorithms exist. However, we do give algorithms with running time $O(c^wn^{k+1})$. Thus if the diameter of the graph is moderately small and the number of districts is very small, our algorithm is useable.}, }
Endnote
%0 Report %A Cohen-Addad, Vincent %A Klein, Philip N. %A Marx, D&#225;niel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Computational Tractability of a Geographic Clustering Problem Arising in Redistricting : %G eng %U http://hdl.handle.net/21.11116/0000-0007-495A-3 %U https://arxiv.org/abs/2009.00188 %D 2020 %X Redistricting is the problem of dividing a state into a number $k$ of regions, called districts. Voters in each district elect a representative. The primary criteria are: each district is connected, district populations are equal (or nearly equal), and districts are "compact". There are multiple competing definitions of compactness, usually minimizing some quantity. One measure that has been recently promoted by Duchin and others is number of cut edges. In redistricting, one is given atomic regions out of which each district must be built. The populations of the atomic regions are given. Consider the graph with one vertex per atomic region (with weight equal to the region's population) and an edge between atomic regions that share a boundary. A districting plan is a partition of vertices into $k$ parts, each connnected, of nearly equal weight. The districts are considered compact to the extent that the plan minimizes the number of edges crossing between different parts. Consider two problems: find the most compact districting plan, and sample districting plans under a compactness constraint uniformly at random. Both problems are NP-hard so we restrict the input graph to have branchwidth at most $w$. (A planar graph's branchwidth is bounded by its diameter.) If both $k$ and $w$ are bounded by constants, the problems are solvable in polynomial time. Assume vertices have weight~1. One would like algorithms whose running times are of the form $O(f(k,w) n^c)$ for some constant $c$ independent of $k$ and $w$, in which case the problems are said to be fixed-parameter tractable with respect to $k$ and $w$). We show that, under a complexity-theoretic assumption, no such algorithms exist. However, we do give algorithms with running time $O(c^wn^{k+1})$. Thus if the diameter of the graph is moderately small and the number of districts is very small, our algorithm is useable. %K Computer Science, Data Structures and Algorithms, cs.DS
[25]
C. Coupette and C. Lenzen, “A Breezing Proof of the KMW Bound,” 2020. [Online]. Available: https://arxiv.org/abs/2002.06005. (arXiv: 2002.06005)
Abstract
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum degree $\Delta$ on which $\Omega(\min\{\sqrt{\log n/\log \log n},\log \Delta/\log \log \Delta\})$ (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching. Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings. Today, more than $15$ years later, there is still no proof of this result that is easy on the reader. Setting out to change this, in this work, we provide a fully self-contained and $\mathit{simple}$ proof of the KMW lower bound. The key argument is algorithmic, and it relies on an invariant that can be readily verified from the generation rules of the lower bound graphs.
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@online{Coupette_arXiv2002.06005, TITLE = {A Breezing Proof of the {KMW} Bound}, AUTHOR = {Coupette, Corinna and Lenzen, Christoph}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2002.06005}, EPRINT = {2002.06005}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum degree $\Delta$ on which $\Omega(\min\{\sqrt{\log n/\log \log n},\log \Delta/\log \log \Delta\})$ (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching. Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings. Today, more than $15$ years later, there is still no proof of this result that is easy on the reader. Setting out to change this, in this work, we provide a fully self-contained and $\mathit{simple}$ proof of the KMW lower bound. The key argument is algorithmic, and it relies on an invariant that can be readily verified from the generation rules of the lower bound graphs.}, }
Endnote
%0 Report %A Coupette, Corinna %A Lenzen, Christoph %+ Internet Architecture, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Breezing Proof of the KMW Bound : %G eng %U http://hdl.handle.net/21.11116/0000-0007-46DC-3 %U https://arxiv.org/abs/2002.06005 %D 2020 %X In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum degree $\Delta$ on which $\Omega(\min\{\sqrt{\log n/\log \log n},\log \Delta/\log \log \Delta\})$ (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching. Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings. Today, more than $15$ years later, there is still no proof of this result that is easy on the reader. Setting out to change this, in this work, we provide a fully self-contained and $\mathit{simple}$ proof of the KMW lower bound. The key argument is algorithmic, and it relies on an invariant that can be readily verified from the generation rules of the lower bound graphs. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Computational Complexity, cs.CC,Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS
[26]
N. R. Dayama, M. Shiripour, A. Oulasvirta, E. Ivanko, and A. Karrenbauer, “Foraging-based Optimization of Menu Systems,” 2020. . (arXiv: 2005.01292)
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[27]
B. Doerr and M. Künnemann, “Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem,” IEEE Transactions on Information Theory, vol. 66, no. 9, 2020.
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@article{Doerr2020, TITLE = {Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem}, AUTHOR = {Doerr, Benjamin and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, ISSN = {0018-9448}, DOI = {10.1109/TIT.2020.2978385}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2020}, DATE = {2020}, JOURNAL = {IEEE Transactions on Information Theory}, VOLUME = {66}, NUMBER = {9}, PAGES = {5729--5741}, }
Endnote
%0 Journal Article %A Doerr, Benjamin %A K&#252;nnemann, Marvin %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem : %G eng %U http://hdl.handle.net/21.11116/0000-0006-FAC1-6 %R 10.1109/TIT.2020.2978385 %7 2020 %D 2020 %J IEEE Transactions on Information Theory %V 66 %N 9 %& 5729 %P 5729 - 5741 %I IEEE %C Piscataway, NJ %@ false
[28]
E. Facca, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Directed Physarum Model,” Theoretical Computer Science, vol. 816, 2020.
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@article{FaccaTCS2020, TITLE = {Convergence of the Non-Uniform Directed Physarum Model}, AUTHOR = {Facca, Enrico and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2020.01.034}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Theoretical Computer Science}, VOLUME = {816}, PAGES = {184--194}, }
Endnote
%0 Journal Article %A Facca, Enrico %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Convergence of the Non-Uniform Directed Physarum Model : %G eng %U http://hdl.handle.net/21.11116/0000-0006-97B9-F %R 10.1016/j.tcs.2020.01.034 %7 2020 %D 2020 %J Theoretical Computer Science %V 816 %& 184 %P 184 - 194 %I Elsevier %C Amsterdam %@ false
[29]
Y. Faenza and T. Kavitha, “Quasi-popular Matchings, Optimality, and Extended Formulations,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.
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@inproceedings{Faenza_SODA20, TITLE = {Quasi-popular Matchings, Optimality, and Extended Formulations}, AUTHOR = {Faenza, Yuri and Kavitha, Telikepalli}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.5555/3381089.3381109}, PUBLISHER = {SIAM}, YEAR = {2020}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {325--344}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Faenza, Yuri %A Kavitha, Telikepalli %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Quasi-popular Matchings, Optimality, and Extended Formulations : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F26C-0 %R 10.5555/3381089.3381109 %D 2020 %B 31st Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2020-01-05 - 2020-01-08 %C Salt Lake City, UT, USA %B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms %E Chawla, Shuchi %P 325 - 344 %I SIAM %@ 978-1-61197-599-4
[30]
S. Forster, D. Nanongkai, L. Yang, T. Saranurak, and S. Yingchareonthawornchai, “Computing and Testing Small Connectivity in Near-Linear Time and Queries via Fast Local Cut Algorithms,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.
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@inproceedings{Forster_SODA20, TITLE = {Computing and Testing Small Connectivity in Near-Linear Time and Queries via Fast Local Cut Algorithms}, AUTHOR = {Forster, Sebastian and Nanongkai, Danupon and Yang, Liu and Saranurak, Thatchaphol and Yingchareonthawornchai, Sorrachai}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.5555/3381089.3381215}, PUBLISHER = {SIAM}, YEAR = {2020}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {2046--2065}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Forster, Sebastian %A Nanongkai, Danupon %A Yang, Liu %A Saranurak, Thatchaphol %A Yingchareonthawornchai, Sorrachai %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Computing and Testing Small Connectivity in Near-Linear Time and Queries via Fast Local Cut Algorithms : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F274-6 %R 10.5555/3381089.3381215 %D 2020 %B 31st Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2020-01-05 - 2020-01-08 %C Salt Lake City, UT, USA %B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms %E Chawla, Shuchi %P 2046 - 2065 %I SIAM %@ 978-1-61197-599-4
[31]
A. Göke, D. Marx, and M. Mnich, “Hitting Long Directed Cycles Is Fixed-Parameter Tractable,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Goeke_ICALP2020, TITLE = {Hitting Long Directed Cycles Is Fixed-Parameter Tractable}, AUTHOR = {G{\"o}ke, Alexander and Marx, D{\'a}niel and Mnich, Matthias}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124664}, DOI = {10.4230/LIPIcs.ICALP.2020.59}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {59}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A G&#246;ke, Alexander %A Marx, D&#225;niel %A Mnich, Matthias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Hitting Long Directed Cycles Is Fixed-Parameter Tractable : %G eng %U http://hdl.handle.net/21.11116/0000-0007-491E-7 %R 10.4230/LIPIcs.ICALP.2020.59 %U urn:nbn:de:0030-drops-124664 %D 2020 %B 47th International Colloquium on Automata, Languages, and Programming %Z date of event: 2020-07-08 - 2020-07-11 %C Saarbr&#252;cken, Germany (Virtual Conference) %B 47th International Colloquium on Automata, Languages, and Programming %E Czumaj, Artur; Dawa, Anuj; Merelli, Emanuela %Z sequence number: 59 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12466/https://creativecommons.org/licenses/by/3.0/legalcode
[32]
A. Göke, D. Marx, and M. Mnich, “Hitting Long Directed Cycles is Fixed-Parameter Tractable,” 2020. [Online]. Available: https://arxiv.org/abs/2003.05267. (arXiv: 2003.05267)
Abstract
In the Directed Long Cycle Hitting Set} problem we are given a directed graph $G$, and the task is to find a set $S$ of at most $k$ vertices/arcs such that $G-S$ has no cycle of length longer than $\ell$. We show that the problem can be solved in time $2^{\mathcal O(\ell k^3\log k + k^5\log k\log\ell)}\cdot n^{\mathcal O(1)}$, that is, it is fixed-parameter tractable (FPT) parameterized by $k$ and $\ell$. This algorithm can be seen as a far-reaching generalization of the fixed-parameter tractability of {\sc Mixed Graph Feedback Vertex Set} [Bonsma and Lokshtanov WADS 2011], which is already a common generalization of the fixed-parameter tractability of (undirected) {\sc Feedback Vertex Set} and the {\sc Directed Feedback Vertex Set} problems, two classic results in parameterized algorithms. The algorithm requires significant insights into the structure of graphs without directed cycles length longer than $\ell$ and can be seen as an exact version of the approximation algorithm following from the Erd{\H{o}}s-P{\'o}sa property for long cycles in directed graphs proved by Kreutzer and Kawarabayashi [STOC 2015].
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@online{Goeke_arXiv2003.05267, TITLE = {Hitting Long Directed Cycles is Fixed-Parameter Tractable}, AUTHOR = {G{\"o}ke, Alexander and Marx, D{\'a}niel and Mnich, Matthias}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.05267}, EPRINT = {2003.05267}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {In the Directed Long Cycle Hitting Set} problem we are given a directed graph $G$, and the task is to find a set $S$ of at most $k$ vertices/arcs such that $G-S$ has no cycle of length longer than $\ell$. We show that the problem can be solved in time $2^{\mathcal O(\ell k^3\log k + k^5\log k\log\ell)}\cdot n^{\mathcal O(1)}$, that is, it is fixed-parameter tractable (FPT) parameterized by $k$ and $\ell$. This algorithm can be seen as a far-reaching generalization of the fixed-parameter tractability of {\sc Mixed Graph Feedback Vertex Set} [Bonsma and Lokshtanov WADS 2011], which is already a common generalization of the fixed-parameter tractability of (undirected) {\sc Feedback Vertex Set} and the {\sc Directed Feedback Vertex Set} problems, two classic results in parameterized algorithms. The algorithm requires significant insights into the structure of graphs without directed cycles length longer than $\ell$ and can be seen as an exact version of the approximation algorithm following from the Erd{\H{o}}s-P{\'o}sa property for long cycles in directed graphs proved by Kreutzer and Kawarabayashi [STOC 2015].}, }
Endnote
%0 Report %A G&#246;ke, Alexander %A Marx, D&#225;niel %A Mnich, Matthias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Hitting Long Directed Cycles is Fixed-Parameter Tractable : %G eng %U http://hdl.handle.net/21.11116/0000-0007-4923-0 %U https://arxiv.org/abs/2003.05267 %D 2020 %X In the Directed Long Cycle Hitting Set} problem we are given a directed graph $G$, and the task is to find a set $S$ of at most $k$ vertices/arcs such that $G-S$ has no cycle of length longer than $\ell$. We show that the problem can be solved in time $2^{\mathcal O(\ell k^3\log k + k^5\log k\log\ell)}\cdot n^{\mathcal O(1)}$, that is, it is fixed-parameter tractable (FPT) parameterized by $k$ and $\ell$. This algorithm can be seen as a far-reaching generalization of the fixed-parameter tractability of {\sc Mixed Graph Feedback Vertex Set} [Bonsma and Lokshtanov WADS 2011], which is already a common generalization of the fixed-parameter tractability of (undirected) {\sc Feedback Vertex Set} and the {\sc Directed Feedback Vertex Set} problems, two classic results in parameterized algorithms. The algorithm requires significant insights into the structure of graphs without directed cycles length longer than $\ell$ and can be seen as an exact version of the approximation algorithm following from the Erd{\H{o}}s-P{\'o}sa property for long cycles in directed graphs proved by Kreutzer and Kawarabayashi [STOC 2015]. %K Computer Science, Data Structures and Algorithms, cs.DS
[33]
A. Göke, D. Marx, and M. Mnich, “Parameterized Algorithms for Generalizations of Directed Feedback Vertex Set,” 2020. [Online]. Available: https://arxiv.org/abs/2003.02483. (arXiv: 2003.02483)
Abstract
The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph~$G$ and seeks a smallest vertex set~$S$ that hits all cycles in $G$. This is one of Karp's 21 $\mathsf{NP}$-complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. [STOC 2008, J. ACM 2008] showed its fixed-parameter tractability via a $4^kk! n^{\mathcal{O}(1)}$-time algorithm, where $k = |S|$. Here we show fixed-parameter tractability of two generalizations of DFVS: - Find a smallest vertex set $S$ such that every strong component of $G - S$ has size at most~$s$: we give an algorithm solving this problem in time $4^k(ks+k+s)!\cdot n^{\mathcal{O}(1)}$. This generalizes an algorithm by Xiao [JCSS 2017] for the undirected version of the problem. - Find a smallest vertex set $S$ such that every non-trivial strong component of $G - S$ is 1-out-regular: we give an algorithm solving this problem in time $2^{\mathcal{O}(k^3)}\cdot n^{\mathcal{O}(1)}$. We also solve the corresponding arc versions of these problems by fixed-parameter algorithms.
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@online{Goeke_arXiv2003.02483, TITLE = {Parameterized Algorithms for Generalizations of Directed Feedback Vertex Set}, AUTHOR = {G{\"o}ke, Alexander and Marx, D{\'a}niel and Mnich, Matthias}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.02483}, EPRINT = {2003.02483}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph~$G$ and seeks a smallest vertex set~$S$ that hits all cycles in $G$. This is one of Karp's 21 $\mathsf{NP}$-complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. [STOC 2008, J. ACM 2008] showed its fixed-parameter tractability via a $4^kk! n^{\mathcal{O}(1)}$-time algorithm, where $k = |S|$. Here we show fixed-parameter tractability of two generalizations of DFVS: -- Find a smallest vertex set $S$ such that every strong component of $G -- S$ has size at most~$s$: we give an algorithm solving this problem in time $4^k(ks+k+s)!\cdot n^{\mathcal{O}(1)}$. This generalizes an algorithm by Xiao [JCSS 2017] for the undirected version of the problem. -- Find a smallest vertex set $S$ such that every non-trivial strong component of $G -- S$ is 1-out-regular: we give an algorithm solving this problem in time $2^{\mathcal{O}(k^3)}\cdot n^{\mathcal{O}(1)}$. We also solve the corresponding arc versions of these problems by fixed-parameter algorithms.}, }
Endnote
%0 Report %A G&#246;ke, Alexander %A Marx, D&#225;niel %A Mnich, Matthias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Parameterized Algorithms for Generalizations of Directed Feedback Vertex Set : %G eng %U http://hdl.handle.net/21.11116/0000-0007-4920-3 %U https://arxiv.org/abs/2003.02483 %D 2020 %X The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph~$G$ and seeks a smallest vertex set~$S$ that hits all cycles in $G$. This is one of Karp's 21 $\mathsf{NP}$-complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. [STOC 2008, J. ACM 2008] showed its fixed-parameter tractability via a $4^kk! n^{\mathcal{O}(1)}$-time algorithm, where $k = |S|$. Here we show fixed-parameter tractability of two generalizations of DFVS: - Find a smallest vertex set $S$ such that every strong component of $G - S$ has size at most~$s$: we give an algorithm solving this problem in time $4^k(ks+k+s)!\cdot n^{\mathcal{O}(1)}$. This generalizes an algorithm by Xiao [JCSS 2017] for the undirected version of the problem. - Find a smallest vertex set $S$ such that every non-trivial strong component of $G - S$ is 1-out-regular: we give an algorithm solving this problem in time $2^{\mathcal{O}(k^3)}\cdot n^{\mathcal{O}(1)}$. We also solve the corresponding arc versions of these problems by fixed-parameter algorithms. %K Computer Science, Data Structures and Algorithms, cs.DS
[34]
D. Halperin, S. Har-Peled, K. Mehlhorn, E. Oh, and M. Sharir, “The Maximum-Level Vertex in an Arrangement of Lines,” 2020. [Online]. Available: http://arxiv.org/abs/2003.00518. (arXiv: 2003.00518)
Abstract
Let $L$ be a set of $n$ lines in the plane, not necessarily in general position. We present an efficient algorithm for finding all the vertices of the arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the number of lines of $L$ that pass strictly below $v$. The problem, posed in Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it seems, as this vertex might not be on the upper envelope of the lines. We first assume that all the lines of $L$ are distinct, and distinguish between two cases, depending on whether or not the upper envelope of $L$ contains a bounded edge. In the former case, we show that the number of lines of $L$ that pass above any maximum level vertex $v_0$ is only $O(\log n)$. In the latter case, we establish a similar property that holds after we remove some of the lines that are incident to the single vertex of the upper envelope. We present algorithms that run, in both cases, in optimal $O(n\log n)$ time. We then consider the case where the lines of $L$ are not necessarily distinct. This setup is more challenging, and the best we have is an algorithm that computes all the maximum-level vertices in time $O(n^{4/3}\log^{3}n)$. Finally, we consider a related combinatorial question for degenerate arrangements, where many lines may intersect in a single point, but all the lines are distinct: We bound the complexity of the weighted $k$-level in such an arrangement, where the weight of a vertex is the number of lines that pass through the vertex. We show that the bound in this case is $O(n^{4/3})$, which matches the corresponding bound for non-degenerate arrangements, and we use this bound in the analysis of one of our algorithms.
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@online{Halperin_arXiv2003.00518, TITLE = {The Maximum-Level Vertex in an Arrangement of Lines}, AUTHOR = {Halperin, Dan and Har-Peled, Sariel and Mehlhorn, Kurt and Oh, Eunjin and Sharir, Micha}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/2003.00518}, EPRINT = {2003.00518}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Let $L$ be a set of $n$ lines in the plane, not necessarily in general position. We present an efficient algorithm for finding all the vertices of the arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the number of lines of $L$ that pass strictly below $v$. The problem, posed in Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it seems, as this vertex might not be on the upper envelope of the lines. We first assume that all the lines of $L$ are distinct, and distinguish between two cases, depending on whether or not the upper envelope of $L$ contains a bounded edge. In the former case, we show that the number of lines of $L$ that pass above any maximum level vertex $v_0$ is only $O(\log n)$. In the latter case, we establish a similar property that holds after we remove some of the lines that are incident to the single vertex of the upper envelope. We present algorithms that run, in both cases, in optimal $O(n\log n)$ time. We then consider the case where the lines of $L$ are not necessarily distinct. This setup is more challenging, and the best we have is an algorithm that computes all the maximum-level vertices in time $O(n^{4/3}\log^{3}n)$. Finally, we consider a related combinatorial question for degenerate arrangements, where many lines may intersect in a single point, but all the lines are distinct: We bound the complexity of the weighted $k$-level in such an arrangement, where the weight of a vertex is the number of lines that pass through the vertex. We show that the bound in this case is $O(n^{4/3})$, which matches the corresponding bound for non-degenerate arrangements, and we use this bound in the analysis of one of our algorithms.}, }
Endnote
%0 Report %A Halperin, Dan %A Har-Peled, Sariel %A Mehlhorn, Kurt %A Oh, Eunjin %A Sharir, Micha %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T The Maximum-Level Vertex in an Arrangement of Lines : %G eng %U http://hdl.handle.net/21.11116/0000-0006-AFB1-D %U http://arxiv.org/abs/2003.00518 %D 2020 %X Let $L$ be a set of $n$ lines in the plane, not necessarily in general position. We present an efficient algorithm for finding all the vertices of the arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the number of lines of $L$ that pass strictly below $v$. The problem, posed in Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it seems, as this vertex might not be on the upper envelope of the lines. We first assume that all the lines of $L$ are distinct, and distinguish between two cases, depending on whether or not the upper envelope of $L$ contains a bounded edge. In the former case, we show that the number of lines of $L$ that pass above any maximum level vertex $v_0$ is only $O(\log n)$. In the latter case, we establish a similar property that holds after we remove some of the lines that are incident to the single vertex of the upper envelope. We present algorithms that run, in both cases, in optimal $O(n\log n)$ time. We then consider the case where the lines of $L$ are not necessarily distinct. This setup is more challenging, and the best we have is an algorithm that computes all the maximum-level vertices in time $O(n^{4/3}\log^{3}n)$. Finally, we consider a related combinatorial question for degenerate arrangements, where many lines may intersect in a single point, but all the lines are distinct: We bound the complexity of the weighted $k$-level in such an arrangement, where the weight of a vertex is the number of lines that pass through the vertex. We show that the bound in this case is $O(n^{4/3})$, which matches the corresponding bound for non-degenerate arrangements, and we use this bound in the analysis of one of our algorithms. %K Computer Science, Computational Geometry, cs.CG
[35]
P. Jain, L. Kanesh, and P. Misra, “Conflict Free Version of Covering Problems on Graphs: Classical and Parameterized,” Theory of Computing Systems, 2020.
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@article{Jain2020, TITLE = {Conflict Free Version of Covering Problems on Graphs: {C}lassical and Parameterized}, AUTHOR = {Jain, Pallavi and Kanesh, Lawqueen and Misra, Pranabendu}, LANGUAGE = {eng}, ISSN = {1432-4350}, DOI = {10.1007/s00224-019-09964-6}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2020}, JOURNAL = {Theory of Computing Systems}, }
Endnote
%0 Journal Article %A Jain, Pallavi %A Kanesh, Lawqueen %A Misra, Pranabendu %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Conflict Free Version of Covering Problems on Graphs: Classical and Parameterized : %G eng %U http://hdl.handle.net/21.11116/0000-0006-90BA-5 %R 10.1007/s00224-019-09964-6 %7 2020 %D 2020 %J Theory of Computing Systems %I Springer %C New York, NY %@ false
[36]
A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Physarum Dynamics,” Theoretical Computer Science, vol. 816, 2020.
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@article{KarrenbauerTCS2020, TITLE = {Convergence of the Non-Uniform Physarum Dynamics}, AUTHOR = {Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2020.02.032}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Theoretical Computer Science}, VOLUME = {816}, PAGES = {260--269}, }
Endnote
%0 Journal Article %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Convergence of the Non-Uniform Physarum Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0006-97C1-5 %R 10.1016/j.tcs.2020.02.032 %7 2020 %D 2020 %J Theoretical Computer Science %V 816 %& 260 %P 260 - 269 %I Elsevier %C Amsterdam %@ false
[37]
P. Kleer and G. Schäfer, “Computation and Efficiency of Potential Function Minimizers of Combinatorial Congestion Games,” Mathematical Programming, 2020.
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@article{Kleer2020, TITLE = {Computation and Efficiency of Potential Function Minimizers of Combinatorial Congestion Games}, AUTHOR = {Kleer, Pieter and Sch{\"a}fer, Guido}, LANGUAGE = {eng}, DOI = {10.1007/s10107-020-01546-6}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2020}, JOURNAL = {Mathematical Programming}, }
Endnote
%0 Journal Article %A Kleer, Pieter %A Sch&#228;fer, Guido %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Computation and Efficiency of Potential Function Minimizers of Combinatorial Congestion Games : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F285-2 %R 10.1007/s10107-020-01546-6 %7 2020 %D 2020 %J Mathematical Programming %I Springer %C New York, NY
[38]
M. Künnemann and D. Marx, “Finding Small Satisfying Assignments Faster Than Brute Force: A Fine-Grained Perspective into Boolean Constraint Satisfaction,” in 35th Computational Complexity Conference (CCC 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Kuennemann_CCC2020, TITLE = {Finding Small Satisfying Assignments Faster Than Brute Force: {A} Fine-Grained Perspective into Boolean Constraint Satisfaction}, AUTHOR = {K{\"u}nnemann, Marvin and Marx, D{\'a}niel}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-156-6}, URL = {urn:nbn:de:0030-drops-125791}, DOI = {10.4230/LIPIcs.CCC.2020.27}, PUBLISHER = {Schlos Dagstuhl}, YEAR = {2020}, BOOKTITLE = {35th Computational Complexity Conference (CCC 2020)}, EDITOR = {Saraf, Shubhangi}, EID = {27}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {169}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A K&#252;nnemann, Marvin %A Marx, D&#225;niel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Finding Small Satisfying Assignments Faster Than Brute Force: A Fine-Grained Perspective into Boolean Constraint Satisfaction : %G eng %U http://hdl.handle.net/21.11116/0000-0007-491C-9 %R 10.4230/LIPIcs.CCC.2020.27 %U urn:nbn:de:0030-drops-125791 %D 2020 %B 35th Computational Complexity Conference %Z date of event: 2020-07-28 - 2020-07-31 %C Saarbr&#252;cken, Germany (Virtual Conference) %B 35th Computational Complexity Conference %E Saraf, Shubhangi %Z sequence number: 27 %I Schlos Dagstuhl %@ 978-3-95977-156-6 %B Leibniz International Proceedings in Informatics %N 169 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12579/https://creativecommons.org/licenses/by/3.0/legalcode
[39]
M. Künnemann and D. Marx, “Finding Small Satisfying Assignments Faster Than Brute Force: A Fine-grained Perspective into Boolean Constraint Satisfaction,” 2020. [Online]. Available: https://arxiv.org/abs/2005.11541. (arXiv: 2005.11541)
Abstract
To study the question under which circumstances small solutions can be found faster than by exhaustive search (and by how much), we study the fine-grained complexity of Boolean constraint satisfaction with size constraint exactly $k$. More precisely, we aim to determine, for any finite constraint family, the optimal running time $f(k)n^{g(k)}$ required to find satisfying assignments that set precisely $k$ of the $n$ variables to $1$. Under central hardness assumptions on detecting cliques in graphs and 3-uniform hypergraphs, we give an almost tight characterization of $g(k)$ into four regimes: (1) Brute force is essentially best-possible, i.e., $g(k) = (1\pm o(1))k$, (2) the best algorithms are as fast as current $k$-clique algorithms, i.e., $g(k)=(\omega/3\pm o(1))k$, (3) the exponent has sublinear dependence on $k$ with $g(k) \in [\Omega(\sqrt[3]{k}), O(\sqrt{k})]$, or (4) the problem is fixed-parameter tractable, i.e., $g(k) = O(1)$. This yields a more fine-grained perspective than a previous FPT/W[1]-hardness dichotomy (Marx, Computational Complexity 2005). Our most interesting technical contribution is a $f(k)n^{4\sqrt{k}}$-time algorithm for SubsetSum with precedence constraints parameterized by the target $k$ -- particularly the approach, based on generalizing a bound on the Frobenius coin problem to a setting with precedence constraints, might be of independent interest.
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@online{Kuennemann_arXiv2005.11541, TITLE = {Finding Small Satisfying Assignments Faster Than Brute Force: {A} Fine-grained Perspective into {B}oolean Constraint Satisfaction}, AUTHOR = {K{\"u}nnemann, Marvin and Marx, D{\'a}niel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2005.11541}, EPRINT = {2005.11541}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {To study the question under which circumstances small solutions can be found faster than by exhaustive search (and by how much), we study the fine-grained complexity of Boolean constraint satisfaction with size constraint exactly $k$. More precisely, we aim to determine, for any finite constraint family, the optimal running time $f(k)n^{g(k)}$ required to find satisfying assignments that set precisely $k$ of the $n$ variables to $1$. Under central hardness assumptions on detecting cliques in graphs and 3-uniform hypergraphs, we give an almost tight characterization of $g(k)$ into four regimes: (1) Brute force is essentially best-possible, i.e., $g(k) = (1\pm o(1))k$, (2) the best algorithms are as fast as current $k$-clique algorithms, i.e., $g(k)=(\omega/3\pm o(1))k$, (3) the exponent has sublinear dependence on $k$ with $g(k) \in [\Omega(\sqrt[3]{k}), O(\sqrt{k})]$, or (4) the problem is fixed-parameter tractable, i.e., $g(k) = O(1)$. This yields a more fine-grained perspective than a previous FPT/W[1]-hardness dichotomy (Marx, Computational Complexity 2005). Our most interesting technical contribution is a $f(k)n^{4\sqrt{k}}$-time algorithm for SubsetSum with precedence constraints parameterized by the target $k$ -- particularly the approach, based on generalizing a bound on the Frobenius coin problem to a setting with precedence constraints, might be of independent interest.}, }
Endnote
%0 Report %A K&#252;nnemann, Marvin %A Marx, D&#225;niel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Finding Small Satisfying Assignments Faster Than Brute Force: A Fine-grained Perspective into Boolean Constraint Satisfaction : %G eng %U http://hdl.handle.net/21.11116/0000-0007-492E-5 %U https://arxiv.org/abs/2005.11541 %D 2020 %X To study the question under which circumstances small solutions can be found faster than by exhaustive search (and by how much), we study the fine-grained complexity of Boolean constraint satisfaction with size constraint exactly $k$. More precisely, we aim to determine, for any finite constraint family, the optimal running time $f(k)n^{g(k)}$ required to find satisfying assignments that set precisely $k$ of the $n$ variables to $1$. Under central hardness assumptions on detecting cliques in graphs and 3-uniform hypergraphs, we give an almost tight characterization of $g(k)$ into four regimes: (1) Brute force is essentially best-possible, i.e., $g(k) = (1\pm o(1))k$, (2) the best algorithms are as fast as current $k$-clique algorithms, i.e., $g(k)=(\omega/3\pm o(1))k$, (3) the exponent has sublinear dependence on $k$ with $g(k) \in [\Omega(\sqrt[3]{k}), O(\sqrt{k})]$, or (4) the problem is fixed-parameter tractable, i.e., $g(k) = O(1)$. This yields a more fine-grained perspective than a previous FPT/W[1]-hardness dichotomy (Marx, Computational Complexity 2005). Our most interesting technical contribution is a $f(k)n^{4\sqrt{k}}$-time algorithm for SubsetSum with precedence constraints parameterized by the target $k$ -- particularly the approach, based on generalizing a bound on the Frobenius coin problem to a setting with precedence constraints, might be of independent interest. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[40]
W. Liu, F. Lombardi, M. Shulte, D. J. Miller, Z. Xiang, G. Kesidis, A. Oulasvirta, N. R. Dayama, M. Shiripour, M. John, A. Karrenbauer, and A. Allerhand, “Scanning the Issue,” Proceedings of the IEEE, vol. 108, no. 3, 2020.
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@article{Liu2020, TITLE = {Scanning the Issue}, AUTHOR = {Liu, Weiqiang and Lombardi, Fabrizio and Shulte, Michael and Miller, David J. and Xiang, Zhen and Kesidis, George and Oulasvirta, Antti and Dayama, Niraj Ramesh and Shiripour, Morteza and John, Maximilian and Karrenbauer, Andreas and Allerhand, Adam}, LANGUAGE = {eng}, ISSN = {0018-9219}, DOI = {10.1109/JPROC.2020.2975522}, PUBLISHER = {IEEE}, ADDRESS = {New York, NY}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Proceedings of the IEEE}, VOLUME = {108}, NUMBER = {3}, PAGES = {400--401}, }
Endnote
%0 Journal Article %A Liu, Weiqiang %A Lombardi, Fabrizio %A Shulte, Michael %A Miller, David J. %A Xiang, Zhen %A Kesidis, George %A Oulasvirta, Antti %A Dayama, Niraj Ramesh %A Shiripour, Morteza %A John, Maximilian %A Karrenbauer, Andreas %A Allerhand, Adam %+ External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Scanning the Issue : %G eng %U http://hdl.handle.net/21.11116/0000-0007-4670-C %R 10.1109/JPROC.2020.2975522 %7 2020 %D 2020 %J Proceedings of the IEEE %O Proc. IEEE %V 108 %N 3 %& 400 %P 400 - 401 %I IEEE %C New York, NY %@ false
[41]
D. Lokshtanov, P. Misra, J. Mukherjee, F. Panolan, G. Philip, and S. Saurabh, “2-Approximating Feedback Vertex Set in Tournaments,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.
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@inproceedings{Lokshtanov_SODA20, TITLE = {2-Approximating Feedback Vertex Set in Tournaments}, AUTHOR = {Lokshtanov, Daniel and Misra, Pranabendu and Mukherjee, Joydeep and Panolan, Fahad and Philip, Geevarghese and Saurabh, Saket}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.5555/3381089.3381150}, PUBLISHER = {SIAM}, YEAR = {2020}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {1010--1018}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Lokshtanov, Daniel %A Misra, Pranabendu %A Mukherjee, Joydeep %A Panolan, Fahad %A Philip, Geevarghese %A Saurabh, Saket %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T 2-Approximating Feedback Vertex Set in Tournaments : %G eng %U http://hdl.handle.net/21.11116/0000-0006-F276-4 %R 10.5555/3381089.3381150 %D 2020 %B 31st Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2020-01-05 - 2020-01-08 %C Salt Lake City, UT, USA %B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms %E Chawla, Shuchi %P 1010 - 1018 %I SIAM %@ 978-1-61197-599-4
[42]
D. Marx, “Four Shorts Stories on Surprising Algorithmic Uses of Treewidth,” in Treewidth, Kernels, and Algorithms, Berlin: Springer, 2020.
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@incollection{Marx_Four2020, TITLE = {Four Shorts Stories on Surprising Algorithmic Uses of Treewidth}, AUTHOR = {Marx, D{\'a}niel}, LANGUAGE = {eng}, ISBN = {978-3-030-42070-3}, DOI = {10.1007/978-3-030-42071-0_10}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2020}, DATE = {2020}, BOOKTITLE = {Treewidth, Kernels, and Algorithms}, EDITOR = {Fomin, Fedor V. and Kratsch, Stefan and van Leeuwen, Erik Jan}, PAGES = {129--144}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12160}, }
Endnote
%0 Book Section %A Marx, D&#225;niel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Four Shorts Stories on Surprising Algorithmic Uses of Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0007-4911-4 %R 10.1007/978-3-030-42071-0_10 %D 2020 %B Treewidth, Kernels, and Algorithms %E Fomin, Fedor V.; Kratsch, Stefan; van Leeuwen, Erik Jan %P 129 - 144 %I Springer %C Berlin %@ 978-3-030-42070-3 %S Lecture Notes in Computer Science %N 12160
[43]
D. Marx and R. B. Sandeep, “Incompressibility of H-free Edge Modification Problems: Towards a Dichotomy,” 2020. [Online]. Available: https://arxiv.org/abs/2004.11761. (arXiv: 2004.11761)
Abstract
Given a graph $G$ and an integer $k$, the $H$-free Edge Editing problem is to find whether there exists at most $k$ pairs of vertices in $G$ such that changing the adjacency of the pairs in $G$ results in a graph without any induced copy of $H$. The existence of polynomial kernels for $H$-free Edge Editing received significant attention in the parameterized complexity literature. Nontrivial polynomial kernels are known to exist for some graphs $H$ with at most 4 vertices, but starting from 5 vertices, polynomial kernels are known only if $H$ is either complete or empty. This suggests the conjecture that there is no other $H$ with at least 5 vertices were $H$-free Edge Editing admits a polynomial kernel. Towards this goal, we obtain a set $\mathcal{H}$ of nine 5-vertex graphs such that if for every $H\in\mathcal{H}$, $H$-free Edge Editing is incompressible and the complexity assumption $NP \not\subseteq coNP/poly$ holds, then $H$-free Edge Editing is incompressible for every graph $H$ with at least five vertices that is neither complete nor empty. That is, proving incompressibility for these nine graphs would give a complete classification of the kernelization complexity of $H$-free Edge Editing for every $H$ with at least 5 vertices. We obtain similar result also for $H$-free Edge Deletion. Here the picture is more complicated due to the existence of another infinite family of graphs $H$ where the problem is trivial (graphs with exactly one edge). We obtain a larger set $\mathcal{H}$ of nineteen graphs whose incompressibility would give a complete classification of the kernelization complexity of $H$-free Edge Deletion for every graph $H$ with at least 5 vertices. Analogous results follow also for the $H$-free Edge Completion problem by simple complementation.
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@online{, TITLE = {Incompressibility of H-free Edge Modification Problems: Towards a Dichotomy}, AUTHOR = {Marx, D{\'a}niel and Sandeep, R. B.}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2004.11761}, EPRINT = {2004.11761}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Given a graph $G$ and an integer $k$, the $H$-free Edge Editing problem is to find whether there exists at most $k$ pairs of vertices in $G$ such that changing the adjacency of the pairs in $G$ results in a graph without any induced copy of $H$. The existence of polynomial kernels for $H$-free Edge Editing received significant attention in the parameterized complexity literature. Nontrivial polynomial kernels are known to exist for some graphs $H$ with at most 4 vertices, but starting from 5 vertices, polynomial kernels are known only if $H$ is either complete or empty. This suggests the conjecture that there is no other $H$ with at least 5 vertices were $H$-free Edge Editing admits a polynomial kernel. Towards this goal, we obtain a set $\mathcal{H}$ of nine 5-vertex graphs such that if for every $H\in\mathcal{H}$, $H$-free Edge Editing is incompressible and the complexity assumption $NP \not\subseteq coNP/poly$ holds, then $H$-free Edge Editing is incompressible for every graph $H$ with at least five vertices that is neither complete nor empty. That is, proving incompressibility for these nine graphs would give a complete classification of the kernelization complexity of $H$-free Edge Editing for every $H$ with at least 5 vertices. We obtain similar result also for $H$-free Edge Deletion. Here the picture is more complicated due to the existence of another infinite family of graphs $H$ where the problem is trivial (graphs with exactly one edge). We obtain a larger set $\mathcal{H}$ of nineteen graphs whose incompressibility would give a complete classification of the kernelization complexity of $H$-free Edge Deletion for every graph $H$ with at least 5 vertices. Analogous results follow also for the $H$-free Edge Completion problem by simple complementation.}, }
Endnote
%0 Report %A Marx, D&#225;niel %A Sandeep, R. B. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Incompressibility of H-free Edge Modification Problems: Towards a Dichotomy : %G eng %U http://hdl.handle.net/21.11116/0000-0007-492A-9 %U https://arxiv.org/abs/2004.11761 %D 2020 %X Given a graph $G$ and an integer $k$, the $H$-free Edge Editing problem is to find whether there exists at most $k$ pairs of vertices in $G$ such that changing the adjacency of the pairs in $G$ results in a graph without any induced copy of $H$. The existence of polynomial kernels for $H$-free Edge Editing received significant attention in the parameterized complexity literature. Nontrivial polynomial kernels are known to exist for some graphs $H$ with at most 4 vertices, but starting from 5 vertices, polynomial kernels are known only if $H$ is either complete or empty. This suggests the conjecture that there is no other $H$ with at least 5 vertices were $H$-free Edge Editing admits a polynomial kernel. Towards this goal, we obtain a set $\mathcal{H}$ of nine 5-vertex graphs such that if for every $H\in\mathcal{H}$, $H$-free Edge Editing is incompressible and the complexity assumption $NP \not\subseteq coNP/poly$ holds, then $H$-free Edge Editing is incompressible for every graph $H$ with at least five vertices that is neither complete nor empty. That is, proving incompressibility for these nine graphs would give a complete classification of the kernelization complexity of $H$-free Edge Editing for every $H$ with at least 5 vertices. We obtain similar result also for $H$-free Edge Deletion. Here the picture is more complicated due to the existence of another infinite family of graphs $H$ where the problem is trivial (graphs with exactly one edge). We obtain a larger set $\mathcal{H}$ of nineteen graphs whose incompressibility would give a complete classification of the kernelization complexity of $H$-free Edge Deletion for every graph $H$ with at least 5 vertices. Analogous results follow also for the $H$-free Edge Completion problem by simple complementation. %K Computer Science, Data Structures and Algorithms, cs.DS
[44]
D. Marx, “Four Short Stories on Surprising Algorithmic Uses of Treewidth,” 2020. [Online]. Available: https://arxiv.org/abs/2008.07968. (arXiv: 2008.07968)
Abstract
This article briefly describes four algorithmic problems where the notion of treewidth is very useful. Even though the problems themselves have nothing to do with treewidth, it turns out that combining known results on treewidth allows us to easily describe very clean and high-level algorithms.
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@online{Marx_arXiv2008.07968, TITLE = {Four Short Stories on Surprising Algorithmic Uses of Treewidth}, AUTHOR = {Marx, D{\'a}niel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2008.07968}, EPRINT = {2008.07968}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {This article briefly describes four algorithmic problems where the notion of treewidth is very useful. Even though the problems themselves have nothing to do with treewidth, it turns out that combining known results on treewidth allows us to easily describe very clean and high-level algorithms.}, }
Endnote
%0 Report %A Marx, D&#225;niel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Four Short Stories on Surprising Algorithmic Uses of Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0007-4950-D %U https://arxiv.org/abs/2008.07968 %D 2020 %X This article briefly describes four algorithmic problems where the notion of treewidth is very useful. Even though the problems themselves have nothing to do with treewidth, it turns out that combining known results on treewidth allows us to easily describe very clean and high-level algorithms. %K Computer Science, Data Structures and Algorithms, cs.DS
[45]
E. Oh and H.-K. Ahn, “Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon,” Discrete & Computational Geometry, vol. 63, no. 2, 2020.
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@article{Oh2020, TITLE = {Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon}, AUTHOR = {Oh, Eunjin and Ahn, Hee-Kap}, LANGUAGE = {eng}, ISSN = {0179-5376}, DOI = {10.1007/s00454-019-00063-4}, PUBLISHER = {Springer}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Discrete \& Computational Geometry}, VOLUME = {63}, NUMBER = {2}, PAGES = {418--454}, }
Endnote
%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon : %G eng %U http://hdl.handle.net/21.11116/0000-0006-8E04-6 %R 10.1007/s00454-019-00063-4 %7 2019 %D 2020 %J Discrete & Computational Geometry %V 63 %N 2 %& 418 %P 418 - 454 %I Springer %@ false
[46]
A. Oulasvirta, N. R. Dayama, M. Shiripour, M. John, and A. Karrenbauer, “Combinatorial Optimization of Graphical User Interface Designs,” Proceedings of the IEEE, vol. 108, no. 3, 2020.
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@article{Oulasvirta2020, TITLE = {Combinatorial Optimization of Graphical User Interface Designs}, AUTHOR = {Oulasvirta, Antti and Dayama, Niraj Ramesh and Shiripour, Morteza and John, Maximilian and Karrenbauer, Andreas}, LANGUAGE = {eng}, ISSN = {0018-9219}, DOI = {10.1109/JPROC.2020.2969687}, PUBLISHER = {IEEE}, ADDRESS = {New York, N.Y.}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Proceedings of the IEEE}, VOLUME = {108}, NUMBER = {3}, PAGES = {434--464}, }
Endnote
%0 Journal Article %A Oulasvirta, Antti %A Dayama, Niraj Ramesh %A Shiripour, Morteza %A John, Maximilian %A Karrenbauer, Andreas %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Combinatorial Optimization of Graphical User Interface Designs : %G eng %U http://hdl.handle.net/21.11116/0000-0006-99BA-C %R 10.1109/JPROC.2020.2969687 %7 2020 %D 2020 %J Proceedings of the IEEE %O Proc. IEEE %V 108 %N 3 %& 434 %P 434 - 464 %I IEEE %C New York, N.Y. %@ false
[47]
B. Ray Chaudhury, J. Garg, and K. Mehlhorn, “EFX exists for three agents,” 2020. [Online]. Available: http://arxiv.org/abs/2002.05119. (arXiv: 2002.05119)
Abstract
We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts by many researchers for several years, the existence of EFX allocations has not been settled beyond the simple case of two agents. In this paper, we show constructively that an EFX allocation always exists for three agents. Furthermore, we falsify the conjecture by Caragiannis et al. by showing an instance with three agents for which there is a partial EFX allocation (some items are not allocated) with higher Nash welfare than that of any complete EFX allocation.
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@online{RayChaudhury_arXiv2002.05119, TITLE = {{EFX} exists for three agents}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/2002.05119}, EPRINT = {2002.05119}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts by many researchers for several years, the existence of EFX allocations has not been settled beyond the simple case of two agents. In this paper, we show constructively that an EFX allocation always exists for three agents. Furthermore, we falsify the conjecture by Caragiannis et al. by showing an instance with three agents for which there is a partial EFX allocation (some items are not allocated) with higher Nash welfare than that of any complete EFX allocation.}, }
Endnote
%0 Report %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T EFX exists for three agents : %G eng %U http://hdl.handle.net/21.11116/0000-0006-AF99-9 %U http://arxiv.org/abs/2002.05119 %D 2020 %X We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts by many researchers for several years, the existence of EFX allocations has not been settled beyond the simple case of two agents. In this paper, we show constructively that an EFX allocation always exists for three agents. Furthermore, we falsify the conjecture by Caragiannis et al. by showing an instance with three agents for which there is a partial EFX allocation (some items are not allocated) with higher Nash welfare than that of any complete EFX allocation. %K Computer Science, Computer Science and Game Theory, cs.GT,
[48]
B. Ray Chaudhury, T. Kavitha, K. Mehlhorn, and A. Sgouritsa, “A Little Charity Guarantees Almost Envy-Freeness,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.
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@inproceedings{RayChaudhury_SODA20, TITLE = {A Little Charity Guarantees Almost Envy-Freeness}, AUTHOR = {Ray Chaudhury, Bhaskar and Kavitha, Telikepalli and Mehlhorn, Kurt and Sgouritsa, Alkmini}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.1137/1.9781611975994.162}, PUBLISHER = {SIAM}, YEAR = {2020}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {2658 --2672}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Ray Chaudhury, Bhaskar %A Kavitha, Telikepalli %A Mehlhorn, Kurt %A Sgouritsa, Alkmini %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Little Charity Guarantees Almost Envy-Freeness : %G eng %U http://hdl.handle.net/21.11116/0000-0006-AF89-B %R 10.1137/1.9781611975994.162 %D 2020 %B 31st Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2020-01-05 - 2020-01-08 %C Salt Lake City, UT, USA %B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms %E Chawla, Shuchi %P 2658 - 2672 %I SIAM %@ 978-1-61197-599-4
[49]
B. Ray Chaudhury, J. Garg, and K. Mehlhorn, “EFX Exists for Three Agents,” in EC’20, 21st ACM Conference on Economics and Computation, Virtual Event, Hungary, 2020.
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@inproceedings{RayChaudhury_EC2020, TITLE = {{EFX} Exists for Three Agents}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISBN = {978-1-4503-7975-5}, DOI = {10.1145/3391403.3399511}, PUBLISHER = {ACM}, YEAR = {2020}, BOOKTITLE = {EC'20, 21st ACM Conference on Economics and Computation}, EDITOR = {Bir{\'o}, P{\'e}ter and Hartline, Jason}, PAGES = {1--19}, ADDRESS = {Virtual Event, Hungary}, }
Endnote
%0 Conference Proceedings %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T EFX Exists for Three Agents : %G eng %U http://hdl.handle.net/21.11116/0000-0007-223A-2 %R 10.1145/3391403.3399511 %D 2020 %B 21st ACM Conference on Economics and Computation %Z date of event: 2020-07-13 - 2020-07-17 %C Virtual Event, Hungary %B EC'20 %E Bir&#243;, P&#233;ter; Hartline, Jason %P 1 - 19 %I ACM %@ 978-1-4503-7975-5
[50]
M. Roth and P. Wellnitz, “Counting and Finding Homomorphisms is Universal for Parameterized Complexity Theory,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.
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@inproceedings{Roth_SODA20, TITLE = {Counting and Finding Homomorphisms is Universal for Parameterized Complexity Theory}, AUTHOR = {Roth, Marc and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.1137/1.9781611975994.133}, PUBLISHER = {SIAM}, YEAR = {2020}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {2161--2180}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Roth, Marc %A Wellnitz, Philip %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting and Finding Homomorphisms is Universal for Parameterized Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0005-8665-2 %R 10.1137/1.9781611975994.133 %D 2020 %B 31st Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2020-01-05 - 2020-01-08 %C Salt Lake City, UT, USA %B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms %E Chawla, Shuchi %P 2161 - 2180 %I SIAM %@ 978-1-61197-599-4
[51]
S. Saurabh, U. dos S. Souza, and P. Tale, “On the Parameterized Complexity of Grid Contraction,” in 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020), órshavn, Faroe Islands, 2020.
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@inproceedings{Saket_SWAT2020, TITLE = {On the Parameterized Complexity of Grid Contraction}, AUTHOR = {Saurabh, Saket and Souza, U{\'e}verton dos Santos and Tale, Prafullkumar}, LANGUAGE = {eng}, ISBN = {978-3-95977-150-4}, URL = {urn:nbn:de:0030-drops-122810}, DOI = {10.4230/LIPIcs.SWAT.2020.34}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)}, EDITOR = {Albers, Susanne}, EID = {34}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {162}, ADDRESS = {{\'o}rshavn, Faroe Islands}, }
Endnote
%0 Conference Proceedings %A Saurabh, Saket %A Souza, U&#233;verton dos Santos %A Tale, Prafullkumar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Parameterized Complexity of Grid Contraction : %G eng %U http://hdl.handle.net/21.11116/0000-0006-8BA6-2 %R 10.4230/LIPIcs.SWAT.2020.34 %U urn:nbn:de:0030-drops-122810 %D 2020 %B 17th Scandinavian Symposiumand Workshops on Algorithm Theory %Z date of event: 2020-06-22 - 2020-06-24 %C &#243;rshavn, Faroe Islands %B 17th Scandinavian Symposium and Workshops on Algorithm Theory %E Albers, Susanne %Z sequence number: 34 %I Schloss Dagstuhl %@ 978-3-95977-150-4 %B Leibniz International Proceedings in Informatics %N 162 %U https://drops.dagstuhl.de/opus/volltexte/2020/12281/
2019
[52]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “SETH-Based Lower Bounds for Subset Sum and Bicriteria Path,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Abboud_SODA19b, TITLE = {{SETH}-Based Lower Bounds for Subset Sum and Bicriteria Path}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.3}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {41--57}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T SETH-Based Lower Bounds for Subset Sum and Bicriteria Path : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E12-8 %R 10.1137/1.9781611975482.3 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 41 - 57 %I SIAM %@ 978-1-61197-548-2
[53]
M. Abdulaziz, K. Mehlhorn, and T. Nipkow, “Trustworthy Graph Algorithms,” 2019. [Online]. Available: http://arxiv.org/abs/1907.04065. (arXiv: 1907.04065)
Abstract
The goal of the LEDA project was to build an easy-to-use and extendable library of correct and efficient data structures, graph algorithms and geometric algorithms. We report on the use of formal program verification to achieve an even higher level of trustworthiness. Specifically, we report on an ongoing and largely finished verification of the blossom-shrinking algorithm for maximum cardinality matching.
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@online{Abdulaziz_arXiv1907.04065, TITLE = {Trustworthy Graph Algorithms}, AUTHOR = {Abdulaziz, Mohammad and Mehlhorn, Kurt and Nipkow, Tobias}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1907.04065}, EPRINT = {1907.04065}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The goal of the LEDA project was to build an easy-to-use and extendable library of correct and efficient data structures, graph algorithms and geometric algorithms. We report on the use of formal program verification to achieve an even higher level of trustworthiness. Specifically, we report on an ongoing and largely finished verification of the blossom-shrinking algorithm for maximum cardinality matching.}, }
Endnote
%0 Report %A Abdulaziz, Mohammad %A Mehlhorn, Kurt %A Nipkow, Tobias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Trustworthy Graph Algorithms : %G eng %U http://hdl.handle.net/21.11116/0000-0005-4FA8-6 %U http://arxiv.org/abs/1907.04065 %D 2019 %X The goal of the LEDA project was to build an easy-to-use and extendable library of correct and efficient data structures, graph algorithms and geometric algorithms. We report on the use of formal program verification to achieve an even higher level of trustworthiness. Specifically, we report on an ongoing and largely finished verification of the blossom-shrinking algorithm for maximum cardinality matching. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Logic in Computer Science, cs.LO,Computer Science, Software Engineering, cs.SE
[54]
M. Abdulaziz, K. Mehlhorn, and T. Nipkow, “Trustworthy Graph Algorithms,” in 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019), Aachen, Germany, 2019.
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@inproceedings{Abdulaziz_MFCS, TITLE = {Trustworthy Graph Algorithms}, AUTHOR = {Abdulaziz, Mohammad and Mehlhorn, Kurt and Nipkow, Tobias}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-117-7}, URL = {urn:nbn:de:0030-drops-109456}, DOI = {10.4230/LIPIcs.MFCS.2019.1}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, EDITOR = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, EID = {1}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {138}, ADDRESS = {Aachen, Germany}, }
Endnote
%0 Conference Proceedings %A Abdulaziz, Mohammad %A Mehlhorn, Kurt %A Nipkow, Tobias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Trustworthy Graph Algorithms : %G eng %U http://hdl.handle.net/21.11116/0000-0005-4F89-9 %R 10.4230/LIPIcs.MFCS.2019.1 %U urn:nbn:de:0030-drops-109456 %D 2019 %B 44th International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2019-08-26 - 2019-08-30 %C Aachen, Germany %B 44th International Symposium on Mathematical Foundations of Computer Science %E Rossmanith, Peter; Heggernes, Pinar; Katoen, Joost-Pieter %Z sequence number: 1 %I Schloss Dagstuhl %@ 978-3-95977-117-7 %B Leibniz International Proceedings in Informatics %N 138 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10945/http://drops.dagstuhl.de/doku/urheberrecht1.html
[55]
P. Afshani, M. Agrawal, B. Doerr, C. Doerr, K. G. Larsen, and K. Mehlhorn, “The Query Complexity of a Permutation-based Variant of Mastermind,” Discrete Applied Mathematics, vol. 260, 2019.
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@article{AFSHANI2019, TITLE = {The query complexity of a permutation-based variant of {M}astermind}, AUTHOR = {Afshani, Peyman and Agrawal, Manindra and Doerr, Benjamin and Doerr, Carola and Larsen, Kasper Green and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {0166-218X}, DOI = {10.1016/j.dam.2019.01.007}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Discrete Applied Mathematics}, VOLUME = {260}, PAGES = {28--50}, }
Endnote
%0 Journal Article %A Afshani, Peyman %A Agrawal, Manindra %A Doerr, Benjamin %A Doerr, Carola %A Larsen, Kasper Green %A Mehlhorn, Kurt %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T The Query Complexity of a Permutation-based Variant of Mastermind : %G eng %U http://hdl.handle.net/21.11116/0000-0002-FE83-C %R 10.1016/j.dam.2019.01.007 %7 2019 %D 2019 %J Discrete Applied Mathematics %V 260 %& 28 %P 28 - 50 %I North-Holland %C Amsterdam %@ false
[56]
H.-K. Ahn, E. Oh, L. Schlipf, F. Stehn, and D. Strash, “On Romeo and Juliet Problems: Minimizing Distance-to-Sight,” Computational Geometry: Theory and Applications, vol. 84, 2019.
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@article{Ahn2019, TITLE = {On Romeo and {J}uliet problems: {M}inimizing distance-to-sight}, AUTHOR = {Ahn, Hee-Kap and Oh, E. and Schlipf, Lena and Stehn, Fabian and Strash, Darren}, LANGUAGE = {eng}, ISSN = {0925-7721}, DOI = {10.1016/j.comgeo.2019.07.003}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Computational Geometry: Theory and Applications}, VOLUME = {84}, PAGES = {12--21}, }
Endnote
%0 Journal Article %A Ahn, Hee-Kap %A Oh, E. %A Schlipf, Lena %A Stehn, Fabian %A Strash, Darren %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T On Romeo and Juliet Problems: Minimizing Distance-to-Sight : %G eng %U http://hdl.handle.net/21.11116/0000-0004-E582-6 %R 10.1016/j.comgeo.2019.07.003 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 84 %& 12 %P 12 - 21 %I Elsevier %C Amsterdam %@ false
[57]
H.-K. Ahn, T. Ahn, S. W. Bae, J. Choi, M. Kim, E. Oh, C.-S. Shin, and S. D. Yoon, “Minimum-width Annulus with Outliers: Circular, Square, and Rectangular Cases,” Information Processing Letters, vol. 145, 2019.
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@article{Ahn2019, TITLE = {Minimum-width Annulus with Outliers: {C}ircular, Square, and Rectangular Cases}, AUTHOR = {Ahn, Hee-Kap and Ahn, Taehoon and Bae, Sang Won and Choi, Jongmin and Kim, Mincheol and Oh, Eunjin and Shin, Chan-Su and Yoon, Sang Duk}, LANGUAGE = {eng}, ISSN = {0020-0190}, DOI = {10.1016/j.ipl.2019.01.004}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Information Processing Letters}, VOLUME = {145}, PAGES = {16--23}, }
Endnote
%0 Journal Article %A Ahn, Hee-Kap %A Ahn, Taehoon %A Bae, Sang Won %A Choi, Jongmin %A Kim, Mincheol %A Oh, Eunjin %A Shin, Chan-Su %A Yoon, Sang Duk %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Minimum-width Annulus with Outliers: Circular, Square, and Rectangular Cases : %G eng %U http://hdl.handle.net/21.11116/0000-0003-4FD4-6 %R 10.1016/j.ipl.2019.01.004 %7 2019 %D 2019 %J Information Processing Letters %V 145 %& 16 %P 16 - 23 %I Elsevier %C Amsterdam %@ false
[58]
H. Akrami, K. Mehlhorn, and T. Odland, “Ratio-Balanced Maximum Flows,” 2019. [Online]. Available: http://arxiv.org/abs/1902.11047. (arXiv: 1902.11047)
Abstract
When a loan is approved for a person or company, the bank is subject to \emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a bank will require some form of \emph{security}, which will be collected if the lender defaults. Accounts can be secured by several securities and a security can be used for several accounts. The goal is to fractionally assign the securities to the accounts so as to balance the risk. This situation can be modelled by a bipartite graph. We have a set $S$ of securities and a set $A$ of accounts. Each security has a \emph{value} $v_i$ and each account has an \emph{exposure} $e_j$. If a security $i$ can be used to secure an account $j$, we have an edge from $i$ to $j$. Let $f_{ij}$ be part of security $i$'s value used to secure account $j$. We are searching for a maximum flow that send at most $v_i$ units out of node $i \in S$ and at most $e_j$ units into node $j \in A$. Then $s_j = e_j - \sum_i f_{ij}$ is the unsecured part of account $j$. We are searching for the maximum flow that minimizes $\sum_j s_j^2/e_j$.
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@online{Akrami_arXiv1902.11047, TITLE = {Ratio-Balanced Maximum Flows}, AUTHOR = {Akrami, Hannaneh and Mehlhorn, Kurt and Odland, Tommy}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1902.11047}, EPRINT = {1902.11047}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {When a loan is approved for a person or company, the bank is subject to \emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a bank will require some form of \emph{security}, which will be collected if the lender defaults. Accounts can be secured by several securities and a security can be used for several accounts. The goal is to fractionally assign the securities to the accounts so as to balance the risk. This situation can be modelled by a bipartite graph. We have a set $S$ of securities and a set $A$ of accounts. Each security has a \emph{value} $v_i$ and each account has an \emph{exposure} $e_j$. If a security $i$ can be used to secure an account $j$, we have an edge from $i$ to $j$. Let $f_{ij}$ be part of security $i$'s value used to secure account $j$. We are searching for a maximum flow that send at most $v_i$ units out of node $i \in S$ and at most $e_j$ units into node $j \in A$. Then $s_j = e_j -- \sum_i f_{ij}$ is the unsecured part of account $j$. We are searching for the maximum flow that minimizes $\sum_j s_j^2/e_j$.}, }
Endnote
%0 Report %A Akrami, Hannaneh %A Mehlhorn, Kurt %A Odland, Tommy %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Ratio-Balanced Maximum Flows : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B2FE-6 %U http://arxiv.org/abs/1902.11047 %D 2019 %X When a loan is approved for a person or company, the bank is subject to \emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a bank will require some form of \emph{security}, which will be collected if the lender defaults. Accounts can be secured by several securities and a security can be used for several accounts. The goal is to fractionally assign the securities to the accounts so as to balance the risk. This situation can be modelled by a bipartite graph. We have a set $S$ of securities and a set $A$ of accounts. Each security has a \emph{value} $v_i$ and each account has an \emph{exposure} $e_j$. If a security $i$ can be used to secure an account $j$, we have an edge from $i$ to $j$. Let $f_{ij}$ be part of security $i$'s value used to secure account $j$. We are searching for a maximum flow that send at most $v_i$ units out of node $i \in S$ and at most $e_j$ units into node $j \in A$. Then $s_j = e_j - \sum_i f_{ij}$ is the unsecured part of account $j$. We are searching for the maximum flow that minimizes $\sum_j s_j^2/e_j$. %K Computer Science, Data Structures and Algorithms, cs.DS
[59]
H. Akrami, K. Mehlhorn, and T. Odland, “Ratio-Balanced Maximum Flows,” Information Processing Letters, vol. 150, 2019.
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@article{Akrami_2019, TITLE = {Ratio-Balanced Maximum Flows}, AUTHOR = {Akrami, Hannaneh and Mehlhorn, Kurt and Odland, Tommy}, LANGUAGE = {eng}, ISSN = {0020-0190}, DOI = {10.1016/j.ipl.2019.06.003}, PUBLISHER = {Elsevier}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Information Processing Letters}, VOLUME = {150}, PAGES = {13--17}, }
Endnote
%0 Journal Article %A Akrami, Hannaneh %A Mehlhorn, Kurt %A Odland, Tommy %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Ratio-Balanced Maximum Flows : %G eng %U http://hdl.handle.net/21.11116/0000-0004-8FF0-C %R 10.1016/j.ipl.2019.06.003 %7 2019 %D 2019 %J Information Processing Letters %V 150 %& 13 %P 13 - 17 %I Elsevier %@ false
[60]
S. A. Amiri, S. Kreutzer, D. Marx, and R. Rabinovich, “Routing with Congestion in Acyclic Digraphs,” Information Processing Letters, vol. 151, 2019.
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@article{DBLP:journals/ipl/AmiriKMR19, TITLE = {Routing with Congestion in Acyclic Digraphs}, AUTHOR = {Amiri, Saeed Akhoondian and Kreutzer, Stephan and Marx, D{\'a}niel and Rabinovich, Roman}, LANGUAGE = {eng}, ISSN = {0020-0190}, DOI = {10.1016/j.ipl.2019.105836}, PUBLISHER = {Elsevier}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Information Processing Letters}, VOLUME = {151}, EID = {105836}, }
Endnote
%0 Journal Article %A Amiri, Saeed Akhoondian %A Kreutzer, Stephan %A Marx, D&#225;niel %A Rabinovich, Roman %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Routing with Congestion in Acyclic Digraphs : %G eng %U http://hdl.handle.net/21.11116/0000-0004-B836-0 %R 10.1016/j.ipl.2019.105836 %7 2019 %D 2019 %J Information Processing Letters %V 151 %Z sequence number: 105836 %I Elsevier %@ false
[61]
S. A. Amiri, S. Dudycz, M. Parham, S. Schmid, and S. Wiederrecht, “On Polynomial-Time Congestion-Free Software-Defined Network Updates,” in IFIP Networking Conference, Warsaw, Poland, 2019.
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@inproceedings{Amiri_IFIP2019, TITLE = {On Polynomial-Time Congestion-Free Software-Defined Network Updates}, AUTHOR = {Amiri, Saeed Akhoondian and Dudycz, Szymon and Parham, Mahmoud and Schmid, Stefan and Wiederrecht, Sebastian}, LANGUAGE = {eng}, DOI = {10.23919/IFIPNetworking.2019.8816833}, PUBLISHER = {IEEE}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {IFIP Networking Conference}, ADDRESS = {Warsaw, Poland}, }
Endnote
%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Dudycz, Szymon %A Parham, Mahmoud %A Schmid, Stefan %A Wiederrecht, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T On Polynomial-Time Congestion-Free Software-Defined Network Updates : %G eng %U http://hdl.handle.net/21.11116/0000-0004-B83C-A %R 10.23919/IFIPNetworking.2019.8816833 %D 2019 %B IFIP Networking Conference %Z date of event: 2019-05-20 - 2019-05-22 %C Warsaw, Poland %B IFIP Networking Conference %I IEEE
[62]
S. A. Amiri, S. Schmid, and S. Siebertz, “Distributed Dominating Set Approximations beyond Planar Graphs,” ACM Transactions on Algorithms, vol. 15, no. 3, 2019.
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@article{Amiri2019, TITLE = {Distributed Dominating Set Approximations beyond Planar Graphs}, AUTHOR = {Amiri, Saeed Akhoondian and Schmid, Stefan and Siebertz, Sebastian}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3326170}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {15}, NUMBER = {3}, EID = {39}, }
Endnote
%0 Journal Article %A Amiri, Saeed Akhoondian %A Schmid, Stefan %A Siebertz, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Distributed Dominating Set Approximations beyond Planar Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0004-8335-C %R 10.1145/3326170 %7 2019 %D 2019 %J ACM Transactions on Algorithms %V 15 %N 3 %Z sequence number: 39 %I ACM %C New York, NY %@ false
[63]
A. Antoniadis, C.-C. Huang, and S. Ott, “A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State,” Algorithmica, vol. 81, no. 9, 2019.
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@article{Antoniadis2019, TITLE = {A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State}, AUTHOR = {Antoniadis, Antonios and Huang, Chien-Chung and Ott, Sebastian}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-019-00596-3}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Algorithmica}, VOLUME = {81}, NUMBER = {9}, PAGES = {3725 --3745}, }
Endnote
%0 Journal Article %A Antoniadis, Antonios %A Huang, Chien-Chung %A Ott, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State : %G eng %U http://hdl.handle.net/21.11116/0000-0004-AAC7-C %R 10.1007/s00453-019-00596-3 %7 2019 %D 2019 %J Algorithmica %V 81 %N 9 %& 3725 %P 3725 - 3745 %I Springer %C New York, NY %@ false
[64]
A. Antoniadis, N. Barcelo, M. Nugent, K. Pruhs, and M. Scquizzato, “A o(n)-Competitive Deterministic Algorithm for Online Matching on a Line,” Algorithmica, vol. 81, no. 7, 2019.
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@article{Antoniadis2019, TITLE = {A $o(n)$-Competitive Deterministic Algorithm for Online Matching on a Line}, AUTHOR = {Antoniadis, Antonios and Barcelo, Neal and Nugent, Michael and Pruhs, Kirk and Scquizzato, Michele}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-019-00565-w}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Algorithmica}, VOLUME = {81}, NUMBER = {7}, PAGES = {2917--2933}, }
Endnote
%0 Journal Article %A Antoniadis, Antonios %A Barcelo, Neal %A Nugent, Michael %A Pruhs, Kirk %A Scquizzato, Michele %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T A o(n)-Competitive Deterministic Algorithm for Online Matching on a Line : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7DA-B %R 10.1007/s00453-019-00565-w %7 2019 %D 2019 %J Algorithmica %V 81 %N 7 %& 2917 %P 2917 - 2933 %I Springer %C New York, NY %@ false
[65]
A. Antoniadis, K. Fleszar, R. Hoeksma, and K. Schewior, “A PTAS for Euclidean TSP with Hyperplane Neighborhoods,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Antoniadis_SODA19, TITLE = {A {PTAS} for {E}uclidean {TSP} with Hyperplane Neighborhoods}, AUTHOR = {Antoniadis, Antonios and Fleszar, Krzysztof and Hoeksma, Ruben and Schewior, Kevin}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.67}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {1089--1105}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Fleszar, Krzysztof %A Hoeksma, Ruben %A Schewior, Kevin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A PTAS for Euclidean TSP with Hyperplane Neighborhoods : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F3A-B %R 10.1137/1.9781611975482.67 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 1089 - 1105 %I SIAM %@ 978-1-61197-548-2
[66]
A. Antoniadis, F. Biermeier, A. Cristi, C. Damerius, R. Hoeksma, D. Kaaser, P. Kling, and ukas Nölke, “On the Complexity of Anchored Rectangle Packing,” in 27th Annual European Symposium on Algorithms (ESA 2019), Munich/Garching, Germany, 2019.
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@inproceedings{Antoniadis_ESA2019, TITLE = {On the Complexity of Anchored Rectangle Packing}, AUTHOR = {Antoniadis, Antonios and Biermeier, Felix and Cristi, Andr{\'e}s and Damerius, Christoph and Hoeksma, Ruben and Kaaser, Dominik and Kling, Peter and N{\"o}lke, ukas}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-124-5}, URL = {urn:nbn:de:0030-drops-111297}, DOI = {10.4230/LIPIcs.ESA.2019.8}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {27th Annual European Symposium on Algorithms (ESA 2019)}, EDITOR = {Bender, Michael A. and Svensson, Ola and German, Grzegorz}, PAGES = {1--14}, EID = {268}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {144}, ADDRESS = {Munich/Garching, Germany}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Biermeier, Felix %A Cristi, Andr&#233;s %A Damerius, Christoph %A Hoeksma, Ruben %A Kaaser, Dominik %A Kling, Peter %A N&#246;lke, ukas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations %T On the Complexity of Anchored Rectangle Packing : %G eng %U http://hdl.handle.net/21.11116/0000-0007-317F-4 %R 10.4230/LIPIcs.ESA.2019.8 %U urn:nbn:de:0030-drops-111297 %D 2019 %B 27th Annual European Symposium on Algorithms %Z date of event: 2019-09-09 - 2019-09-11 %C Munich/Garching, Germany %B 27th Annual European Symposium on Algorithms %E Bender, Michael A.; Svensson, Ola; German, Grzegorz %P 1 - 14 %Z sequence number: 268 %I Schloss Dagstuhl %@ 978-3-95977-124-5 %B Leibniz International Proceedings in Informatics %N 144 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2019/11129/https://creativecommons.org/licenses/by/3.0/legalcode
[67]
G. Ballard, C. Ikenmeyer, J. M. Landsberg, and N. Ryder, “The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices,” Journal of Pure and Applied Algebra, vol. 223, no. 8, 2019.
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@article{Ballard2018, TITLE = {The geometry of rank decompositions of matrix multiplication II: $3\times 3$ matrices}, AUTHOR = {Ballard, Grey and Ikenmeyer, Christian and Landsberg, J. M. and Ryder, Nick}, LANGUAGE = {eng}, ISSN = {0022-4049}, DOI = {10.1016/j.jpaa.2018.10.014}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {223}, NUMBER = {8}, PAGES = {3205--3224}, }
Endnote
%0 Journal Article %A Ballard, Grey %A Ikenmeyer, Christian %A Landsberg, J. M. %A Ryder, Nick %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AB17-4 %R 10.1016/j.jpaa.2018.10.014 %7 2018 %D 2019 %J Journal of Pure and Applied Algebra %O J. Pure Appl. Algebra %V 223 %N 8 %& 3205 %P 3205 - 3224 %I North-Holland %C Amsterdam %@ false
[68]
A. Balliu, J. Hirvonen, C. Lenzen, D. Olivetti, and J. Suomela, “Locality of Not-so-Weak Coloring,” in Structural Information and Communication Complexity (SIROCCO 2019), L’Aquila, Italy, 2019.
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@inproceedings{Balliu_SIROCCO2019, TITLE = {Locality of Not-so-Weak Coloring}, AUTHOR = {Balliu, Alkida and Hirvonen, Juho and Lenzen, Christoph and Olivetti, Dennis and Suomela, Jukka}, LANGUAGE = {eng}, ISBN = {978-3-030-24921-2; 978-3-030-24922-9}, DOI = {10.1007/978-3-030-24922-9_3}, PUBLISHER = {Springer}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Structural Information and Communication Complexity (SIROCCO 2019)}, EDITOR = {Censor-Hillel, Keren and Flammini, Michele}, PAGES = {37--51}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {11639}, ADDRESS = {L{\textquoteright}Aquila, Italy}, }
Endnote
%0 Conference Proceedings %A Balliu, Alkida %A Hirvonen, Juho %A Lenzen, Christoph %A Olivetti, Dennis %A Suomela, Jukka %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Locality of Not-so-Weak Coloring : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1BF2-C %R 10.1007/978-3-030-24922-9_3 %D 2019 %B 26th International Colloquium on Structural Information and Communication Complexity %Z date of event: 2019-07-01 - 2019-07-04 %C L&#8217;Aquila, Italy %B Structural Information and Communication Complexity %E Censor-Hillel, Keren; Flammini, Michele %P 37 - 51 %I Springer %@ 978-3-030-24921-2 978-3-030-24922-9 %B Lecture Notes in Computer Science %N 11639
[69]
A. Balliu, J. Hirvonen, C. Lenzen, D. Olivetti, and J. Suomela, “Locality of Not-So-Weak Coloring,” 2019. [Online]. Available: http://arxiv.org/abs/1904.05627. (arXiv: 1904.05627)
Abstract
Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes: - "Easy": solvable in $O(\log^* n)$ rounds with both deterministic and randomized distributed algorithms. - "Hard": requires at least $\Omega(\log n)$ rounds with deterministic and $\Omega(\log \log n)$ rounds with randomized distributed algorithms. Hence for any parameterized LCL problem, when we move from local problems towards global problems, there is some point at which complexity suddenly jumps from easy to hard. For example, for vertex coloring in $d$-regular graphs it is now known that this jump is at precisely $d$ colors: coloring with $d+1$ colors is easy, while coloring with $d$ colors is hard. However, it is currently poorly understood where this jump takes place when one looks at defective colorings. To study this question, we define $k$-partial $c$-coloring as follows: nodes are labeled with numbers between $1$ and $c$, and every node is incident to at least $k$ properly colored edges. It is known that $1$-partial $2$-coloring (a.k.a. weak $2$-coloring) is easy for any $d \ge 1$. As our main result, we show that $k$-partial $2$-coloring becomes hard as soon as $k \ge 2$, no matter how large a $d$ we have. We also show that this is fundamentally different from $k$-partial $3$-coloring: no matter which $k \ge 3$ we choose, the problem is always hard for $d = k$ but it becomes easy when $d \gg k$. The same was known previously for partial $c$-coloring with $c \ge 4$, but the case of $c < 4$ was open.
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@online{Balliu_arXiv1904.05627, TITLE = {Locality of Not-So-Weak Coloring}, AUTHOR = {Balliu, Alkida and Hirvonen, Juho and Lenzen, Christoph and Olivetti, Dennis and Suomela, Jukka}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1904.05627}, EPRINT = {1904.05627}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes: -- "Easy": solvable in $O(\log^* n)$ rounds with both deterministic and randomized distributed algorithms. -- "Hard": requires at least $\Omega(\log n)$ rounds with deterministic and $\Omega(\log \log n)$ rounds with randomized distributed algorithms. Hence for any parameterized LCL problem, when we move from local problems towards global problems, there is some point at which complexity suddenly jumps from easy to hard. For example, for vertex coloring in $d$-regular graphs it is now known that this jump is at precisely $d$ colors: coloring with $d+1$ colors is easy, while coloring with $d$ colors is hard. However, it is currently poorly understood where this jump takes place when one looks at defective colorings. To study this question, we define $k$-partial $c$-coloring as follows: nodes are labeled with numbers between $1$ and $c$, and every node is incident to at least $k$ properly colored edges. It is known that $1$-partial $2$-coloring (a.k.a. weak $2$-coloring) is easy for any $d \ge 1$. As our main result, we show that $k$-partial $2$-coloring becomes hard as soon as $k \ge 2$, no matter how large a $d$ we have. We also show that this is fundamentally different from $k$-partial $3$-coloring: no matter which $k \ge 3$ we choose, the problem is always hard for $d = k$ but it becomes easy when $d \gg k$. The same was known previously for partial $c$-coloring with $c \ge 4$, but the case of $c < 4$ was open.}, }
Endnote
%0 Report %A Balliu, Alkida %A Hirvonen, Juho %A Lenzen, Christoph %A Olivetti, Dennis %A Suomela, Jukka %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Locality of Not-So-Weak Coloring : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B39F-0 %U http://arxiv.org/abs/1904.05627 %D 2019 %X Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes: - "Easy": solvable in $O(\log^* n)$ rounds with both deterministic and randomized distributed algorithms. - "Hard": requires at least $\Omega(\log n)$ rounds with deterministic and $\Omega(\log \log n)$ rounds with randomized distributed algorithms. Hence for any parameterized LCL problem, when we move from local problems towards global problems, there is some point at which complexity suddenly jumps from easy to hard. For example, for vertex coloring in $d$-regular graphs it is now known that this jump is at precisely $d$ colors: coloring with $d+1$ colors is easy, while coloring with $d$ colors is hard. However, it is currently poorly understood where this jump takes place when one looks at defective colorings. To study this question, we define $k$-partial $c$-coloring as follows: nodes are labeled with numbers between $1$ and $c$, and every node is incident to at least $k$ properly colored edges. It is known that $1$-partial $2$-coloring (a.k.a. weak $2$-coloring) is easy for any $d \ge 1$. As our main result, we show that $k$-partial $2$-coloring becomes hard as soon as $k \ge 2$, no matter how large a $d$ we have. We also show that this is fundamentally different from $k$-partial $3$-coloring: no matter which $k \ge 3$ we choose, the problem is always hard for $d = k$ but it becomes easy when $d \gg k$. The same was known previously for partial $c$-coloring with $c \ge 4$, but the case of $c < 4$ was open. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Computational Complexity, cs.CC
[70]
F. Ban, V. Bhattiprolu, K. Bringmann, P. Kolev, E. Lee, and D. Woodruff, “A PTAS for l_p-Low Rank Approximation,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Ban_SODA19a, TITLE = {A {PTAS} for $\ell_p$-Low Rank Approximation}, AUTHOR = {Ban, Frank and Bhattiprolu, Vijay and Bringmann, Karl and Kolev, Pavel and Lee, Euiwoong and Woodruff, David}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.47}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {747--766}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Ban, Frank %A Bhattiprolu, Vijay %A Bringmann, Karl %A Kolev, Pavel %A Lee, Euiwoong %A Woodruff, David %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A PTAS for l_p-Low Rank Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E0E-E %R 10.1137/1.9781611975482.47 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 747 - 766 %I SIAM %@ 978-1-61197-548-2
[71]
L. Becchetti, A. Clementi, E. Natale, F. Pasquale, and G. Posta, “Self-Stabilizing Repeated Balls-into-Bins,” Distributed Computing, vol. 32, no. 1, 2019.
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@article{Becchetti2019, TITLE = {Self-Stabilizing Repeated Balls-into-Bins}, AUTHOR = {Becchetti, Luca and Clementi, Andrea and Natale, Emanuele and Pasquale, Francesco and Posta, Gustavo}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-017-0320-4}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Distributed Computing}, VOLUME = {32}, NUMBER = {1}, PAGES = {59--68}, }
Endnote
%0 Journal Article %A Becchetti, Luca %A Clementi, Andrea %A Natale, Emanuele %A Pasquale, Francesco %A Posta, Gustavo %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Self-Stabilizing Repeated Balls-into-Bins : %G eng %U http://hdl.handle.net/21.11116/0000-0002-F6C1-E %R 10.1007/s00446-017-0320-4 %7 2017 %D 2019 %J Distributed Computing %V 32 %N 1 %& 59 %P 59 - 68 %I Springer International %C Berlin %@ false
[72]
R. Becker, V. Bonifaci, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Two Results on Slime Mold Computations,” Theoretical Computer Science, vol. 773, 2019.
Abstract
In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points.
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@article{BBKKM2018, TITLE = {Two Results on Slime Mold Computations}, AUTHOR = {Becker, Ruben and Bonifaci, Vincenzo and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2018.08.027}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, ABSTRACT = {In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points.}, JOURNAL = {Theoretical Computer Science}, VOLUME = {773}, PAGES = {79--106}, }
Endnote
%0 Journal Article %A Becker, Ruben %A Bonifaci, Vincenzo %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Two Results on Slime Mold Computations : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A3AE-2 %R 10.1016/j.tcs.2018.08.027 %7 2018 %D 2019 %X In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points. %K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Dynamical Systems, math.DS,Mathematics, Optimization and Control, math.OC, Physics, Biological Physics, physics.bio-ph %J Theoretical Computer Science %V 773 %& 79 %P 79 - 106 %I Elsevier %C Amsterdam %@ false
[73]
R. Becker, Y. Emek, and C. Lenzen, “Low Diameter Graph Decompositions by Approximate Distance Computation,” 2019. [Online]. Available: http://arxiv.org/abs/1909.09002. (arXiv: 1909.09002)
Abstract
In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of such decompositions inherently rely on the subtractive form of the triangle inequality. The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 13), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the Congest, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 96) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only O(log n) times, which is of interest for capacitated problems and simulating Congest algorithms on the tree into which the graph is embedded.
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@online{Becker_arXIv1909.09002, TITLE = {Low Diameter Graph Decompositions by Approximate Distance Computation}, AUTHOR = {Becker, Ruben and Emek, Yuval and Lenzen, Christoph}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1909.09002}, EPRINT = {1909.09002}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of such decompositions inherently rely on the subtractive form of the triangle inequality. The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 13), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the Congest, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 96) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only O(log n) times, which is of interest for capacitated problems and simulating Congest algorithms on the tree into which the graph is embedded.}, }
Endnote
%0 Report %A Becker, Ruben %A Emek, Yuval %A Lenzen, Christoph %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Low Diameter Graph Decompositions by Approximate Distance Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1C65-B %U http://arxiv.org/abs/1909.09002 %D 2019 %X In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of such decompositions inherently rely on the subtractive form of the triangle inequality. The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 13), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the Congest, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 96) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only O(log n) times, which is of interest for capacitated problems and simulating Congest algorithms on the tree into which the graph is embedded. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[74]
R. Becker, Y. Emek, M. Ghaffari, and C. Lenzen, “Distributed Algorithms for Low Stretch Spanning Trees,” in 33rd International Symposiumon Distributed Computing (DISC 2019), Budapest, Hungary, 2019.
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@inproceedings{Becker_DISC2019, TITLE = {Distributed Algorithms for Low Stretch Spanning Trees}, AUTHOR = {Becker, Ruben and Emek, Yuval and Ghaffari, Mohsen and Lenzen, C.}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-126-9}, URL = {urn:nbn:de:0030-drops-113116}, DOI = {10.4230/LIPIcs.DISC.2019.4}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {33rd International Symposiumon Distributed Computing (DISC 2019)}, EDITOR = {Suomela, Jukka}, PAGES = {1--14}, EID = {4}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {146}, ADDRESS = {Budapest, Hungary}, }
Endnote
%0 Conference Proceedings %A Becker, Ruben %A Emek, Yuval %A Ghaffari, Mohsen %A Lenzen, C. %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Distributed Algorithms for Low Stretch Spanning Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1C52-0 %R 10.4230/LIPIcs.DISC.2019.4 %U urn:nbn:de:0030-drops-113116 %D 2019 %B 33rd International Symposiumon Distributed Computing %Z date of event: 2019-10-14 - 2019-10-18 %C Budapest, Hungary %B 33rd International Symposiumon Distributed Computing %E Suomela, Jukka %P 1 - 14 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-126-9 %B Leibniz International Proceedings in Informatics %N 146 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/11311http://drops.dagstuhl.de/doku/urheberrecht1.html
[75]
X. Bei, J. Garg, M. Hoefer, and K. Mehlhorn, “Earning and Utility Limits in Fisher Markets,” ACM Transactions on Economics and Computation, vol. 7, no. 2, 2019.
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@article{Bei2019, TITLE = {Earning and Utility Limits in Fisher Markets}, AUTHOR = {Bei, Xiaohui and Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt}, LANGUAGE = {eng}, DOI = {10.1145/3340234}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Economics and Computation}, VOLUME = {7}, NUMBER = {2}, EID = {10}, }
Endnote
%0 Journal Article %A Bei, Xiaohui %A Garg, Jugal %A Hoefer, Martin %A Mehlhorn, Kurt %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Earning and Utility Limits in Fisher Markets : %G eng %U http://hdl.handle.net/21.11116/0000-0005-4F7A-B %R 10.1145/3340234 %7 2019 %D 2019 %J ACM Transactions on Economics and Computation %O TEAC %V 7 %N 2 %Z sequence number: 10 %I ACM %C New York, NY
[76]
O. Beyersdorff, L. Chew, and K. Sreenivasaiah, “A Game Characterisation of Tree-like Q-Resolution Size,” Journal of Computer and System Sciences, vol. 104, 2019.
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@article{Beyersdorff2017, TITLE = {A Game Characterisation of Tree-like {Q-Resolution} Size}, AUTHOR = {Beyersdorff, Olaf and Chew, Leroy and Sreenivasaiah, Karteek}, LANGUAGE = {eng}, ISSN = {0022-0000}, DOI = {10.1016/j.jcss.2016.11.011}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Journal of Computer and System Sciences}, VOLUME = {104}, PAGES = {82--101}, }
Endnote
%0 Journal Article %A Beyersdorff, Olaf %A Chew, Leroy %A Sreenivasaiah, Karteek %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Game Characterisation of Tree-like Q-Resolution Size : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5F80-F %R 10.1016/j.jcss.2016.11.011 %7 2017 %D 2019 %J Journal of Computer and System Sciences %V 104 %& 82 %P 82 - 101 %I Elsevier %C Amsterdam %@ false
[77]
V. Bhargava, M. Bläser, G. Jindal, and A. Pandey, “A Deterministic PTAS for the Algebraic Rank of Bounded Degree Polynomials,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Bhargava_SODA19d, TITLE = {A Deterministic {PTAS} for the Algebraic Rank of Bounded Degree Polynomials}, AUTHOR = {Bhargava, Vishwas and Bl{\"a}ser, Markus and Jindal, Gorav and Pandey, Anurag}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.41}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {647--661}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Bhargava, Vishwas %A Bl&#228;ser, Markus %A Jindal, Gorav %A Pandey, Anurag %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Deterministic PTAS for the Algebraic Rank of Bounded Degree Polynomials : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ABAD-B %R 10.1137/1.9781611975482.41 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 647 - 661 %I SIAM %@ 978-1-61197-548-2
[78]
M. Bläser, C. Ikenmeyer, V. Lysikov, A. Pandey, and F.-O. Schreyer, “Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory,” 2019. [Online]. Available: http://arxiv.org/abs/1911.02534. (arXiv: 1911.02534)
Abstract
We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the set of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all 3-tensors of slice rank at most $r$. We show that the membership testing problem for the slice rank variety is $\NP$-hard. While the slice rank variety is a union of orbit closures, we define another variety, the minrank variety, expressible as a single orbit closure. Our next result is the $\NP$-hardness of membership testing in the minrank variety, hence we establish the $\NP$-hardness of the orbit closure containment problem for 3-tensors. Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk and independently by Grochow, Kumar, Saks and Saraf. Bl\"aser et al. gave a version of an algebraic natural proof barrier for the matrix completion problem which relies on $\coNP \subseteq \exists \BPP$. It implied that constructing equations for the corresponding variety should be hard. We generalize their approach to work with any family of varieties for which the membership problem is $\NP$-hard and for which we can efficiently generate a dense subset. Therefore, a similar barrier holds for the slice rank and the minrank varieties, too. This allows us to set up the slice rank and the minrank varieties as a test-bed for geometric complexity theory (GCT). We determine the stabilizers of the tensors that generate the orbit closures of the two varieties and prove that these tensors are almost characterized by their symmetries. We prove several nontrivial equations for both the varieties using different GCT methods. Many equations also work in the regime where membership testing in the slice rank or minrank varieties is $\NP$-hard. We view this as a promising sign that the GCT approach might indeed be successful.
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@online{Blaeser_arXiv1911.02534, TITLE = {Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory}, AUTHOR = {Bl{\"a}ser, Markus and Ikenmeyer, Christian and Lysikov, Vladimir and Pandey, Anurag and Schreyer, Frank-Olaf}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1911.02534}, EPRINT = {1911.02534}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the set of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all 3-tensors of slice rank at most $r$. We show that the membership testing problem for the slice rank variety is $\NP$-hard. While the slice rank variety is a union of orbit closures, we define another variety, the minrank variety, expressible as a single orbit closure. Our next result is the $\NP$-hardness of membership testing in the minrank variety, hence we establish the $\NP$-hardness of the orbit closure containment problem for 3-tensors. Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk and independently by Grochow, Kumar, Saks and Saraf. Bl\"aser et al. gave a version of an algebraic natural proof barrier for the matrix completion problem which relies on $\coNP \subseteq \exists \BPP$. It implied that constructing equations for the corresponding variety should be hard. We generalize their approach to work with any family of varieties for which the membership problem is $\NP$-hard and for which we can efficiently generate a dense subset. Therefore, a similar barrier holds for the slice rank and the minrank varieties, too. This allows us to set up the slice rank and the minrank varieties as a test-bed for geometric complexity theory (GCT). We determine the stabilizers of the tensors that generate the orbit closures of the two varieties and prove that these tensors are almost characterized by their symmetries. We prove several nontrivial equations for both the varieties using different GCT methods. Many equations also work in the regime where membership testing in the slice rank or minrank varieties is $\NP$-hard. We view this as a promising sign that the GCT approach might indeed be successful.}, }
Endnote
%0 Report %A Bl&#228;ser, Markus %A Ikenmeyer, Christian %A Lysikov, Vladimir %A Pandey, Anurag %A Schreyer, Frank-Olaf %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1D77-6 %U http://arxiv.org/abs/1911.02534 %D 2019 %X We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the set of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all 3-tensors of slice rank at most $r$. We show that the membership testing problem for the slice rank variety is $\NP$-hard. While the slice rank variety is a union of orbit closures, we define another variety, the minrank variety, expressible as a single orbit closure. Our next result is the $\NP$-hardness of membership testing in the minrank variety, hence we establish the $\NP$-hardness of the orbit closure containment problem for 3-tensors. Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk and independently by Grochow, Kumar, Saks and Saraf. Bl\"aser et al. gave a version of an algebraic natural proof barrier for the matrix completion problem which relies on $\coNP \subseteq \exists \BPP$. It implied that constructing equations for the corresponding variety should be hard. We generalize their approach to work with any family of varieties for which the membership problem is $\NP$-hard and for which we can efficiently generate a dense subset. Therefore, a similar barrier holds for the slice rank and the minrank varieties, too. This allows us to set up the slice rank and the minrank varieties as a test-bed for geometric complexity theory (GCT). We determine the stabilizers of the tensors that generate the orbit closures of the two varieties and prove that these tensors are almost characterized by their symmetries. We prove several nontrivial equations for both the varieties using different GCT methods. Many equations also work in the regime where membership testing in the slice rank or minrank varieties is $\NP$-hard. We view this as a promising sign that the GCT approach might indeed be successful. %K Computer Science, Computational Complexity, cs.CC,Mathematics, Algebraic Geometry, math.AG,Mathematics, Representation Theory, math.RT
[79]
L. Boczkowski, A. Korman, and E. Natale, “Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits,” Distributed Computing, vol. 32, no. 3, 2019.
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@article{Boczkowski2019, TITLE = {Minimizing Message Size in Stochastic Communication Patterns: {F}ast Self-Stabilizing Protocols with 3 bits}, AUTHOR = {Boczkowski, Lucas and Korman, Amos and Natale, Emanuele}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-018-0330-x}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Distributed Computing}, VOLUME = {32}, NUMBER = {3}, PAGES = {173--191}, }
Endnote
%0 Journal Article %A Boczkowski, Lucas %A Korman, Amos %A Natale, Emanuele %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B2F2-2 %R 10.1007/s00446-018-0330-x %7 2018 %D 2019 %J Distributed Computing %V 32 %N 3 %& 173 %P 173 - 191 %I Springer International %C Berlin %@ false
[80]
M. Borassi and E. Natale, “KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation,” Journal of Experimental Algorithmics, vol. 24, no. 1, 2019.
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@article{Borassi2019, TITLE = {{KADABRA} is an {ADaptive} Algorithm for Betweenness via Random Approximation}, AUTHOR = {Borassi, Michele and Natale, Emanuele}, LANGUAGE = {eng}, ISSN = {1084-6654}, DOI = {10.1145/3284359}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Experimental Algorithmics}, VOLUME = {24}, NUMBER = {1}, EID = {1.2}, }
Endnote
%0 Journal Article %A Borassi, Michele %A Natale, Emanuele %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0003-7A10-2 %R 10.1145/3284359 %7 2019 %D 2019 %J Journal of Experimental Algorithmics %V 24 %N 1 %Z sequence number: 1.2 %I ACM %C New York, NY %@ false
[81]
M. Bressan, S. Leucci, and A. Panconesi, “Motivo: Fast Motif Counting via Succinct Color Coding and Adaptive Sampling,” Proccedings of the VLDB Endowment, vol. 12, no. 11, 2019.
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@article{Bressan_2019, TITLE = {Motivo: Fast Motif Counting via Succinct Color Coding and Adaptive Sampling}, AUTHOR = {Bressan, Marco and Leucci, Stefano and Panconesi, Alessandro}, LANGUAGE = {eng}, ISSN = {2150-8097}, DOI = {10.14778/3342263.3342640}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, JOURNAL = {Proccedings of the VLDB Endowment}, VOLUME = {12}, NUMBER = {11}, PAGES = {1651--1663}, }
Endnote
%0 Journal Article %A Bressan, Marco %A Leucci, Stefano %A Panconesi, Alessandro %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Motivo: Fast Motif Counting via Succinct Color Coding and Adaptive Sampling : %G eng %U http://hdl.handle.net/21.11116/0000-0005-6A05-F %R 10.14778/3342263.3342640 %7 2019 %D 2019 %J Proccedings of the VLDB Endowment %V 12 %N 11 %& 1651 %P 1651 - 1663 %I ACM %C New York, NY %@ false
[82]
K. Bringmann, F. Grandoni, B. Saha, and V. Vassilevska Williams, “Truly Subcubic Algorithms for Language Edit Distance and RNA Folding via Fast Bounded-Difference Min-Plus Product,” SIAM Journal on Computing, vol. 48, no. 2, 2019.
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@article{Bringmann_Truly2019, TITLE = {Truly Subcubic Algorithms for Language Edit Distance and {RNA} Folding via Fast Bounded-Difference Min-Plus Product}, AUTHOR = {Bringmann, Karl and Grandoni, Fabrizio and Saha, Barna and Vassilevska Williams, Virginia}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/17M112720X}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {48}, NUMBER = {2}, PAGES = {481--512}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Grandoni, Fabrizio %A Saha, Barna %A Vassilevska Williams, Virginia %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Truly Subcubic Algorithms for Language Edit Distance and RNA Folding via Fast Bounded-Difference Min-Plus Product : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7E4-F %R 10.1137/17M112720X %7 2019 %D 2019 %J SIAM Journal on Computing %V 48 %N 2 %& 481 %P 481 - 512 %I SIAM %C Philadelphia, PA %@ false
[83]
K. Bringmann, S. Kisfaludi-Bak, M. Pilipczuk, and E. J. van Leeuwen, “On Geometric Set Cover for Orthants,” in 27th Annual European Symposium on Algorithms (ESA 2019), Munich/Garching, Germany, 2019.
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@inproceedings{Bringmann_ESA2019, TITLE = {On Geometric Set Cover for Orthants}, AUTHOR = {Bringmann, Karl and Kisfaludi-Bak, S{\'a}ndor and Pilipczuk, Michal and van Leeuwen, Erik Jan}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-124-5}, URL = {urn:nbn:de:0030-drops-111476}, DOI = {10.4230/LIPIcs.ESA.2019.26}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {27th Annual European Symposium on Algorithms (ESA 2019)}, EDITOR = {Bender, Michael A. and Svensson, Ola and German, Grzegorz}, PAGES = {1--18}, EID = {26}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {144}, ADDRESS = {Munich/Garching, Germany}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Kisfaludi-Bak, S&#225;ndor %A Pilipczuk, Michal %A van Leeuwen, Erik Jan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T On Geometric Set Cover for Orthants : %G eng %U http://hdl.handle.net/21.11116/0000-0005-2040-E %R 10.4230/LIPIcs.ESA.2019.26 %U urn:nbn:de:0030-drops-111476 %D 2019 %B 27th Annual European Symposium on Algorithms %Z date of event: 2019-09-09 - 2019-09-11 %C Munich/Garching, Germany %B 27th Annual European Symposium on Algorithms %E Bender, Michael A.; Svensson, Ola; German, Grzegorz %P 1 - 18 %Z sequence number: 26 %I Schloss Dagstuhl %@ 978-3-95977-124-5 %B Leibniz International Proceedings in Informatics %N 144 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/11147/http://drops.dagstuhl.de/doku/urheberrecht1.html
[84]
K. Bringmann, T. Husfeldt, and M. Magnusson, “Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth,” in 13th International Symposium on Parameterized and Exact Computation (IPEC 2018), Helsinki, Finland, 2019.
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@inproceedings{Bringmann_IPEC2018, TITLE = {Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth}, AUTHOR = {Bringmann, Karl and Husfeldt, Thore and Magnusson, M{\aa}ns}, LANGUAGE = {eng}, ISBN = {978-3-95977-084-2}, URL = {urn:nbn:de:0030-drops-102050}, DOI = {10.4230/LIPIcs.IPEC.2018.4}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {13th International Symposium on Parameterized and Exact Computation (IPEC 2018)}, EDITOR = {Paul, Christophe and Pilipczuk, Michal}, PAGES = {1--13}, EID = {4}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {115}, ADDRESS = {Helsinki, Finland}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Husfeldt, Thore %A Magnusson, M&#229;ns %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9CFE-1 %R 10.4230/LIPIcs.IPEC.2018.4 %U urn:nbn:de:0030-drops-102050 %D 2019 %B 13th International Symposium on Parameterized and Exact Computation %Z date of event: 2018-08-20 - 2018-08-24 %C Helsinki, Finland %B 13th International Symposium on Parameterized and Exact Computation %E Paul, Christophe; Pilipczuk, Michal %P 1 - 13 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-084-2 %B Leibniz International Proceedings in Informatics %N 115 %U http://drops.dagstuhl.de/opus/volltexte/2019/10205/http://drops.dagstuhl.de/doku/urheberrecht1.html
[85]
K. Bringmann, R. Keusch, and J. Lengler, “Geometric Inhomogeneous Random Graphs,” Theoretical Computer Science, vol. 760, 2019.
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@article{BringmannTCS2019, TITLE = {Geometric Inhomogeneous Random Graphs}, AUTHOR = {Bringmann, Karl and Keusch, Ralph and Lengler, Johannes}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2018.08.014}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Theoretical Computer Science}, VOLUME = {760}, PAGES = {35--54}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Keusch, Ralph %A Lengler, Johannes %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Geometric Inhomogeneous Random Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0B00-1 %R 10.1016/j.tcs.2018.08.014 %7 2018 %D 2019 %J Theoretical Computer Science %V 760 %& 35 %P 35 - 54 %I Elsevier %C Amsterdam %@ false
[86]
K. Bringmann, “Fine-Grained Complexity Theory (Tutorial),” in 36th Symposium on Theoretical Aspects of Computer Science (STACS 2019), Berlin, Germany, 2019.
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@inproceedings{Bringmann_STACS2019, TITLE = {Fine-Grained Complexity Theory (Tutorial)}, AUTHOR = {Bringmann, Karl}, LANGUAGE = {eng}, ISBN = {978-3-95977-100-9}, DOI = {10.4230/LIPIcs.STACS.2019.4}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {36th Symposium on Theoretical Aspects of Computer Science (STACS 2019)}, EDITOR = {Niedermeier, Rolf and Paul, Christophe}, PAGES = {1--7}, EID = {4}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {126}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity Theory (Tutorial) : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B36E-8 %R 10.4230/LIPIcs.STACS.2019.4 %D 2019 %B 36th Symposium on Theoretical Aspects of Computer Science %Z date of event: 2019-03-13 - 2019-03-16 %C Berlin, Germany %B 36th Symposium on Theoretical Aspects of Computer Science %E Niedermeier, Rolf; Paul, Christophe %P 1 - 7 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-100-9 %B Leibniz International Proceedings in Informatics %N 126 %U http://drops.dagstuhl.de/opus/volltexte/2019/10243/http://drops.dagstuhl.de/doku/urheberrecht1.html
[87]
K. Bringmann, M. Künnemann, and K. Węgrzycki, “Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max,” in STOC’19, 51st Annual ACM Symposium on the Theory of Computing, Phoenix, AZ, USA, 2019.
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@inproceedings{Bringmann_STOC2019, TITLE = {Approximating {APSP} without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, ISBN = {978-1-4503-6705-9}, DOI = {10.1145/3313276.3316373}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC'19, 51st Annual ACM Symposium on the Theory of Computing}, EDITOR = {Charikar, Moses and Cohen, Edith}, PAGES = {943--954}, ADDRESS = {Phoenix, AZ, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A W&#281;grzycki, Karol %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max : %G eng %U http://hdl.handle.net/21.11116/0000-0002-FC7A-A %R 10.1145/3313276.3316373 %D 2019 %B 51st Annual ACM Symposium on the Theory of Computing %Z date of event: 2019-06-23 - 2019-06-26 %C Phoenix, AZ, USA %B STOC'19 %E Charikar, Moses; Cohen, Edith %P 943 - 954 %I ACM %@ 978-1-4503-6705-9
[88]
K. Bringmann, M. Künnemann, and K. Węgrzycki, “Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max,” 2019. [Online]. Available: http://arxiv.org/abs/1907.11078. (arXiv: 1907.11078)
Abstract
Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound. Since Zwick's algorithm uses the scaling technique, it has a factor $\log W$ in the running time. In this paper, we study whether APSP and related problems admit approximation schemes avoiding the scaling technique. That is, the number of arithmetic operations should be independent of $W$; this is called strongly polynomial. Our main results are as follows. - We design approximation schemes in strongly polynomial time $O(\frac{n^\omega}{\varepsilon} \text{polylog}(\frac{n}{\varepsilon}))$ for APSP on undirected graphs as well as for the graph characteristics diameter, radius, median, minimum-weight triangle, and minimum-weight cycle on directed or undirected graphs. - For APSP on directed graphs we design an approximation scheme in strongly polynomial time $O(n^{\frac{\omega + 3}{2}} \varepsilon^{-1} \text{polylog}(\frac{n}{\varepsilon}))$. This is significantly faster than the best exact algorithm. - We explain why our approximation scheme for APSP on directed graphs has a worse exponent than $\omega$: Any improvement over our exponent $\frac{\omega + 3}{2}$ would improve the best known algorithm for Min-Max Product In fact, we prove that approximating directed APSP and exactly computing the Min-Max Product are equivalent.
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@online{BRingmann_arXiv1907.11078, TITLE = {Approximating {APSP} without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1907.11078}, EPRINT = {1907.11078}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound. Since Zwick's algorithm uses the scaling technique, it has a factor $\log W$ in the running time. In this paper, we study whether APSP and related problems admit approximation schemes avoiding the scaling technique. That is, the number of arithmetic operations should be independent of $W$; this is called strongly polynomial. Our main results are as follows. -- We design approximation schemes in strongly polynomial time $O(\frac{n^\omega}{\varepsilon} \text{polylog}(\frac{n}{\varepsilon}))$ for APSP on undirected graphs as well as for the graph characteristics diameter, radius, median, minimum-weight triangle, and minimum-weight cycle on directed or undirected graphs. -- For APSP on directed graphs we design an approximation scheme in strongly polynomial time $O(n^{\frac{\omega + 3}{2}} \varepsilon^{-1} \text{polylog}(\frac{n}{\varepsilon}))$. This is significantly faster than the best exact algorithm. -- We explain why our approximation scheme for APSP on directed graphs has a worse exponent than $\omega$: Any improvement over our exponent $\frac{\omega + 3}{2}$ would improve the best known algorithm for Min-Max Product In fact, we prove that approximating directed APSP and exactly computing the Min-Max Product are equivalent.}, }
Endnote
%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A W&#281;grzycki, Karol %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max : %G eng %U http://hdl.handle.net/21.11116/0000-0005-3D73-6 %U http://arxiv.org/abs/1907.11078 %D 2019 %X Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound. Since Zwick's algorithm uses the scaling technique, it has a factor $\log W$ in the running time. In this paper, we study whether APSP and related problems admit approximation schemes avoiding the scaling technique. That is, the number of arithmetic operations should be independent of $W$; this is called strongly polynomial. Our main results are as follows. - We design approximation schemes in strongly polynomial time $O(\frac{n^\omega}{\varepsilon} \text{polylog}(\frac{n}{\varepsilon}))$ for APSP on undirected graphs as well as for the graph characteristics diameter, radius, median, minimum-weight triangle, and minimum-weight cycle on directed or undirected graphs. - For APSP on directed graphs we design an approximation scheme in strongly polynomial time $O(n^{\frac{\omega + 3}{2}} \varepsilon^{-1} \text{polylog}(\frac{n}{\varepsilon}))$. This is significantly faster than the best exact algorithm. - We explain why our approximation scheme for APSP on directed graphs has a worse exponent than $\omega$: Any improvement over our exponent $\frac{\omega + 3}{2}$ would improve the best known algorithm for Min-Max Product In fact, we prove that approximating directed APSP and exactly computing the Min-Max Product are equivalent. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[89]
K. Bringmann, N. Fischer, and M. Künnemann, “A Fine-Grained Analogue of Schaefer’s Theorem in P: Dichotomy of ∃k∀-Quantified First-Order Graph Properties,” in 34th Computational Complexity Conference (CCC 2019), New Brunswick, NJ, USA, 2019.
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@inproceedings{Bringmann_CCC2019, TITLE = {A Fine-Grained Analogue of {S}chaefer's Theorem in {P}: {D}ichotomy of {Exists^k-Forall}-Quantified First-Order Graph Properties}, AUTHOR = {Bringmann, Karl and Fischer, Nick and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-116-0}, URL = {urn:nbn:de:0030-drops-108533}, DOI = {10.4230/LIPIcs.CCC.2019.31}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {34th Computational Complexity Conference (CCC 2019)}, EDITOR = {Shpilka, Amir}, PAGES = {1--27}, EID = {31}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {137}, ADDRESS = {New Brunswick, NJ, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Fischer, Nick %A K&#252;nnemann, Marvin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Fine-Grained Analogue of Schaefer's Theorem in P: Dichotomy of &#8707;k&#8704;-Quantified First-Order Graph Properties : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1FAF-5 %R 10.4230/LIPIcs.CCC.2019.31 %U urn:nbn:de:0030-drops-108533 %D 2019 %B 34th Computational Complexity Conference %Z date of event: 2019-07-18 - 2019-07-20 %C New Brunswick, NJ, USA %B 34th Computational Complexity Conference %E Shpilka, Amir %P 1 - 27 %Z sequence number: 31 %I Schloss Dagstuhl %@ 978-3-95977-116-0 %B Leibniz International Proceedings in Informatics %N 137 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10853/http://drops.dagstuhl.de/doku/urheberrecht1.html
[90]
K. Bringmann, M. Künnemann, and P. Wellnitz, “Few Matches or Almost Periodicity: Faster Pattern Matching with Mismatches in Compressed Texts,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Bringmann_SODA19c, TITLE = {Few Matches or Almost Periodicity: {F}aster Pattern Matching with Mismatches in Compressed Texts}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.69}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {1126--1145}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Few Matches or Almost Periodicity: Faster Pattern Matching with Mismatches in Compressed Texts : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E1F-B %R 10.1137/1.9781611975482.69 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 1126 - 1145 %I SIAM %@ 978-1-61197-548-2
[91]
K. Bringmann, M. Künnemann, and A. Nusser, “Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance,” 2019. [Online]. Available: http://arxiv.org/abs/1901.01504. (arXiv: 1901.01504)
Abstract
The Fr\'echet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Fr\'echet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Fr\'echet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Fr\'echet distance. In this work, we present a fast, certifying implementation for deciding the Fr\'echet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure.
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@online{Bringmann_arXiv1901.01504, TITLE = {Walking the Dog Fast in Practice: {A}lgorithm Engineering of the {F}r\'{e}chet Distance}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1901.01504}, EPRINT = {1901.01504}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The Fr\'echet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Fr\'echet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Fr\'echet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Fr\'echet distance. In this work, we present a fast, certifying implementation for deciding the Fr\'echet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure.}, }
Endnote
%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Walking the Dog Fast in Practice: Algorithm Engineering of the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-0005-3D76-3 %U http://arxiv.org/abs/1901.01504 %D 2019 %X The Fr\'echet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Fr\'echet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Fr\'echet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Fr\'echet distance. In this work, we present a fast, certifying implementation for deciding the Fr\'echet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure. %K Computer Science, Computational Geometry, cs.CG
[92]
K. Bringmann, M. Künnemann, and A. Nusser, “Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance,” in 35th International Symposium on Computational Geometry (SoCG 2019), Portland, OR, USA, 2019.
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@inproceedings{Bringmann_SoCG2019, TITLE = {Walking the Dog Fast in Practice: {A}lgorithm Engineering of the {F}r\'{e}chet Distance}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-104-7}, URL = {urn:nbn:de:0030-drops-104219}, DOI = {10.4230/LIPIcs.SoCG.2019.17}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {35th International Symposium on Computational Geometry (SoCG 2019)}, EDITOR = {Barequet, Gill and Wang, Yusu}, PAGES = {1--21}, EID = {17}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {129}, ADDRESS = {Portland, OR, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Walking the Dog Fast in Practice: Algorithm Engineering of the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-0003-65C1-1 %R 10.4230/LIPIcs.SoCG.2019.17 %U urn:nbn:de:0030-drops-104219 %D 2019 %B 35th International Symposium on Computational Geometry %Z date of event: 2019-06-18 - 2019-06-21 %C Portland, OR, USA %B 35th International Symposium on Computational Geometry %E Barequet, Gill; Wang, Yusu %P 1 - 21 %Z sequence number: 17 %I Schloss Dagstuhl %@ 978-3-95977-104-7 %B Leibniz International Proceedings in Informatics %N 129 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10421/http://drops.dagstuhl.de/doku/urheberrecht1.html
[93]
K. Bringmann, M. Künnemann, and A. Nusser, “Fréchet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Bringmann_SODA19d, TITLE = {{F}r\'{e}chet Distance Under Translation: {C}onditional Hardness and an Algorithm via Offline Dynamic Grid Reachability}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.180}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {2902--2921}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fr&#233;chet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E29-F %R 10.1137/1.9781611975482.180 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 2902 - 2921 %I SIAM %@ 978-1-61197-548-2
[94]
K. Bringmann and B. Ray Chaudhury, “Polyline Simplification has Cubic Complexity,” in 35th International Symposium on Computational Geometry (SoCG 2019), Portland, OR, USA, 2019.
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@inproceedings{Bringmann_SoCG2019b, TITLE = {Polyline Simplification has Cubic Complexity}, AUTHOR = {Bringmann, Karl and Ray Chaudhury, Bhaskar}, LANGUAGE = {eng}, ISBN = {978-3-95977-104-7}, URL = {urn:nbn:de:0030-drops-104224}, DOI = {10.4230/LIPIcs.SoCG.2019.18}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {35th International Symposium on Computational Geometry (SoCG 2019)}, EDITOR = {Barequet, Gill and Wang, Yusu}, PAGES = {1--16}, EID = {18}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {129}, ADDRESS = {Portland, OR, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Ray Chaudhury, Bhaskar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Polyline Simplification has Cubic Complexity : %G eng %U http://hdl.handle.net/21.11116/0000-0003-65C8-A %R 10.4230/LIPIcs.SoCG.2019.18 %U urn:nbn:de:0030-drops-104224 %D 2019 %B 35th International Symposium on Computational Geometry %Z date of event: 2019-06-18 - 2019-06-21 %C Portland, OR, USA %B 35th International Symposium on Computational Geometry %E Barequet, Gill; Wang, Yusu %P 1 - 16 %Z sequence number: 18 %I Schloss Dagstuhl %@ 978-3-95977-104-7 %B Leibniz International Proceedings in Informatics %N 129 %U http://drops.dagstuhl.de/opus/volltexte/2019/10422/http://drops.dagstuhl.de/doku/urheberrecht1.html
[95]
K. Buchin, A. Driemel, N. van de L’Isle, and A. Nusser, “klcluster: Center-based Clustering of Trajectories,” in 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2019), Chicago, IL, USA, 2019.
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@inproceedings{Buchin_._SIGSPATIAL/GIS_2019, TITLE = {{klcluster}: {C}enter-based Clustering of Trajectories}, AUTHOR = {Buchin, Kevin and Driemel, Anne and van de L'Isle, Natasja and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISBN = {978-1-4503-6909-1}, DOI = {10.1145/3347146.3359111}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2019)}, EDITOR = {Banaei-Kashani, Farnoush and Trajcevski, Goce and G{\"u}ting, Ralf Hartmut and Kulik, Lars and Newsam, Shawn}, PAGES = {496--499}, ADDRESS = {Chicago, IL, USA}, }
Endnote
%0 Conference Proceedings %A Buchin, Kevin %A Driemel, Anne %A van de L'Isle, Natasja %A Nusser, Andr&#233; %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T klcluster: Center-based Clustering of Trajectories : %G eng %U http://hdl.handle.net/21.11116/0000-0005-8705-D %R 10.1145/3347146.3359111 %D 2019 %B 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems %Z date of event: 2019-11-05 - 2019-11-08 %C Chicago, IL, USA %B 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems %E Banaei-Kashani, Farnoush; Trajcevski, Goce; G&#252;ting, Ralf Hartmut; Kulik, Lars; Newsam, Shawn %P 496 - 499 %I ACM %@ 978-1-4503-6909-1
[96]
J. Bund, C. Lenzen, and M. Medina, “Optimal Metastability-Containing Sorting via Parallel Prefix Computation,” 2019. [Online]. Available: http://arxiv.org/abs/1911.00267. (arXiv: 1911.00267)
Abstract
Friedrichs et al. (TC 2018) showed that metastability can be contained when sorting inputs arising from time-to-digital converters, i.e., measurement values can be correctly sorted without resolving metastability using synchronizers first. However, this work left open whether this can be done by small circuits. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Our solution utilizes the parallel prefix computation (PPC) framework (JACM 1980). We improve this construction by bounding its fan-out by an arbitrary $f \geq 3$, without affecting depth and increasing circuit size by a small constant factor only. Thus, we obtain the first PPC circuits with asymptotically optimal size, constant fan-out, and optimal depth. To show that applying the PPC framework to the sorting task is feasible, we prove that the latter can, despite potential metastability, be decomposed such that the core operation is associative. We obtain asymptotically optimal metastability-containing sorting networks. We complement these results with simulations, independently verifying the correctness as well as small size and delay of our circuits.
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@online{Bund_arXIv1911.00267, TITLE = {Optimal Metastability-Containing Sorting via Parallel Prefix Computation}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1911.00267}, EPRINT = {1911.00267}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Friedrichs et al. (TC 2018) showed that metastability can be contained when sorting inputs arising from time-to-digital converters, i.e., measurement values can be correctly sorted without resolving metastability using synchronizers first. However, this work left open whether this can be done by small circuits. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Our solution utilizes the parallel prefix computation (PPC) framework (JACM 1980). We improve this construction by bounding its fan-out by an arbitrary $f \geq 3$, without affecting depth and increasing circuit size by a small constant factor only. Thus, we obtain the first PPC circuits with asymptotically optimal size, constant fan-out, and optimal depth. To show that applying the PPC framework to the sorting task is feasible, we prove that the latter can, despite potential metastability, be decomposed such that the core operation is associative. We obtain asymptotically optimal metastability-containing sorting networks. We complement these results with simulations, independently verifying the correctness as well as small size and delay of our circuits.}, }
Endnote
%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-Containing Sorting via Parallel Prefix Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1C6B-5 %U http://arxiv.org/abs/1911.00267 %D 2019 %X Friedrichs et al. (TC 2018) showed that metastability can be contained when sorting inputs arising from time-to-digital converters, i.e., measurement values can be correctly sorted without resolving metastability using synchronizers first. However, this work left open whether this can be done by small circuits. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Our solution utilizes the parallel prefix computation (PPC) framework (JACM 1980). We improve this construction by bounding its fan-out by an arbitrary $f \geq 3$, without affecting depth and increasing circuit size by a small constant factor only. Thus, we obtain the first PPC circuits with asymptotically optimal size, constant fan-out, and optimal depth. To show that applying the PPC framework to the sorting task is feasible, we prove that the latter can, despite potential metastability, be decomposed such that the core operation is associative. We obtain asymptotically optimal metastability-containing sorting networks. We complement these results with simulations, independently verifying the correctness as well as small size and delay of our circuits. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Architecture, cs.AR
[97]
J. Bund, C. Lenzen, and W. Rosenbaum, “Fault Tolerant Gradient Clock Synchronization,” in PODC’19, ACM Symposium on Principles of Distributed Computing, Toronto, Canada, 2019.
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@inproceedings{Bund_PODC2019, TITLE = {Fault Tolerant Gradient Clock Synchronization}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Rosenbaum, Will}, LANGUAGE = {eng}, ISBN = {978-1-4503-6217-7}, DOI = {10.1145/3293611.3331637}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {PODC'19, ACM Symposium on Principles of Distributed Computing}, PAGES = {357--365}, ADDRESS = {Toronto, Canada}, }
Endnote
%0 Conference Proceedings %A Bund, Johannes %A Lenzen, Christoph %A Rosenbaum, Will %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fault Tolerant Gradient Clock Synchronization : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1BE3-D %R 10.1145/3293611.3331637 %D 2019 %B ACM Symposium on Principles of Distributed Computing %Z date of event: 2019-07-29 - 2019-08-02 %C Toronto, Canada %B PODC'19 %P 357 - 365 %I ACM %@ 978-1-4503-6217-7
[98]
J. Bund, C. Lenzen, and W. Rosenbaum, “Fault Tolerant Gradient Clock Synchronization,” 2019. [Online]. Available: http://arxiv.org/abs/1902.08042. (arXiv: 1902.08042)
Abstract
Synchronizing clocks in distributed systems is well-understood, both in terms of fault-tolerance in fully connected systems and the dependence of local and global worst-case skews (i.e., maximum clock difference between neighbors and arbitrary pairs of nodes, respectively) on the diameter of fault-free systems. However, so far nothing non-trivial is known about the local skew that can be achieved in topologies that are not fully connected even under a single Byzantine fault. Put simply, in this work we show that the most powerful known techniques for fault-tolerant and gradient clock synchronization are compatible, in the sense that the best of both worlds can be achieved simultaneously. Concretely, we combine the Lynch-Welch algorithm [Welch1988] for synchronizing a clique of $n$ nodes despite up to $f<n/3$ Byzantine faults with the gradient clock synchronization (GCS) algorithm by Lenzen et al. [Lenzen2010] in order to render the latter resilient to faults. As this is not possible on general graphs, we augment an input graph $\mathcal{G}$ by replacing each node by $3f+1$ fully connected copies, which execute an instance of the Lynch-Welch algorithm. We then interpret these clusters as supernodes executing the GCS algorithm, where for each cluster its correct nodes' Lynch-Welch clocks provide estimates of the logical clock of the supernode in the GCS algorithm. By connecting clusters corresponding to neighbors in $\mathcal{G}$ in a fully bipartite manner, supernodes can inform each other about (estimates of) their logical clock values. This way, we achieve asymptotically optimal local skew, granted that no cluster contains more than $f$ faulty nodes, at factor $O(f)$ and $O(f^2)$ overheads in terms of nodes and edges, respectively. Note that tolerating $f$ faulty neighbors trivially requires degree larger than $f$, so this is asymptotically optimal as well.
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@online{Bund_arXiv1902.08042, TITLE = {Fault Tolerant Gradient Clock Synchronization}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Rosenbaum, Will}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1902.08042}, EPRINT = {1902.08042}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Synchronizing clocks in distributed systems is well-understood, both in terms of fault-tolerance in fully connected systems and the dependence of local and global worst-case skews (i.e., maximum clock difference between neighbors and arbitrary pairs of nodes, respectively) on the diameter of fault-free systems. However, so far nothing non-trivial is known about the local skew that can be achieved in topologies that are not fully connected even under a single Byzantine fault. Put simply, in this work we show that the most powerful known techniques for fault-tolerant and gradient clock synchronization are compatible, in the sense that the best of both worlds can be achieved simultaneously. Concretely, we combine the Lynch-Welch algorithm [Welch1988] for synchronizing a clique of $n$ nodes despite up to $f<n/3$ Byzantine faults with the gradient clock synchronization (GCS) algorithm by Lenzen et al. [Lenzen2010] in order to render the latter resilient to faults. As this is not possible on general graphs, we augment an input graph $\mathcal{G}$ by replacing each node by $3f+1$ fully connected copies, which execute an instance of the Lynch-Welch algorithm. We then interpret these clusters as supernodes executing the GCS algorithm, where for each cluster its correct nodes' Lynch-Welch clocks provide estimates of the logical clock of the supernode in the GCS algorithm. By connecting clusters corresponding to neighbors in $\mathcal{G}$ in a fully bipartite manner, supernodes can inform each other about (estimates of) their logical clock values. This way, we achieve asymptotically optimal local skew, granted that no cluster contains more than $f$ faulty nodes, at factor $O(f)$ and $O(f^2)$ overheads in terms of nodes and edges, respectively. Note that tolerating $f$ faulty neighbors trivially requires degree larger than $f$, so this is asymptotically optimal as well.}, }
Endnote
%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Rosenbaum, Will %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fault Tolerant Gradient Clock Synchronization : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0CD6-F %U http://arxiv.org/abs/1902.08042 %D 2019 %X Synchronizing clocks in distributed systems is well-understood, both in terms of fault-tolerance in fully connected systems and the dependence of local and global worst-case skews (i.e., maximum clock difference between neighbors and arbitrary pairs of nodes, respectively) on the diameter of fault-free systems. However, so far nothing non-trivial is known about the local skew that can be achieved in topologies that are not fully connected even under a single Byzantine fault. Put simply, in this work we show that the most powerful known techniques for fault-tolerant and gradient clock synchronization are compatible, in the sense that the best of both worlds can be achieved simultaneously. Concretely, we combine the Lynch-Welch algorithm [Welch1988] for synchronizing a clique of $n$ nodes despite up to $f<n/3$ Byzantine faults with the gradient clock synchronization (GCS) algorithm by Lenzen et al. [Lenzen2010] in order to render the latter resilient to faults. As this is not possible on general graphs, we augment an input graph $\mathcal{G}$ by replacing each node by $3f+1$ fully connected copies, which execute an instance of the Lynch-Welch algorithm. We then interpret these clusters as supernodes executing the GCS algorithm, where for each cluster its correct nodes' Lynch-Welch clocks provide estimates of the logical clock of the supernode in the GCS algorithm. By connecting clusters corresponding to neighbors in $\mathcal{G}$ in a fully bipartite manner, supernodes can inform each other about (estimates of) their logical clock values. This way, we achieve asymptotically optimal local skew, granted that no cluster contains more than $f$ faulty nodes, at factor $O(f)$ and $O(f^2)$ overheads in terms of nodes and edges, respectively. Note that tolerating $f$ faulty neighbors trivially requires degree larger than $f$, so this is asymptotically optimal as well. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Data Structures and Algorithms, cs.DS
[99]
P. Bürgisser, C. Ikenmeyer, and G. Panova, “No Occurrence Obstructions in Geometric Complexity Theory,” Journal of the American Mathematical Society, vol. 32, 2019.
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@article{Buergisser2019, TITLE = {No Occurrence Obstructions in Geometric Complexity Theory}, AUTHOR = {B{\"u}rgisser, Peter and Ikenmeyer, Christian and Panova, Greta}, LANGUAGE = {eng}, ISSN = {0894-0347}, DOI = {10.1090/jams/908}, PUBLISHER = {The Society}, ADDRESS = {Providence, R.I.}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Journal of the American Mathematical Society}, VOLUME = {32}, PAGES = {163--193}, }
Endnote
%0 Journal Article %A B&#252;rgisser, Peter %A Ikenmeyer, Christian %A Panova, Greta %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T No Occurrence Obstructions in Geometric Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0002-72B9-D %R 10.1090/jams/908 %7 2018 %D 2019 %J Journal of the American Mathematical Society %O J. Amer. Math. Soc. %V 32 %& 163 %P 163 - 193 %I The Society %C Providence, R.I. %@ false
[100]
P. Chalermsook, A. Schmid, and S. Uniyal, “A Tight Extremal Bound on the Lovász Cactus Number in Planar Graphs,” in 36th Symposium on Theoretical Aspects of Computer Science (STACS 2019), Berlin, Germany, 2019.
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@inproceedings{Chalermsook_STACS2019, TITLE = {A Tight Extremal Bound on the {Lov\'{a}sz} Cactus Number in Planar Graphs}, AUTHOR = {Chalermsook, Parinya and Schmid, Andreas and Uniyal, Sumedha}, LANGUAGE = {eng}, ISBN = {978-3-95977-100-9}, DOI = {10.4230/LIPIcs.STACS.2019.19}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {36th Symposium on Theoretical Aspects of Computer Science (STACS 2019)}, EDITOR = {Niedermeier, Rolf and Paul, Christophe}, PAGES = {1--14}, EID = {19}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {126}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Chalermsook, Parinya %A Schmid, Andreas %A Uniyal, Sumedha %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Tight Extremal Bound on the Lov&#225;sz Cactus Number in Planar Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5D6-A %R 10.4230/LIPIcs.STACS.2019.19 %D 2019 %B 36th Symposium on Theoretical Aspects of Computer Science %Z date of event: 2019-03-13 - 2019-03-16 %C Berlin, Germany %B 36th Symposium on Theoretical Aspects of Computer Science %E Niedermeier, Rolf; Paul, Christophe %P 1 - 14 %Z sequence number: 19 %I Schloss Dagstuhl %@ 978-3-95977-100-9 %B Leibniz International Proceedings in Informatics %N 126 %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2019/10258/
[101]
L. S. Chandran, D. Issac, and S. Zhou, “Hadwiger’s Conjecture for Squares of 2-Trees,” European Journal of Combinatorics, vol. 76, 2019.
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@article{CHANDRAN2019hadwiger, TITLE = {Hadwiger's Conjecture for Squares of 2-Trees}, AUTHOR = {Chandran, L. Sunil and Issac, Davis and Zhou, Sanming}, LANGUAGE = {eng}, ISSN = {0195-6698}, DOI = {10.1016/j.ejc.2018.10.003}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {European Journal of Combinatorics}, VOLUME = {76}, PAGES = {159--174}, }
Endnote
%0 Journal Article %A Chandran, L. Sunil %A Issac, Davis %A Zhou, Sanming %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Hadwiger's Conjecture for Squares of 2-Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E5B-7 %R 10.1016/j.ejc.2018.10.003 %7 2018 %D 2019 %J European Journal of Combinatorics %V 76 %& 159 %P 159 - 174 %I Elsevier %C Amsterdam %@ false
[102]
L. Chen, F. Eberle, N. Megow, K. Schewior, and C. Stein, “A General Framework for Handling Commitment in Online Admission Control,” in Integer Programming and Combinatorial Optimization (IPCO 2019), Ann Arbor, MI, USA. (Accepted/in press)
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@inproceedings{SchewiorIPCO2019, TITLE = {A General Framework for Handling Commitment in Online Admission Control}, AUTHOR = {Chen, Lin and Eberle, Franziska and Megow, Nicole and Schewior, Kevin and Stein, Clifford}, LANGUAGE = {eng}, PUBLISHER = {Springer}, YEAR = {2019}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Integer Programming and Combinatorial Optimization (IPCO 2019)}, ADDRESS = {Ann Arbor, MI, USA}, }
Endnote
%0 Conference Proceedings %A Chen, Lin %A Eberle, Franziska %A Megow, Nicole %A Schewior, Kevin %A Stein, Clifford %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A General Framework for Handling Commitment in Online Admission Control : %G eng %U http://hdl.handle.net/21.11116/0000-0002-F4CC-5 %D 2019 %B 20th Conference on Integer Programming and Combinatorial Optimization %Z date of event: 2019-05-22 - 2019-05-24 %C Ann Arbor, MI, USA %B Integer Programming and Combinatorial Optimization %I Springer
[103]
N. Chen, M. Hoefer, M. Künnemann, C. Lin, and P. Miao, “Secretary Markets with Local Information,” Distributed Computing, vol. 32, no. 5, 2019.
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@article{Chen2018, TITLE = {Secretary Markets with Local Information}, AUTHOR = {Chen, Ning and Hoefer, Martin and K{\"u}nnemann, Marvin and Lin, Chengyu and Miao, Peihan}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-018-0327-5}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Distributed Computing}, VOLUME = {32}, NUMBER = {5}, PAGES = {361--378}, }
Endnote
%0 Journal Article %A Chen, Ning %A Hoefer, Martin %A K&#252;nnemann, Marvin %A Lin, Chengyu %A Miao, Peihan %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Secretary Markets with Local Information : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A90C-3 %R 10.1007/s00446-018-0327-5 %7 2019 %D 2019 %J Distributed Computing %V 32 %N 5 %& 361 %P 361 - 378 %I Springer International %C Berlin %@ false
[104]
Y. K. Cheung, M. Hoefer, and P. Nakhe, “Tracing Equilibrium in Dynamic Markets via Distributed Adaptation,” in AAMAS’19, 18th International Conference on Autonomous Agents and Multiagent Systems, Montreal, Canada, 2019.
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@inproceedings{aamas19-CHN, TITLE = {Tracing Equilibrium in Dynamic Markets via Distributed Adaptation}, AUTHOR = {Cheung, Yun Kuen and Hoefer, Martin and Nakhe, Paresh}, LANGUAGE = {eng}, ISBN = {978-1-4503-6309-9}, URL = {http://dl.acm.org/citation.cfm?id=3306127.3331825}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {AAMAS'19, 18th International Conference on Autonomous Agents and Multiagent Systems}, PAGES = {1225--1233}, ADDRESS = {Montreal, Canada}, }
Endnote
%0 Conference Proceedings %A Cheung, Yun Kuen %A Hoefer, Martin %A Nakhe, Paresh %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Tracing Equilibrium in Dynamic Markets via Distributed Adaptation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5FE-E %U http://dl.acm.org/citation.cfm?id=3306127.3331825 %D 2019 %B 18th International Conference on Autonomous Agents and Multiagent Systems %Z date of event: 2019-05-13 - 2019-05-17 %C Montreal, Canada %B AAMAS'19 %P 1225 - 1233 %I ACM %@ 978-1-4503-6309-9
[105]
L. Chiantini, C. Ikenmeyer, J. M. Landsberg, and G. Ottaviani, “The Geometry of Rank Decompositions of Matrix Multiplication I: 2x2 Matrices,” Experimental Mathematics, vol. 28, no. 3, 2019.
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@article{Chiantini2017, TITLE = {The geometry of rank decompositions of matrix multiplication I: $2\times 2$ matrices}, AUTHOR = {Chiantini, Luca and Ikenmeyer, Christian and Landsberg, J. M. and Ottaviani, Giorgio}, LANGUAGE = {eng}, ISSN = {1058-6458}, DOI = {10.1080/10586458.2017.1403981}, PUBLISHER = {Taylor \& Francis}, ADDRESS = {Boston, MA}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Experimental Mathematics}, VOLUME = {28}, NUMBER = {3}, PAGES = {322--327}, }
Endnote
%0 Journal Article %A Chiantini, Luca %A Ikenmeyer, Christian %A Landsberg, J. M. %A Ottaviani, Giorgio %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The Geometry of Rank Decompositions of Matrix Multiplication I: 2x2 Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AB12-9 %R 10.1080/10586458.2017.1403981 %7 2017 %D 2019 %J Experimental Mathematics %V 28 %N 3 %& 322 %P 322 - 327 %I Taylor & Francis %C Boston, MA %@ false
[106]
A. Choudhary, M. Kerber, and S. Raghvendra, “Polynomial-Sized Topological Approximations Using the Permutahedron,” Discrete & Computational Geometry, vol. 61, no. 1, 2019.
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@article{Choudhary-polynomial-dcg, TITLE = {Polynomial-Sized Topological Approximations Using the Permutahedron}, AUTHOR = {Choudhary, Aruni and Kerber, Michael and Raghvendra, Sharat}, LANGUAGE = {eng}, ISSN = {0179-5376}, DOI = {10.1007/s00454-017-9951-2}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Discrete \& Computational Geometry}, VOLUME = {61}, NUMBER = {1}, PAGES = {42--80}, }
Endnote
%0 Journal Article %A Choudhary, Aruni %A Kerber, Michael %A Raghvendra, Sharat %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Polynomial-Sized Topological Approximations Using the Permutahedron : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5B6-E %R 10.1007/s00454-017-9951-2 %7 2017 %D 2019 %J Discrete & Computational Geometry %V 61 %N 1 %& 42 %P 42 - 80 %I Springer %C New York, NY %@ false
[107]
A. Choudhary, M. Kerber, and S. Raghvendra, “Improved Topological Approximations by Digitization,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Choudhary-digital, TITLE = {Improved Topological Approximations by Digitization}, AUTHOR = {Choudhary, Aruni and Kerber, Michael and Raghvendra, Sharath}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.166}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {2675--2688}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Choudhary, Aruni %A Kerber, Michael %A Raghvendra, Sharath %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Improved Topological Approximations by Digitization : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5BC-8 %R 10.1137/1.9781611975482.166 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 2675 - 2688 %I SIAM %@ 978-1-61197-548-2
[108]
A. Choudhary and A. Ghosh, “Delaunay Simplices in Diagonally Distorted Lattices,” Computational Geometry: Theory and Applications. (Accepted/in press)
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@article{Choudhary-diagonal, TITLE = {Delaunay Simplices in Diagonally Distorted Lattices}, AUTHOR = {Choudhary, Aruni and Ghosh, Arijit}, LANGUAGE = {eng}, ISSN = {0925-7721}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, JOURNAL = {Computational Geometry: Theory and Applications}, }
Endnote
%0 Journal Article %A Choudhary, Aruni %A Ghosh, Arijit %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Delaunay Simplices in Diagonally Distorted Lattices : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5C1-1 %D 2019 %J Computational Geometry: Theory and Applications %I Elsevier %C Amsterdam %@ false
[109]
G. Christodoulou and A. Sgouritsa, “Designing Networks with Good Equilibria under Uncertainty,” SIAM Journal on Computing, vol. 48, no. 4, 2019.
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@article{Christodoulou2019SICOMP, TITLE = {Designing Networks with Good Equilibria under Uncertainty}, AUTHOR = {Christodoulou, George and Sgouritsa, Alkmini}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/16M1096694}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {48}, NUMBER = {4}, PAGES = {1364--1396}, }
Endnote
%0 Journal Article %A Christodoulou, George %A Sgouritsa, Alkmini %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Designing Networks with Good Equilibria under Uncertainty : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AEC7-A %R 10.1137/16M1096694 %7 2019 %D 2019 %J SIAM Journal on Computing %V 48 %N 4 %& 1364 %P 1364 - 1396 %I SIAM %C Philadelphia, PA %@ false
[110]
J. Correa, P. Foncea, R. Hoeksma, T. Oosterwijk, and T. Vredeveld, “Recent Developments in Prophet Inequalities,” ACM SIGecom Exchanges, vol. 17, no. 1, 2019.
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@article{Correa2018, TITLE = {Recent Developments in Prophet Inequalities}, AUTHOR = {Correa, Jos{\'e} and Foncea, Patricio and Hoeksma, Ruben and Oosterwijk, Tim and Vredeveld, Tjark}, LANGUAGE = {eng}, ISSN = {1551-9031}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM SIGecom Exchanges}, VOLUME = {17}, NUMBER = {1}, PAGES = {60--61}, }
Endnote
%0 Journal Article %A Correa, Jos&#233; %A Foncea, Patricio %A Hoeksma, Ruben %A Oosterwijk, Tim %A Vredeveld, Tjark %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Recent Developments in Prophet Inequalities : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E6F-1 %7 2019 %D 2019 %J ACM SIGecom Exchanges %V 17 %N 1 %& 60 %P 60 - 61 %I ACM %C New York, NY %@ false %U http://www.sigecom.org/exchanges/volume_17/1/CORREA.pdf
[111]
E. Cruciani, E. Natale, and G. Scornavacca, “Distributed Community Detection via Metastability of the 2-Choices Dynamics,” in Thirty-Third AAAI Conference on Artificial Intelligence, Honolulu, HI, USA, 2019.
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@inproceedings{Cruciani_aaai18, TITLE = {Distributed Community Detection via Metastability of the 2-Choices Dynamics}, AUTHOR = {Cruciani, Emilio and Natale, Emanuele and Scornavacca, Giacomo}, LANGUAGE = {eng}, ISBN = {978-1-57735-809-1}, DOI = {10.1609/aaai.v33i01.33016046}, PUBLISHER = {AAAI}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Thirty-Third AAAI Conference on Artificial Intelligence}, PAGES = {6046--6053}, ADDRESS = {Honolulu, HI, USA}, }
Endnote
%0 Conference Proceedings %A Cruciani, Emilio %A Natale, Emanuele %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Distributed Community Detection via Metastability of the 2-Choices Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A985-9 %R 10.1609/aaai.v33i01.33016046 %D 2019 %B Thirty-Third AAAI Conference on Artificial Intelligence %Z date of event: 2019-01-27 - 2019-02-01 %C Honolulu, HI, USA %B Thirty-Third AAAI Conference on Artificial Intelligence %P 6046 - 6053 %I AAAI %@ 978-1-57735-809-1
[112]
O. Daescu, S. Friedrichs, H. Malik, V. Polishchuk, and C. Schmidt, “Altitude Terrain Guarding and Guarding Uni-monotone Polygons,” Computational Geometry: Theory and Applications, vol. 84, 2019.
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@article{Daescu2019, TITLE = {Altitude Terrain Guarding and Guarding Uni-monotone Polygons}, AUTHOR = {Daescu, Ovidiu and Friedrichs, Stephan and Malik, Hemant and Polishchuk, Valentin and Schmidt, Christiane}, LANGUAGE = {eng}, ISSN = {0925-7721}, DOI = {10.1016/j.comgeo.2019.07.004}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Computational Geometry: Theory and Applications}, VOLUME = {84}, PAGES = {22--35}, }
Endnote
%0 Journal Article %A Daescu, Ovidiu %A Friedrichs, Stephan %A Malik, Hemant %A Polishchuk, Valentin %A Schmidt, Christiane %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Altitude Terrain Guarding and Guarding Uni-monotone Polygons : %G eng %U http://hdl.handle.net/21.11116/0000-0004-E572-9 %R 10.1016/j.comgeo.2019.07.004 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 84 %& 22 %P 22 - 35 %I Elsevier %C Amsterdam %@ false
[113]
H. Dell, M. Roth, and P. Wellnitz, “Counting Answers to Existential Questions,” in 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), Patras, Greece, 2019.
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@inproceedings{Dell_ICALP2019, TITLE = {Counting Answers to Existential Questions}, AUTHOR = {Dell, Holger and Roth, Marc and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-3-95977-109-2}, URL = {urn:nbn:de:0030-drops-106894}, DOI = {10.4230/LIPIcs.ICALP.2019.113}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, EDITOR = {Baier, Christel and Chaztigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, EID = {113}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {132}, ADDRESS = {Patras, Greece}, }
Endnote
%0 Conference Proceedings %A Dell, Holger %A Roth, Marc %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Answers to Existential Questions : %G eng %U http://hdl.handle.net/21.11116/0000-0005-8653-6 %R 10.4230/LIPIcs.ICALP.2019.113 %U urn:nbn:de:0030-drops-106894 %D 2019 %B 46th International Colloquium on Automata, Languages, and Programming %Z date of event: 2019-07-09 - 2019-07-12 %C Patras, Greece %B 46th International Colloquium on Automata, Languages, and Programming %E Baier, Christel; Chaztigiannakis, Ioannis; Flocchini, Paola; Leonardi, Stefano %Z sequence number: 113 %I Schloss Dagstuhl %@ 978-3-95977-109-2 %B Leibniz International Proceedings in Informatics %N 132 %U https://doi.org/10.4230/LIPIcs.ICALP.2019.113https://drops.dagstuhl.de/doku/urheberrecht1.html
[114]
J. Dörfler, M. Roth, J. Schmitt, and P. Wellnitz, “Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness,” in 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019), Aachen, Germany, 2019.
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@inproceedings{Doefler_MFCS, TITLE = {Counting Induced Subgraphs: An Algebraic Approach to \#W[1]-hardness}, AUTHOR = {D{\"o}rfler, Julian and Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-117-7}, URL = {urn:nbn:de:0030-drops-109703}, DOI = {10.4230/LIPIcs.MFCS.2019.26}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, EDITOR = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, EID = {26}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {138}, ADDRESS = {Aachen, Germany}, }
Endnote
%0 Conference Proceedings %A D&#246;rfler, Julian %A Roth, Marc %A Schmitt, Johannes %A Wellnitz, Philip %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness : %G eng %U http://hdl.handle.net/21.11116/0000-0005-85DB-E %R 10.4230/LIPIcs.MFCS.2019.26 %U urn:nbn:de:0030-drops-109703 %D 2019 %B 44th International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2019-08-26 - 2019-08-30 %C Aachen, Germany %B 44th International Symposium on Mathematical Foundations of Computer Science %E Rossmanith, Peter; Heggernes, Pinar; Katoen, Joost-Pieter %Z sequence number: 26 %I Schloss Dagstuhl %@ 978-3-95977-117-7 %B Leibniz International Proceedings in Informatics %N 138 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10970/https://drops.dagstuhl.de/doku/urheberrecht1.html
[115]
J. Dörfler, C. Ikenmeyer, and G. Panova, “On Geometric Complexity Theory: Multiplicity Obstructions are Stronger than Occurrence Obstructions,” 2019. [Online]. Available: http://arxiv.org/abs/1901.04576. (arXiv: 1901.04576)
Abstract
Geometric Complexity Theory as initiated by Mulmuley and Sohoni in two papers (SIAM J Comput 2001, 2008) aims to separate algebraic complexity classes via representation theoretic multiplicities in coordinate rings of specific group varieties. The papers also conjecture that the vanishing behavior of these multiplicities would be sufficient to separate complexity classes (so-called occurrence obstructions). The existence of such strong occurrence obstructions has been recently disproven in 2016 in two successive papers, Ikenmeyer-Panova (Adv. Math.) and B\"urgisser-Ikenmeyer-Panova (J. AMS). This raises the question whether separating group varieties via representation theoretic multiplicities is stronger than separating them via occurrences. This paper provides for the first time a setting where separating with multiplicities can be achieved, while the separation with occurrences is provably impossible. Our setting is surprisingly simple and natural: We study the variety of products of homogeneous linear forms (the so-called Chow variety) and the variety of polynomials of bounded border Waring rank (i.e. a higher secant variety of the Veronese variety). As a side result we prove a slight generalization of Hermite's reciprocity theorem, which proves Foulkes' conjecture for a new infinite family of cases.
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@online{Doerfler_arXiv1901.04576, TITLE = {On Geometric Complexity Theory: {M}ultiplicity Obstructions are Stronger than Occurrence Obstructions}, AUTHOR = {D{\"o}rfler, Julian and Ikenmeyer, Christian and Panova, Greta}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1901.04576}, EPRINT = {1901.04576}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Geometric Complexity Theory as initiated by Mulmuley and Sohoni in two papers (SIAM J Comput 2001, 2008) aims to separate algebraic complexity classes via representation theoretic multiplicities in coordinate rings of specific group varieties. The papers also conjecture that the vanishing behavior of these multiplicities would be sufficient to separate complexity classes (so-called occurrence obstructions). The existence of such strong occurrence obstructions has been recently disproven in 2016 in two successive papers, Ikenmeyer-Panova (Adv. Math.) and B\"urgisser-Ikenmeyer-Panova (J. AMS). This raises the question whether separating group varieties via representation theoretic multiplicities is stronger than separating them via occurrences. This paper provides for the first time a setting where separating with multiplicities can be achieved, while the separation with occurrences is provably impossible. Our setting is surprisingly simple and natural: We study the variety of products of homogeneous linear forms (the so-called Chow variety) and the variety of polynomials of bounded border Waring rank (i.e. a higher secant variety of the Veronese variety). As a side result we prove a slight generalization of Hermite's reciprocity theorem, which proves Foulkes' conjecture for a new infinite family of cases.}, }
Endnote
%0 Report %A D&#246;rfler, Julian %A Ikenmeyer, Christian %A Panova, Greta %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Geometric Complexity Theory: Multiplicity Obstructions are Stronger than Occurrence Obstructions : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B393-C %U http://arxiv.org/abs/1901.04576 %D 2019 %X Geometric Complexity Theory as initiated by Mulmuley and Sohoni in two papers (SIAM J Comput 2001, 2008) aims to separate algebraic complexity classes via representation theoretic multiplicities in coordinate rings of specific group varieties. The papers also conjecture that the vanishing behavior of these multiplicities would be sufficient to separate complexity classes (so-called occurrence obstructions). The existence of such strong occurrence obstructions has been recently disproven in 2016 in two successive papers, Ikenmeyer-Panova (Adv. Math.) and B\"urgisser-Ikenmeyer-Panova (J. AMS). This raises the question whether separating group varieties via representation theoretic multiplicities is stronger than separating them via occurrences. This paper provides for the first time a setting where separating with multiplicities can be achieved, while the separation with occurrences is provably impossible. Our setting is surprisingly simple and natural: We study the variety of products of homogeneous linear forms (the so-called Chow variety) and the variety of polynomials of bounded border Waring rank (i.e. a higher secant variety of the Veronese variety). As a side result we prove a slight generalization of Hermite's reciprocity theorem, which proves Foulkes' conjecture for a new infinite family of cases. %K Computer Science, Computational Complexity, cs.CC,Mathematics, Algebraic Geometry, math.AG,Mathematics, Combinatorics, math.CO,Mathematics, Representation Theory, math.RT,
[116]
L. Duraj, M. Künnemann, and A. Polak, “Tight Conditional Lower Bounds for Longest Common Increasing Subsequence,” Algorithmica, vol. 81, no. 10, 2019.
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@article{Duraj2018, TITLE = {Tight Conditional Lower Bounds for Longest Common Increasing Subsequence}, AUTHOR = {Duraj, Lech and K{\"u}nnemann, Marvin and Polak, Adam}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-018-0485-7}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Algorithmica}, VOLUME = {81}, NUMBER = {10}, PAGES = {3968--3992}, }
Endnote
%0 Journal Article %A Duraj, Lech %A K&#252;nnemann, Marvin %A Polak, Adam %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Tight Conditional Lower Bounds for Longest Common Increasing Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A906-9 %R 10.1007/s00453-018-0485-7 %7 2018 %D 2019 %J Algorithmica %V 81 %N 10 %& 3968 %P 3968 - 3992 %I Springer %C New York, NY %@ false
[117]
T. Eden, D. Ron, and W. Rosenbaum, “The Arboricity Captures the Complexity of Sampling Edges,” 2019. [Online]. Available: http://arxiv.org/abs/1902.08086. (arXiv: 1902.08086)
Abstract
In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $\alpha$, we design an algorithm that performs $O\!\left(\frac{\alpha}{d} \cdot \frac{\log^3 n}{\varepsilon}\right)$ queries in expectation and returns an edge in the graph such that every edge $e \in E$ is sampled with probability $(1 \pm \varepsilon)/m$. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in $\varepsilon$), as $\Omega\!\left(\frac{\alpha}{d} \right)$ queries are necessary for the easier task of sampling edges from any distribution over $E$ that is close to uniform in total variational distance. We also prove that even if $G$ is a tree (i.e., $\alpha = 1$ so that $\frac{\alpha}{d}=\Theta(1)$), $\Omega\left(\frac{\log n}{\log\log n}\right)$ queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a $\mathrm{poly}(\log n)$ factor is necessary for constant $\alpha$. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019).
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@online{Eden_arXiv1902.08086, TITLE = {The Arboricity Captures the Complexity of Sampling Edges}, AUTHOR = {Eden, Talya and Ron, Dana and Rosenbaum, Will}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1902.08086}, EPRINT = {1902.08086}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $\alpha$, we design an algorithm that performs $O\!\left(\frac{\alpha}{d} \cdot \frac{\log^3 n}{\varepsilon}\right)$ queries in expectation and returns an edge in the graph such that every edge $e \in E$ is sampled with probability $(1 \pm \varepsilon)/m$. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in $\varepsilon$), as $\Omega\!\left(\frac{\alpha}{d} \right)$ queries are necessary for the easier task of sampling edges from any distribution over $E$ that is close to uniform in total variational distance. We also prove that even if $G$ is a tree (i.e., $\alpha = 1$ so that $\frac{\alpha}{d}=\Theta(1)$), $\Omega\left(\frac{\log n}{\log\log n}\right)$ queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a $\mathrm{poly}(\log n)$ factor is necessary for constant $\alpha$. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019).}, }
Endnote
%0 Report %A Eden, Talya %A Ron, Dana %A Rosenbaum, Will %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T The Arboricity Captures the Complexity of Sampling Edges : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0CD0-5 %U http://arxiv.org/abs/1902.08086 %D 2019 %X In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $\alpha$, we design an algorithm that performs $O\!\left(\frac{\alpha}{d} \cdot \frac{\log^3 n}{\varepsilon}\right)$ queries in expectation and returns an edge in the graph such that every edge $e \in E$ is sampled with probability $(1 \pm \varepsilon)/m$. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in $\varepsilon$), as $\Omega\!\left(\frac{\alpha}{d} \right)$ queries are necessary for the easier task of sampling edges from any distribution over $E$ that is close to uniform in total variational distance. We also prove that even if $G$ is a tree (i.e., $\alpha = 1$ so that $\frac{\alpha}{d}=\Theta(1)$), $\Omega\left(\frac{\log n}{\log\log n}\right)$ queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a $\mathrm{poly}(\log n)$ factor is necessary for constant $\alpha$. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019). %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[118]
E. Facca, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Directed Physarum Model,” 2019. [Online]. Available: http://arxiv.org/abs/1906.07781. (arXiv: 1906.07781)
Abstract
The directed Physarum dynamics is known to solve positive linear programs: minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector $c$. The directed Physarum dynamics evolves a positive vector $x$ according to the dynamics $\dot{x} = q(x) - x$. Here $q(x)$ is the solution to $Af = b$ that minimizes the "energy" $\sum_i c_i f_i^2/x_i$. In this paper, we study the non-uniform directed dynamics $\dot{x} = D(q(x) - x)$, where $D$ is a positive diagonal matrix. The non-uniform dynamics is more complex than the uniform dynamics (with $D$ being the identity matrix), as it allows each component of $x$ to react with different speed to the differences between $q(x)$ and $x$. Our contribution is to show that the non-uniform directed dynamics solves positive linear programs.
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@online{Facca_arXiv1906.07781, TITLE = {Convergence of the Non-Uniform Directed Physarum Model}, AUTHOR = {Facca, Enrico and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1906.07781}, EPRINT = {1906.07781}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The directed Physarum dynamics is known to solve positive linear programs: minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector $c$. The directed Physarum dynamics evolves a positive vector $x$ according to the dynamics $\dot{x} = q(x) -- x$. Here $q(x)$ is the solution to $Af = b$ that minimizes the "energy" $\sum_i c_i f_i^2/x_i$. In this paper, we study the non-uniform directed dynamics $\dot{x} = D(q(x) - x)$, where $D$ is a positive diagonal matrix. The non-uniform dynamics is more complex than the uniform dynamics (with $D$ being the identity matrix), as it allows each component of $x$ to react with different speed to the differences between $q(x)$ and $x$. Our contribution is to show that the non-uniform directed dynamics solves positive linear programs.}, }
Endnote
%0 Report %A Facca, Enrico %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Convergence of the Non-Uniform Directed Physarum Model : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1DBA-A %U http://arxiv.org/abs/1906.07781 %D 2019 %X The directed Physarum dynamics is known to solve positive linear programs: minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector $c$. The directed Physarum dynamics evolves a positive vector $x$ according to the dynamics $\dot{x} = q(x) - x$. Here $q(x)$ is the solution to $Af = b$ that minimizes the "energy" $\sum_i c_i f_i^2/x_i$. In this paper, we study the non-uniform directed dynamics $\dot{x} = D(q(x) - x)$, where $D$ is a positive diagonal matrix. The non-uniform dynamics is more complex than the uniform dynamics (with $D$ being the identity matrix), as it allows each component of $x$ to react with different speed to the differences between $q(x)$ and $x$. Our contribution is to show that the non-uniform directed dynamics solves positive linear programs. %K Mathematics, Dynamical Systems, math.DS,Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Optimization and Control, math.OC
[119]
P. Fraigniaud and E. Natale, “Noisy Rumor Spreading and Plurality Consensus,” Distributed Computing, vol. 32, no. 4, 2019.
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@article{Fraigniaud2018, TITLE = {Noisy Rumor Spreading and Plurality Consensus}, AUTHOR = {Fraigniaud, Pierre and Natale, Emanuele}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-018-0335-5}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Distributed Computing}, VOLUME = {32}, NUMBER = {4}, PAGES = {257--276}, }
Endnote
%0 Journal Article %A Fraigniaud, Pierre %A Natale, Emanuele %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Noisy Rumor Spreading and Plurality Consensus : %G eng %U http://hdl.handle.net/21.11116/0000-0002-6CD7-3 %R 10.1007/s00446-018-0335-5 %7 2018 %D 2019 %J Distributed Computing %V 32 %N 4 %& 257 %P 257 - 276 %I Springer International %C Berlin %@ false
[120]
S. Funke, T. Rupp, A. Nusser, and S. Storandt, “PATHFINDER: Storage and Indexing of Massive Trajectory Sets,” in SSTD’19, 16th International Symposium onSpatial and Temporal Databases, Vienna, Austria, 2019.
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@inproceedings{Funke_SSTD2019, TITLE = {PATHFINDER: {S}torage and Indexing of Massive Trajectory Sets}, AUTHOR = {Funke, Stefan and Rupp, Tobias and Nusser, Andr{\'e} and Storandt, Sabine}, LANGUAGE = {eng}, ISBN = {978-1-4503-6280-1}, DOI = {10.1145/3340964.3340978}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {SSTD'19, 16th International Symposium onSpatial and Temporal Databases}, EDITOR = {Aref, Walid G. and Bertolotto, Michela and Bouros, Pnagiotis and Jensen, Christian S. and Mahmood, Ahmed and N{\o}rv{\aa}g, Kjetil and Sacharidis, Dimitris and Sarwat, Mohamed}, PAGES = {90--99}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Funke, Stefan %A Rupp, Tobias %A Nusser, Andr&#233; %A Storandt, Sabine %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T PATHFINDER: Storage and Indexing of Massive Trajectory Sets : %G eng %U http://hdl.handle.net/21.11116/0000-0005-870C-6 %R 10.1145/3340964.3340978 %D 2019 %B 16th International Symposium onSpatial and Temporal Databases %Z date of event: 2019-08-19 - 2019-08-21 %C Vienna, Austria %B SSTD'19 %E Aref, Walid G.; Bertolotto, Michela; Bouros, Pnagiotis; Jensen, Christian S.; Mahmood, Ahmed; N&#248;rv&#229;g, Kjetil; Sacharidis, Dimitris; Sarwat, Mohamed %P 90 - 99 %I ACM %@ 978-1-4503-6280-1
[121]
B. Geissmann, S. Leucci, C.-H. Liu, and P. Penna, “Optimal Sorting with Persistent Comparison Errors,” in 27th Annual European Symposium on Algorithms (ESA 2019), Munich/Garching, Germany, 2019.
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@inproceedings{Geissmann_ESA2019, TITLE = {Optimal Sorting with Persistent Comparison Errors}, AUTHOR = {Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-124-5}, URL = {urn:nbn:de:0030-drops-111706}, DOI = {10.4230/LIPIcs.ESA.2019.49}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {27th Annual European Symposium on Algorithms (ESA 2019)}, EDITOR = {Bender, Michael A. and Svensson, Ola and German, Grzegorz}, PAGES = {1--14}, EID = {49}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {144}, ADDRESS = {Munich/Garching, Germany}, }
Endnote
%0 Conference Proceedings %A Geissmann, Barbara %A Leucci, Stefano %A Liu, Chih-Hung %A Penna, Paolo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Optimal Sorting with Persistent Comparison Errors : %G eng %U http://hdl.handle.net/21.11116/0000-0007-3186-A %R 10.4230/LIPIcs.ESA.2019.49 %U urn:nbn:de:0030-drops-111706 %D 2019 %B 27th Annual European Symposium on Algorithms %Z date of event: 2019-09-09 - 2019-09-11 %C Munich/Garching, Germany %B 27th Annual European Symposium on Algorithms %E Bender, Michael A.; Svensson, Ola; German, Grzegorz %P 1 - 14 %Z sequence number: 49 %I Schloss Dagstuhl %@ 978-3-95977-124-5 %B Leibniz International Proceedings in Informatics %N 144 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2019/11170/https://creativecommons.org/licenses/by/3.0/legalcode
[122]
Y. A. Gonczarowski, N. Nisan, R. Ostrovsky, and W. Rosenbaum, “A Stable Marriage Requires Communication,” Games and Economic Behavior, vol. 118, 2019.
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@article{Gonczarowski2019, TITLE = {A Stable Marriage Requires Communication}, AUTHOR = {Gonczarowski, Yannai A. and Nisan, Noam and Ostrovsky, Rafail and Rosenbaum, Will}, LANGUAGE = {eng}, ISSN = {0899-8256}, DOI = {10.1016/j.geb.2018.10.013}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Games and Economic Behavior}, VOLUME = {118}, PAGES = {626--646}, }
Endnote
%0 Journal Article %A Gonczarowski, Yannai A. %A Nisan, Noam %A Ostrovsky, Rafail %A Rosenbaum, Will %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Stable Marriage Requires Communication : %G eng %U http://hdl.handle.net/21.11116/0000-0005-88FD-5 %R 10.1016/j.geb.2018.10.013 %7 2019 %D 2019 %J Games and Economic Behavior %V 118 %& 626 %P 626 - 646 %I Elsevier %C Amsterdam %@ false
[123]
F. Grandoni, B. Laekhanukit, and S. Li, “O(log 2 k/ log log k)-Approximation Algorithm for Directed Steiner Tree: A Tight Quasi-Polynomial-Time Algorithm,” in STOC’19, 51st Annual ACM Symposium on the Theory of Computing, Phoenix, AZ, USA, 2019.
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@inproceedings{Grandoni_STOC2019, TITLE = {{$O(\log^2k/\log\log{k})$}-Approximation Algorithm for Directed {S}teiner Tree: A Tight Quasi-Polynomial-Time Algorithm}, AUTHOR = {Grandoni, Fabrizio and Laekhanukit, Bundit and Li, Shi}, LANGUAGE = {eng}, ISBN = {978-1-4503-6705-9}, DOI = {10.1145/3313276.3316349}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {STOC'19, 51st Annual ACM Symposium on the Theory of Computing}, PAGES = {253--264}, ADDRESS = {Phoenix, AZ, USA}, }
Endnote
%0 Conference Proceedings %A Grandoni, Fabrizio %A Laekhanukit, Bundit %A Li, Shi %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T O(log 2 k/ log log k)-Approximation Algorithm for Directed Steiner Tree: A Tight Quasi-Polynomial-Time Algorithm : %G eng %U http://hdl.handle.net/21.11116/0000-0003-1625-B %R 10.1145/3313276.3316349 %D 2019 %B 51st Annual ACM Symposium on the Theory of Computing %Z date of event: 2019-06-23 - 2019-06-26 %C Phoenix, AZ, USA %B STOC'19 %P 253 - 264 %I ACM %@ 978-1-4503-6705-9
[124]
S. Heydrich and A. Wiese, “Faster Approximation Schemes for the Two-dimensional Knapsack Problem,” ACM Transactions on Algorithms, vol. 15, no. 4, 2019.
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@article{Heydrich19, TITLE = {Faster Approximation Schemes for the Two-dimensional Knapsack Problem}, AUTHOR = {Heydrich, Sandy and Wiese, Andreas}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3338512}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {15}, NUMBER = {4}, EID = {47}, }
Endnote
%0 Journal Article %A Heydrich, Sandy %A Wiese, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Faster Approximation Schemes for the Two-dimensional Knapsack Problem : %G eng %U http://hdl.handle.net/21.11116/0000-0005-6A94-D %R 10.1145/3338512 %7 2019 %D 2019 %J ACM Transactions on Algorithms %V 15 %N 4 %Z sequence number: 47 %I ACM %C New York, NY %@ false
[125]
Y. Ibrahim, M. Riedewald, G. Weikum, and D. Zeinalipour-Yazti, “Bridging Quantities in Tables and Text,” in ICDE 2019, 35th IEEE International Conference on Data Engineering, Macau, China, 2019.
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@inproceedings{Ibrahim_ICDE2019, TITLE = {Bridging Quantities in Tables and Text}, AUTHOR = {Ibrahim, Yusra and Riedewald, Mirek and Weikum, Gerhard and Zeinalipour-Yazti, Demetrios}, LANGUAGE = {eng}, ISBN = {978-1-5386-7474-1}, DOI = {10.1109/ICDE.2019.00094}, PUBLISHER = {IEEE}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {ICDE 2019, 35th IEEE International Conference on Data Engineering}, PAGES = {1010--1021}, ADDRESS = {Macau, China}, }
Endnote
%0 Conference Proceedings %A Ibrahim, Yusra %A Riedewald, Mirek %A Weikum, Gerhard %A Zeinalipour-Yazti, Demetrios %+ Databases and Information Systems, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Databases and Information Systems, MPI for Informatics, Max Planck Society Databases and Information Systems, MPI for Informatics, Max Planck Society %T Bridging Quantities in Tables and Text : %G eng %U http://hdl.handle.net/21.11116/0000-0003-01AB-B %R 10.1109/ICDE.2019.00094 %D 2019 %B 35th IEEE International Conference on Data Engineering %Z date of event: 2019-04-08 - 2019-04-12 %C Macau, China %B ICDE 2019 %P 1010 - 1021 %I IEEE %@ 978-1-5386-7474-1
[126]
C. Ikenmeyer, B. Komarath, C. Lenzen, V. Lysikov, A. Mokhov, and K. Sreenivasaiah, “On the Complexity of Hazard-free Circuits,” Journal of the ACM, vol. 66, no. 4, 2019.
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@article{Ikenmeyer_JACM2019, TITLE = {On the Complexity of Hazard-free Circuits}, AUTHOR = {Ikenmeyer, Christian and Komarath, Balagopal and Lenzen, Christoph and Lysikov, Vladimir and Mokhov, Andrey and Sreenivasaiah, Karteek}, LANGUAGE = {eng}, ISSN = {0004-5411}, DOI = {10.1145/3320123}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Journal of the ACM}, VOLUME = {66}, NUMBER = {4}, EID = {25}, }
Endnote
%0 Journal Article %A Ikenmeyer, Christian %A Komarath, Balagopal %A Lenzen, Christoph %A Lysikov, Vladimir %A Mokhov, Andrey %A Sreenivasaiah, Karteek %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T On the Complexity of Hazard-free Circuits : %G eng %U http://hdl.handle.net/21.11116/0000-0004-8D51-2 %R 10.1145/3320123 %7 2019 %D 2019 %J Journal of the ACM %V 66 %N 4 %Z sequence number: 25 %I ACM %C New York, NY %@ false
[127]
D. Issac, “On some covering, partition and connectivity problems in graphs,” Universität des Saarlandes, Saarbrücken, 2019.
Abstract
We look at some graph problems related to covering, partition, and connectivity. First, we study the problems of covering and partitioning edges with bicliques, especially from the viewpoint of parameterized complexity. For the partition problem, we develop much more efficient algorithms than the ones previously known. In contrast, for the cover problem, our lower bounds show that the known algorithms are probably optimal. Next, we move on to graph coloring, which is probably the most extensively studied partition problem in graphs. Hadwiger’s conjecture is a long-standing open problem related to vertex coloring. We prove the conjecture for a special class of graphs, namely squares of 2-trees, and show that square graphs are important in connection with Hadwiger’s conjecture. Then, we study a coloring problem that has been emerging recently, called rainbow coloring. This problem lies in the intersection of coloring and connectivity. We study different variants of rainbow coloring and present bounds and complexity results on them. Finally, we move on to another parameter related to connectivity called spanning tree congestion (STC). We give tight bounds for STC in general graphs and random graphs. While proving the results on
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@phdthesis{Issacphd2019, TITLE = {On some covering, partition and connectivity problems in graphs}, AUTHOR = {Issac, Davis}, LANGUAGE = {eng}, DOI = {10.22028/D291-29620}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, ABSTRACT = {We look at some graph problems related to covering, partition, and connectivity. First, we study the problems of covering and partitioning edges with bicliques, especially from the viewpoint of parameterized complexity. For the partition problem, we develop much more efficient algorithms than the ones previously known. In contrast, for the cover problem, our lower bounds show that the known algorithms are probably optimal. Next, we move on to graph coloring, which is probably the most extensively studied partition problem in graphs. Hadwiger{\textquoteright}s conjecture is a long-standing open problem related to vertex coloring. We prove the conjecture for a special class of graphs, namely squares of 2-trees, and show that square graphs are important in connection with Hadwiger{\textquoteright}s conjecture. Then, we study a coloring problem that has been emerging recently, called rainbow coloring. This problem lies in the intersection of coloring and connectivity. We study different variants of rainbow coloring and present bounds and complexity results on them. Finally, we move on to another parameter related to connectivity called spanning tree congestion (STC). We give tight bounds for STC in general graphs and random graphs. While proving the results on}, }
Endnote
%0 Thesis %A Issac, Davis %Y Karrenbauer, Andreas %A referee: Mehlhorn, Kurt %A referee: Chandran, L. Sunil %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society International Max Planck Research School, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On some covering, partition and connectivity problems in graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0004-D665-9 %R 10.22028/D291-29620 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2019 %P 191 p. %V phd %9 phd %X We look at some graph problems related to covering, partition, and connectivity. First, we study the problems of covering and partitioning edges with bicliques, especially from the viewpoint of parameterized complexity. For the partition problem, we develop much more efficient algorithms than the ones previously known. In contrast, for the cover problem, our lower bounds show that the known algorithms are probably optimal. Next, we move on to graph coloring, which is probably the most extensively studied partition problem in graphs. Hadwiger&#8217;s conjecture is a long-standing open problem related to vertex coloring. We prove the conjecture for a special class of graphs, namely squares of 2-trees, and show that square graphs are important in connection with Hadwiger&#8217;s conjecture. Then, we study a coloring problem that has been emerging recently, called rainbow coloring. This problem lies in the intersection of coloring and connectivity. We study different variants of rainbow coloring and present bounds and complexity results on them. Finally, we move on to another parameter related to connectivity called spanning tree congestion (STC). We give tight bounds for STC in general graphs and random graphs. While proving the results on %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/28007
[128]
G. Jindal and M. Bläser, “On the Complexity of Symmetric Polynomials,” in 10th Innovations in Theoretical Computer Science (ITCS 2019), San Diego, CA, USA, 2019.
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@inproceedings{Jindal_ITCS2019, TITLE = {On the Complexity of Symmetric Polynomials}, AUTHOR = {Jindal, Gorav and Bl{\"a}ser, Markus}, LANGUAGE = {eng}, ISBN = {978-3-95977-095-8}, URL = {urn:nbn:de:0030-drops-101402}, DOI = {10.4230/LIPIcs.ITCS.2019.47}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {10th Innovations in Theoretical Computer Science (ITCS 2019)}, EDITOR = {Blum, Avrim}, PAGES = {1--14}, EID = {47}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {124}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Jindal, Gorav %A Bl&#228;ser, Markus %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Complexity of Symmetric Polynomials : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ABCC-8 %R 10.4230/LIPIcs.ITCS.2019.47 %U urn:nbn:de:0030-drops-101402 %D 2019 %B 10th Innovations in Theoretical Computer Science %Z date of event: 2019-01-10 - 2019-01-12 %C San Diego, CA, USA %B 10th Innovations in Theoretical Computer Science %E Blum, Avrim %P 1 - 14 %Z sequence number: 47 %I Schloss Dagstuhl %@ 978-3-95977-095-8 %B Leibniz International Proceedings in Informatics %N 124 %U http://drops.dagstuhl.de/opus/volltexte/2018/10140/http://drops.dagstuhl.de/doku/urheberrecht1.html
[129]
M. John and A. Karrenbauer, “Dynamic Sparsification for Quadratic Assignment Problems,” in Mathematical Optimization Theory and Operations Research (MOTOR 2019), Ekaterinburg, Russia, 2019.
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@inproceedings{John_MOTOR2019, TITLE = {Dynamic Sparsification for Quadratic Assignment Problems}, AUTHOR = {John, Maximilian and Karrenbauer, Andreas}, LANGUAGE = {eng}, DOI = {10.1007/978-3-030-22629-9_17}, PUBLISHER = {Springer}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Mathematical Optimization Theory and Operations Research (MOTOR 2019)}, EDITOR = {Khachay, Michael and Kochetov, Yury and Pardalos, Panos}, PAGES = {232--264}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {11548}, ADDRESS = {Ekaterinburg, Russia}, }
Endnote
%0 Conference Proceedings %A John, Maximilian %A Karrenbauer, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Dynamic Sparsification for Quadratic Assignment Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1DA8-E %R 10.1007/978-3-030-22629-9_17 %D 2019 %B 18th International Conference on Mathematical Optimization Theory and Operations Research %Z date of event: 2019-07-08 - 2019-07-12 %C Ekaterinburg, Russia %B Mathematical Optimization Theory and Operations Research %E Khachay, Michael; Kochetov, Yury; Pardalos, Panos %P 232 - 264 %I Springer %B Lecture Notes in Computer Science %N 11548
[130]
A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Physarum Dynamics,” 2019. [Online]. Available: http://arxiv.org/abs/1901.07231. (arXiv: 1901.07231)
Abstract
Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in \mathbb{Z}^n$. We show under fairly general conditions that the non-uniform Physarum dynamics $\dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right)$ converges to the optimum solution $x^*$ of the weighted basis pursuit problem minimize $c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$, and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| - x_e$ at time $t$ and in state $x$. Previously convergence was only shown for the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show convergence for the dynamics $\dot{x}_e = x_e \cdot \left( g_e \left(\frac{|q_e|}{x_e}\right) - 1\right),$ where $g_e$ is an increasing differentiable function with $g_e(1) = 1$. Previously convergence was only shown for the special case of the shortest path problem on a graph consisting of two nodes connected by parallel edges.
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@online{DBLP:journals/corr/abs-1901-07231, TITLE = {Convergence of the Non-Uniform Physarum Dynamics}, AUTHOR = {Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1901.07231}, EPRINT = {1901.07231}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in \mathbb{Z}^n$. We show under fairly general conditions that the non-uniform Physarum dynamics $\dot{x}_e = a_e(x,t) \left(|q_e| -- x_e\right)$ converges to the optimum solution $x^*$ of the weighted basis pursuit problem minimize $c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$, and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| - x_e$ at time $t$ and in state $x$. Previously convergence was only shown for the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show convergence for the dynamics $\dot{x}_e = x_e \cdot \left( g_e \left(\frac{|q_e|}{x_e}\right) -- 1\right),$ where $g_e$ is an increasing differentiable function with $g_e(1) = 1$. Previously convergence was only shown for the special case of the shortest path problem on a graph consisting of two nodes connected by parallel edges.}, }
Endnote
%0 Report %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Convergence of the Non-Uniform Physarum Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-F39F-9 %U http://arxiv.org/abs/1901.07231 %D 2019 %X Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in \mathbb{Z}^n$. We show under fairly general conditions that the non-uniform Physarum dynamics $\dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right)$ converges to the optimum solution $x^*$ of the weighted basis pursuit problem minimize $c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$, and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| - x_e$ at time $t$ and in state $x$. Previously convergence was only shown for the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show convergence for the dynamics $\dot{x}_e = x_e \cdot \left( g_e \left(\frac{|q_e|}{x_e}\right) - 1\right),$ where $g_e$ is an increasing differentiable function with $g_e(1) = 1$. Previously convergence was only shown for the special case of the shortest path problem on a graph consisting of two nodes connected by parallel edges. %K Computer Science, Data Structures and Algorithms, cs.DS
[131]
P. Khanchandani and C. Lenzen, “Self-Stabilizing Byzantine Clock Synchronization with Optimal Precision,” Theory of Computing Systems, vol. 63, no. 2, 2019.
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@article{Khanchandani2018, TITLE = {Self-Stabilizing {B}yzantine Clock Synchronization with Optimal Precision}, AUTHOR = {Khanchandani, Pankaj and Lenzen, Christoph}, LANGUAGE = {eng}, ISSN = {1432-4350}, DOI = {10.1007/s00224-017-9840-3}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Theory of Computing Systems}, VOLUME = {63}, NUMBER = {2}, PAGES = {261--305}, }
Endnote
%0 Journal Article %A Khanchandani, Pankaj %A Lenzen, Christoph %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Self-Stabilizing Byzantine Clock Synchronization with Optimal Precision : %G eng %U http://hdl.handle.net/21.11116/0000-0000-73AC-D %R 10.1007/s00224-017-9840-3 %7 2018-01-20 %D 2019 %J Theory of Computing Systems %V 63 %N 2 %& 261 %P 261 - 305 %I Springer %C New York, NY %@ false
[132]
A. Kinali, “A Physical Sine-to-Square Converter Noise Model,” in IEEE International Frequency Control Symposium (IFCS 2018), Olympic Valley, CA, USA, 2019.
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@inproceedings{Kinali_IFCS2018, TITLE = {A Physical Sine-to-Square Converter Noise Model}, AUTHOR = {Kinali, Attila}, LANGUAGE = {eng}, ISBN = {978-1-5386-3214-7}, DOI = {10.1109/FCS.2018.8597525}, PUBLISHER = {IEEE}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {IEEE International Frequency Control Symposium (IFCS 2018)}, PAGES = {383--388}, ADDRESS = {Olympic Valley, CA, USA}, }
Endnote
%0 Conference Proceedings %A Kinali, Attila %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Physical Sine-to-Square Converter Noise Model : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AC39-D %R 10.1109/FCS.2018.8597525 %D 2019 %B IEEE International Frequency Control Symposium %Z date of event: 2018-05-21 - 2018-05-24 %C Olympic Valley, CA, USA %B IEEE International Frequency Control Symposium %P 383 - 388 %I IEEE %@ 978-1-5386-3214-7
[133]
M. Künnemann, D. Moeller, R. Paturi, and S. Schneider, “Subquadratic Algorithms for Succinct Stable Matching,” Algorithmica, vol. 81, no. 7, 2019.
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@article{Kuennemann2019, TITLE = {Subquadratic Algorithms for Succinct Stable Matching}, AUTHOR = {K{\"u}nnemann, Marvin and Moeller, Daniel and Paturi, Ramamohan and Schneider, Stefan}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-019-00564-x}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Algorithmica}, VOLUME = {81}, NUMBER = {7}, PAGES = {2991--3024}, }
Endnote
%0 Journal Article %A K&#252;nnemann, Marvin %A Moeller, Daniel %A Paturi, Ramamohan %A Schneider, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Subquadratic Algorithms for Succinct Stable Matching : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7E0-3 %R 10.1007/s00453-019-00564-x %7 2019 %D 2019 %J Algorithmica %V 81 %N 7 %& 2991 %P 2991 - 3024 %I Springer %C New York, NY %@ false
[134]
C. Lenzen and J. Rybicki, “Self-Stabilising Byzantine Clock Synchronisation is Almost as Easy as Consensus,” Journal of the ACM, vol. 66, no. 5, 2019.
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@article{Lenzen_JACM2019, TITLE = {Self-Stabilising {B}yzantine Clock Synchronisation is Almost as Easy as Consensus}, AUTHOR = {Lenzen, Christoph and Rybicki, Joel}, LANGUAGE = {eng}, ISSN = {0004-5411}, DOI = {10.1145/3339471}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of the ACM}, VOLUME = {66}, NUMBER = {5}, EID = {32}, }
Endnote
%0 Journal Article %A Lenzen, Christoph %A Rybicki, Joel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Self-Stabilising Byzantine Clock Synchronisation is Almost as Easy as Consensus : %G eng %U http://hdl.handle.net/21.11116/0000-0004-7CF6-C %R 10.1145/3339471 %7 2019 %D 2019 %J Journal of the ACM %V 66 %N 5 %Z sequence number: 32 %I ACM %C New York, NY %@ false
[135]
C. Lenzen, M. Parter, and E. Yogev, “Parallel Balanced Allocations: The Heavily Loaded Case,” 2019. [Online]. Available: http://arxiv.org/abs/1904.07532. (arXiv: 1904.07532)
Abstract
We study parallel algorithms for the classical balls-into-bins problem, in which $m$ balls acting in parallel as separate agents are placed into $n$ bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange messages once. The goal is to minimize the maximal load over all bins using a small number of rounds and few messages. While the case of $m=n$ balls has been extensively studied, little is known about the heavily loaded case. In this work, we consider parallel algorithms for this somewhat neglected regime of $m\gg n$. The naive solution of allocating each ball to a bin chosen uniformly and independently at random results in maximal load $m/n+\Theta(\sqrt{m/n\cdot \log n})$ (for $m\geq n \log n$) w.h.p. In contrast, for the sequential setting Berenbrink et al (SIAM J. Comput 2006) showed that letting each ball join the least loaded bin of two randomly selected bins reduces the maximal load to $m/n+O(\log\log m)$ w.h.p. To date, no parallel variant of such a result is known. We present a simple parallel threshold algorithm that obtains a maximal load of $m/n+O(1)$ w.h.p. within $O(\log\log (m/n)+\log^* n)$ rounds. The algorithm is symmetric (balls and bins all "look the same"), and balls send $O(1)$ messages in expectation per round. The additive term of $O(\log^* n)$ in the complexity is known to be tight for such algorithms (Lenzen and Wattenhofer Distributed Computing 2016). We also prove that our analysis is tight, i.e., algorithms of the type we provide must run for $\Omega(\min\{\log\log (m/n),n\})$ rounds w.h.p. Finally, we give a simple asymmetric algorithm (i.e., balls are aware of a common labeling of the bins) that achieves a maximal load of $m/n + O(1)$ in a constant number of rounds w.h.p. Again, balls send only a single message per round, and bins receive $(1+o(1))m/n+O(\log n)$ messages w.h.p.
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@online{Lenzen_arXiv1904.07532, TITLE = {Parallel Balanced Allocations: {T}he Heavily Loaded Case}, AUTHOR = {Lenzen, Christoph and Parter, Merav and Yogev, Eylon}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1904.07532}, EPRINT = {1904.07532}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study parallel algorithms for the classical balls-into-bins problem, in which $m$ balls acting in parallel as separate agents are placed into $n$ bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange messages once. The goal is to minimize the maximal load over all bins using a small number of rounds and few messages. While the case of $m=n$ balls has been extensively studied, little is known about the heavily loaded case. In this work, we consider parallel algorithms for this somewhat neglected regime of $m\gg n$. The naive solution of allocating each ball to a bin chosen uniformly and independently at random results in maximal load $m/n+\Theta(\sqrt{m/n\cdot \log n})$ (for $m\geq n \log n$) w.h.p. In contrast, for the sequential setting Berenbrink et al (SIAM J. Comput 2006) showed that letting each ball join the least loaded bin of two randomly selected bins reduces the maximal load to $m/n+O(\log\log m)$ w.h.p. To date, no parallel variant of such a result is known. We present a simple parallel threshold algorithm that obtains a maximal load of $m/n+O(1)$ w.h.p. within $O(\log\log (m/n)+\log^* n)$ rounds. The algorithm is symmetric (balls and bins all "look the same"), and balls send $O(1)$ messages in expectation per round. The additive term of $O(\log^* n)$ in the complexity is known to be tight for such algorithms (Lenzen and Wattenhofer Distributed Computing 2016). We also prove that our analysis is tight, i.e., algorithms of the type we provide must run for $\Omega(\min\{\log\log (m/n),n\})$ rounds w.h.p. Finally, we give a simple asymmetric algorithm (i.e., balls are aware of a common labeling of the bins) that achieves a maximal load of $m/n + O(1)$ in a constant number of rounds w.h.p. Again, balls send only a single message per round, and bins receive $(1+o(1))m/n+O(\log n)$ messages w.h.p.}, }
Endnote
%0 Report %A Lenzen, Christoph %A Parter, Merav %A Yogev, Eylon %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Parallel Balanced Allocations: The Heavily Loaded Case : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B3A4-9 %U http://arxiv.org/abs/1904.07532 %D 2019 %X We study parallel algorithms for the classical balls-into-bins problem, in which $m$ balls acting in parallel as separate agents are placed into $n$ bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange messages once. The goal is to minimize the maximal load over all bins using a small number of rounds and few messages. While the case of $m=n$ balls has been extensively studied, little is known about the heavily loaded case. In this work, we consider parallel algorithms for this somewhat neglected regime of $m\gg n$. The naive solution of allocating each ball to a bin chosen uniformly and independently at random results in maximal load $m/n+\Theta(\sqrt{m/n\cdot \log n})$ (for $m\geq n \log n$) w.h.p. In contrast, for the sequential setting Berenbrink et al (SIAM J. Comput 2006) showed that letting each ball join the least loaded bin of two randomly selected bins reduces the maximal load to $m/n+O(\log\log m)$ w.h.p. To date, no parallel variant of such a result is known. We present a simple parallel threshold algorithm that obtains a maximal load of $m/n+O(1)$ w.h.p. within $O(\log\log (m/n)+\log^* n)$ rounds. The algorithm is symmetric (balls and bins all "look the same"), and balls send $O(1)$ messages in expectation per round. The additive term of $O(\log^* n)$ in the complexity is known to be tight for such algorithms (Lenzen and Wattenhofer Distributed Computing 2016). We also prove that our analysis is tight, i.e., algorithms of the type we provide must run for $\Omega(\min\{\log\log (m/n),n\})$ rounds w.h.p. Finally, we give a simple asymmetric algorithm (i.e., balls are aware of a common labeling of the bins) that achieves a maximal load of $m/n + O(1)$ in a constant number of rounds w.h.p. Again, balls send only a single message per round, and bins receive $(1+o(1))m/n+O(\log n)$ messages w.h.p. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[136]
C. Lenzen, M. Parter, and E. Yogev, “Parallel Balanced Allocations: The Heavily Loaded Case,” in SPAA’19, 31st ACM Symposium on Parallelism in Algorithms and Architectures, Phoenix, AZ, USA, 2019.
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@inproceedings{Lenzen_SPAA2019, TITLE = {Parallel Balanced Allocations: {T}he Heavily Loaded Case}, AUTHOR = {Lenzen, Christoph and Parter, Merav and Yogev, Eylon}, LANGUAGE = {eng}, ISBN = {978-1-4503-6184-2}, DOI = {10.1145/3323165.3323203}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {SPAA'19, 31st ACM Symposium on Parallelism in Algorithms and Architectures}, PAGES = {313--322}, ADDRESS = {Phoenix, AZ, USA}, }
Endnote
%0 Conference Proceedings %A Lenzen, Christoph %A Parter, Merav %A Yogev, Eylon %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Parallel Balanced Allocations: The Heavily Loaded Case : %G eng %U http://hdl.handle.net/21.11116/0000-0003-6593-5 %R 10.1145/3323165.3323203 %D 2019 %B 31st ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2019-06-22 - 2019-06-24 %C Phoenix, AZ, USA %B SPAA'19 %P 313 - 322 %I ACM %@ 978-1-4503-6184-2
[137]
C. Lenzen and J. Rybicki, “Near-Optimal Self-stabilising Counting and Firing Squads,” Distributed Computing, vol. 32, no. 4, 2019.
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@article{Lenzen2019, TITLE = {Near-Optimal Self-stabilising Counting and Firing Squads}, AUTHOR = {Lenzen, Christoph and Rybicki, Joel}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-018-0342-6}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Distributed Computing}, VOLUME = {32}, NUMBER = {4}, PAGES = {339--360}, }
Endnote
%0 Journal Article %A Lenzen, Christoph %A Rybicki, Joel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Near-Optimal Self-stabilising Counting and Firing Squads : %G eng %U http://hdl.handle.net/21.11116/0000-0004-7AD6-2 %R 10.1007/s00446-018-0342-6 %7 2018 %D 2019 %J Distributed Computing %V 32 %N 4 %& 339 %P 339 - 360 %I Springer International %C Berlin %@ false
[138]
C. Lenzen, B. Patt-Shamir, and D. Peleg, “Distributed Distance Computation and Routing with Small Messages,” Distributed Computing, vol. 32, no. 2, 2019.
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@article{Lenzen_DC2018, TITLE = {Distributed Distance Computation and Routing with Small Messages}, AUTHOR = {Lenzen, Christoph and Patt-Shamir, Boaz and Peleg, David}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-018-0326-6}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Distributed Computing}, VOLUME = {32}, NUMBER = {2}, PAGES = {133--157}, }
Endnote
%0 Journal Article %A Lenzen, Christoph %A Patt-Shamir, Boaz %A Peleg, David %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Distributed Distance Computation and Routing with Small Messages : %G eng %U http://hdl.handle.net/21.11116/0000-0002-6CD1-9 %R 10.1007/s00446-018-0326-6 %7 2018 %D 2019 %J Distributed Computing %V 32 %N 2 %& 133 %P 133 - 157 %I Springer International %C Berlin %@ false
[139]
S. Leucci, C.-H. Liu, and S. Meierhans, “Resilient Dictionaries for Randomly Unreliable Memory,” in 27th Annual European Symposium on Algorithms (ESA 2019), Munich/Garching, Germany, 2019.
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@inproceedings{Leucci_ESA2019, TITLE = {Resilient Dictionaries for Randomly Unreliable Memory}, AUTHOR = {Leucci, Stefano and Liu, Chih-Hung and Meierhans, Simon}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-124-5}, URL = {urn:nbn:de:0030-drops-111911}, DOI = {10.4230/LIPIcs.ESA.2019.70}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {27th Annual European Symposium on Algorithms (ESA 2019)}, EDITOR = {Bender, Michael A. and Svensson, Ola and German, Grzegorz}, PAGES = {1--16}, EID = {70}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {144}, ADDRESS = {Munich/Garching, Germany}, }
Endnote
%0 Conference Proceedings %A Leucci, Stefano %A Liu, Chih-Hung %A Meierhans, Simon %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Resilient Dictionaries for Randomly Unreliable Memory : %G eng %U http://hdl.handle.net/21.11116/0000-0007-318A-6 %R 10.4230/LIPIcs.ESA.2019.70 %U urn:nbn:de:0030-drops-111911 %D 2019 %B 27th Annual European Symposium on Algorithms %Z date of event: 2019-09-09 - 2019-09-11 %C Munich/Garching, Germany %B 27th Annual European Symposium on Algorithms %E Bender, Michael A.; Svensson, Ola; German, Grzegorz %P 1 - 16 %Z sequence number: 70 %I Schloss Dagstuhl %@ 978-3-95977-124-5 %B Leibniz International Proceedings in Informatics %N 144 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2019/11191/https://creativecommons.org/licenses/by/3.0/legalcode
[140]
A. Miller, B. Patt-Shamir, and W. Rosenbaum, “With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing,” 2019. [Online]. Available: http://arxiv.org/abs/1902.08069. (arXiv: 1902.08069)
Abstract
We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals are subject to a maximum average rate $0\le\rho\le1$ and burstiness $\sigma\ge0$. In this model, we analyze the size of buffers required to avoid overflows in the basic case of a path. Our main results characterize the space required by the average rate and the number of distinct destinations: we show that $O(k d^{1/k})$ space suffice, where $d$ is the number of distinct destinations and $k=\lfloor 1/\rho \rfloor$; and we show that $\Omega(\frac 1 k d^{1/k})$ space is necessary. For directed trees, we describe an algorithm whose buffer space requirement is at most $1 + d' + \sigma$ where $d'$ is the maximum number of destinations on any root-leaf path.
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@online{Miller_arXiv1902.08069, TITLE = {With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing}, AUTHOR = {Miller, Avery and Patt-Shamir, Boaz and Rosenbaum, Will}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1902.08069}, EPRINT = {1902.08069}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals are subject to a maximum average rate $0\le\rho\le1$ and burstiness $\sigma\ge0$. In this model, we analyze the size of buffers required to avoid overflows in the basic case of a path. Our main results characterize the space required by the average rate and the number of distinct destinations: we show that $O(k d^{1/k})$ space suffice, where $d$ is the number of distinct destinations and $k=\lfloor 1/\rho \rfloor$; and we show that $\Omega(\frac 1 k d^{1/k})$ space is necessary. For directed trees, we describe an algorithm whose buffer space requirement is at most $1 + d' + \sigma$ where $d'$ is the maximum number of destinations on any root-leaf path.}, }
Endnote
%0 Report %A Miller, Avery %A Patt-Shamir, Boaz %A Rosenbaum, Will %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0CD3-2 %U http://arxiv.org/abs/1902.08069 %D 2019 %X We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals are subject to a maximum average rate $0\le\rho\le1$ and burstiness $\sigma\ge0$. In this model, we analyze the size of buffers required to avoid overflows in the basic case of a path. Our main results characterize the space required by the average rate and the number of distinct destinations: we show that $O(k d^{1/k})$ space suffice, where $d$ is the number of distinct destinations and $k=\lfloor 1/\rho \rfloor$; and we show that $\Omega(\frac 1 k d^{1/k})$ space is necessary. For directed trees, we describe an algorithm whose buffer space requirement is at most $1 + d' + \sigma$ where $d'$ is the maximum number of destinations on any root-leaf path. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[141]
A. Miller, B. Patt-Shamir, and W. Rosenbaum, “With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing,” in PODC’19, ACM Symposium on Principles of Distributed Computing, Toronto, Canada, 2019.
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@inproceedings{Miller_PODC2019, TITLE = {With Great Speed Come Small Buffers: {S}pace-Bandwidth Tradeoffs for Routing}, AUTHOR = {Miller, Avery and Patt-Shamir, Boaz and Rosenbaum, Will}, LANGUAGE = {eng}, ISBN = {978-1-4503-6217-7}, DOI = {10.1145/3293611.3331614}, PUBLISHER = {ACM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {PODC'19, ACM Symposium on Principles of Distributed Computing}, PAGES = {117--126}, ADDRESS = {Toronto, Canada}, }
Endnote
%0 Conference Proceedings %A Miller, Avery %A Patt-Shamir, Boaz %A Rosenbaum, Will %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing : %G eng %U http://hdl.handle.net/21.11116/0000-0007-1D09-0 %R 10.1145/3293611.3331614 %D 2019 %B ACM Symposium on Principles of Distributed Computing %Z date of event: 2019-07-29 - 2019-08-02 %C Toronto, Canada %B PODC'19 %P 117 - 126 %I ACM %@ 978-1-4503-6217-7
[142]
E. Oh, “Optimal Algorithm for Geodesic Nearest-point Voronoi Diagrams in Simple Polygons,” in Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019), San Diego, CA, USA, 2019.
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@inproceedings{Oh_SODA19d, TITLE = {Optimal Algorithm for Geodesic Nearest-point {V}oronoi Diagrams in Simple Polygons}, AUTHOR = {Oh, Eunjin}, LANGUAGE = {eng}, ISBN = {978-1-61197-548-2}, DOI = {10.1137/1.9781611975482.25}, PUBLISHER = {SIAM}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2019)}, EDITOR = {Chan, Timothy M.}, PAGES = {391--409}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Oh, Eunjin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Optimal Algorithm for Geodesic Nearest-point Voronoi Diagrams in Simple Polygons : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AA78-8 %R 10.1137/1.9781611975482.25 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 391 - 409 %I SIAM %@ 978-1-61197-548-2
[143]
E. Oh and H.-K. Ahn, “Computing the Center Region and its Variants,” Theoretical Computer Science, vol. 789, 2019.
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@article{Oh_2019, TITLE = {Computing the Center Region and its Variants}, AUTHOR = {Oh, Eunjin and Ahn, Hee-Kap}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2018.06.026}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Theoretical Computer Science}, VOLUME = {789}, PAGES = {2--12}, }
Endnote
%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Computing the Center Region and its Variants : %G eng %U http://hdl.handle.net/21.11116/0000-0004-E587-1 %R 10.1016/j.tcs.2018.06.026 %7 2019 %D 2019 %J Theoretical Computer Science %V 789 %& 2 %P 2 - 12 %I Elsevier %C Amsterdam %@ false
[144]
E. Oh and H.-K. Ahn, “A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms,” Algorithmica, vol. 81, no. 7, 2019.
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@article{Oh2019, TITLE = {A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms}, AUTHOR = {Oh, Eunjin and Ahn, Hee-Kap}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-019-00558-9}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Algorithmica}, VOLUME = {81}, NUMBER = {7}, PAGES = {2829--2856}, }
Endnote
%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7DE-7 %R 10.1007/s00453-019-00558-9 %7 2019 %D 2019 %J Algorithmica %V 81 %N 7 %& 2829 %P 2829 - 2856 %I Springer %C New York, NY %@ false
[145]
E. Oh and H.-K. Ahn, “Assigning Weights to Minimize the Covering Radius in the Plane,” Computational Geometry: Theory and Applications, vol. 81, 2019.
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@article{Oh2019, TITLE = {Assigning Weights to Minimize the Covering Radius in the Plane}, AUTHOR = {Oh, Eunjin and Ahn, Hee-Kap}, LANGUAGE = {eng}, ISSN = {0925-7721}, DOI = {10.1016/j.comgeo.2018.10.007}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Computational Geometry: Theory and Applications}, VOLUME = {81}, PAGES = {22--32}, }
Endnote
%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Assigning Weights to Minimize the Covering Radius in the Plane : %G eng %U http://hdl.handle.net/21.11116/0000-0003-C34C-C %R 10.1016/j.comgeo.2018.10.007 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 81 %& 22 %P 22 - 32 %I Elsevier %C Amsterdam %@ false
[146]
B. Patt-Shamir and W. Rosenbaum, “Space-Optimal Packet Routing on Trees,” in IEEE Conference on Computer Communications (IEEE INFOCOM 2019), Paris, France, 2019.
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@inproceedings{Patt-Shamir_INFOCOM2019, TITLE = {Space-Optimal Packet Routing on Trees}, AUTHOR = {Patt-Shamir, Boaz and Rosenbaum, Will}, LANGUAGE = {eng}, ISBN = {978-1-7281-0515-4}, DOI = {10.1109/INFOCOM.2019.8737596}, PUBLISHER = {IEEE}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {IEEE Conference on Computer Communications (IEEE INFOCOM 2019)}, PAGES = {1036--1044}, ADDRESS = {Paris, France}, }
Endnote
%0 Conference Proceedings %A Patt-Shamir, Boaz %A Rosenbaum, Will %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Space-Optimal Packet Routing on Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0004-AAD1-0 %R 10.1109/INFOCOM.2019.8737596 %D 2019 %B IEEE Conference on Computer Communications %Z date of event: 2019-04-29 - 2019-05-02 %C Paris, France %B IEEE Conference on Computer Communications %P 1036 - 1044 %I IEEE %@ 978-1-7281-0515-4
[147]
B. Ray Chaudhury, T. Kavitha, K. Mehlhorn, and A. Sgouritsa, “A Little Charity Guarantees Almost Envy-Freeness,” 2019. [Online]. Available: http://arxiv.org/abs/1907.04596. (arXiv: 1907.04596)
Abstract
Fair division of indivisible goods is a very well-studied problem. The goal of this problem is to distribute $m$ goods to $n$ agents in a "fair" manner, where every agent has a valuation for each subset of goods. We assume general valuations. Envy-freeness is the most extensively studied notion of fairness. However, envy-free allocations do not always exist when goods are indivisible. The notion of fairness we consider here is "envy-freeness up to any good" (EFX) where no agent envies another agent after the removal of any single good from the other agent's bundle. It is not known if such an allocation always exists even when $n=3$. We show there is always a partition of the set of goods into $n+1$ subsets $(X_1,\ldots,X_n,P)$ where for $i \in [n]$, $X_i$ is the bundle allocated to agent $i$ and the set $P$ is unallocated (or donated to charity) such that we have$\colon$ 1) envy-freeness up to any good, 2) no agent values $P$ higher than her own bundle, and 3) fewer than $n$ goods go to charity, i.e., $|P| < n$ (typically $m \gg n$). Our proof is constructive. When agents have additive valuations and $\lvert P \rvert$ is large (i.e., when $|P|$ is close to $n$), our allocation also has a good maximin share (MMS) guarantee. Moreover, a minor variant of our algorithm also shows the existence of an allocation which is $4/7$ groupwise maximin share (GMMS): this is a notion of fairness stronger than MMS. This improves upon the current best bound of $1/2$ known for an approximate GMMS allocation.
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@online{Ray_arXiv1907.04596, TITLE = {A Little Charity Guarantees Almost Envy-Freeness}, AUTHOR = {Ray Chaudhury, Bhaskar and Kavitha, Telikepalli and Mehlhorn, Kurt and Sgouritsa, Alkmini}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1907.04596}, EPRINT = {1907.04596}, EPRINTTYPE = {arXiv}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Fair division of indivisible goods is a very well-studied problem. The goal of this problem is to distribute $m$ goods to $n$ agents in a "fair" manner, where every agent has a valuation for each subset of goods. We assume general valuations. Envy-freeness is the most extensively studied notion of fairness. However, envy-free allocations do not always exist when goods are indivisible. The notion of fairness we consider here is "envy-freeness up to any good" (EFX) where no agent envies another agent after the removal of any single good from the other agent's bundle. It is not known if such an allocation always exists even when $n=3$. We show there is always a partition of the set of goods into $n+1$ subsets $(X_1,\ldots,X_n,P)$ where for $i \in [n]$, $X_i$ is the bundle allocated to agent $i$ and the set $P$ is unallocated (or donated to charity) such that we have$\colon$ 1) envy-freeness up to any good, 2) no agent values $P$ higher than her own bundle, and 3) fewer than $n$ goods go to charity, i.e., $|P| < n$ (typically $m \gg n$). Our proof is constructive. When agents have additive valuations and $\lvert P \rvert$ is large (i.e., when $|P|$ is close to $n$), our allocation also has a good maximin share (MMS) guarantee. Moreover, a minor variant of our algorithm also shows the existence of an allocation which is $4/7$ groupwise maximin share (GMMS): this is a notion of fairness stronger than MMS. This improves upon the current best bound of $1/2$ known for an approximate GMMS allocation.}, }
Endnote
%0 Report %A Ray Chaudhury, Bhaskar %A Kavitha, Telikepalli %A Mehlhorn, Kurt %A Sgouritsa, Alkmini %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Little Charity Guarantees Almost Envy-Freeness : %G eng %U http://hdl.handle.net/21.11116/0000-0005-4FB8-4 %U http://arxiv.org/abs/1907.04596 %D 2019 %X Fair division of indivisible goods is a very well-studied problem. The goal of this problem is to distribute $m$ goods to $n$ agents in a "fair" manner, where every agent has a valuation for each subset of goods. We assume general valuations. Envy-freeness is the most extensively studied notion of fairness. However, envy-free allocations do not always exist when goods are indivisible. The notion of fairness we consider here is "envy-freeness up to any good" (EFX) where no agent envies another agent after the removal of any single good from the other agent's bundle. It is not known if such an allocation always exists even when $n=3$. We show there is always a partition of the set of goods into $n+1$ subsets $(X_1,\ldots,X_n,P)$ where for $i \in [n]$, $X_i$ is the bundle allocated to agent $i$ and the set $P$ is unallocated (or donated to charity) such that we have$\colon$ 1) envy-freeness up to any good, 2) no agent values $P$ higher than her own bundle, and 3) fewer than $n$ goods go to charity, i.e., $|P| < n$ (typically $m \gg n$). Our proof is constructive. When agents have additive valuations and $\lvert P \rvert$ is large (i.e., when $|P|$ is close to $n$), our allocation also has a good maximin share (MMS) guarantee. Moreover, a minor variant of our algorithm also shows the existence of an allocation which is $4/7$ groupwise maximin share (GMMS): this is a notion of fairness stronger than MMS. This improves upon the current best bound of $1/2$ known for an approximate GMMS allocation. %K Computer Science, Computer Science and Game Theory, cs.GT
[148]
P. Sanders, K. Mehlhorn, M. Dietzfelbinger, and R. Dementiev, Sequential and Parallel Algorithms and Data Structures. Cham: Springer, 2019.
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@book{, TITLE = {Sequential and Parallel Algorithms and Data Structures}, AUTHOR = {Sanders, Peter and Mehlhorn, Kurt and Dietzfelbinger, Martin and Dementiev, Roman}, LANGUAGE = {eng}, ISBN = {978-3-030-25208-3; 978-3-030-25209-0}, DOI = {10.1007/978-3-030-25209-0}, PUBLISHER = {Springer}, ADDRESS = {Cham}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, PAGES = {434 p.}, }
Endnote
%0 Book %A Sanders, Peter %A Mehlhorn, Kurt %A Dietzfelbinger, Martin %A Dementiev, Roman %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Sequential and Parallel Algorithms and Data Structures : The Basic Toolbox %G eng %U http://hdl.handle.net/21.11116/0000-0005-3D79-0 %R 10.1007/978-3-030-25209-0 %@ 978-3-030-25208-3 %@ 978-3-030-25209-0 %I Springer %C Cham %D 2019 %P 434 p.
[149]
P. Schroeder, I. Kacem, and G. Schmidt, “Optimal Online Algorithms for the Portfolio Selection Problem, Bi-Directional Trading and -Search with Interrelated Prices,” RAIRO - Operations Research, vol. 53, no. 2, 2019.
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BibTeX
@article{Schroeder2019, TITLE = {Optimal Online Algorithms for the Portfolio Selection Problem, Bi-Directional Trading and -Search with Interrelated Prices}, AUTHOR = {Schroeder, Pascal and Kacem, Imed and Schmidt, G{\"u}nter}, LANGUAGE = {eng}, ISSN = {0399-0559}, DOI = {10.1051/ro/2018064}, PUBLISHER = {EDP Sciences}, ADDRESS = {Les Ulis, France}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, JOURNAL = {RAIRO -- Operations Research}, VOLUME = {53}, NUMBER = {2}, PAGES = {559--576}, }
Endnote
%0 Journal Article %A Schroeder, Pascal %A Kacem, Imed %A Schmidt, G&#252;nter %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Optimal Online Algorithms for the Portfolio Selection Problem, Bi-Directional Trading and -Search with Interrelated Prices : %G eng %U http://hdl.handle.net/21.11116/0000-0004-7AEC-A %R 10.1051/ro/2018064 %7 2019 %D 2019 %J RAIRO - Operations Research %V 53 %N 2 %& 559 %P 559 - 576 %I EDP Sciences %C Les Ulis, France %@ false
2018
[150]
A. Abboud and K. Bringmann, “Tighter Connections Between Formula-SAT and Shaving Logs,” in 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), Prague, Czech Republic, 2018.
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@inproceedings{Abboud_ICALP2018, TITLE = {Tighter Connections Between Formula-{SAT} and Shaving Logs}, AUTHOR = {Abboud, Amir and Bringmann, Karl}, LANGUAGE = {eng}, ISBN = {978-3-95977-076-7}, URL = {urn:nbn:de:0030-drops-90129}, DOI = {10.4230/LIPIcs.ICALP.2018.8}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, EDITOR = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D{\'a}niel and Sannella, Donald}, PAGES = {1--18}, EID = {8}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {107}, ADDRESS = {Prague, Czech Republic}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tighter Connections Between Formula-SAT and Shaving Logs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-16FB-B %R 10.4230/LIPIcs.ICALP.2018.8 %U urn:nbn:de:0030-drops-90129 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 18 %Z sequence number: 8 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9012/http://drops.dagstuhl.de/doku/urheberrecht1.html
[151]
A. Abboud and K. Bringmann, “Tighter Connections Between Formula-SAT and Shaving Logs,” 2018. [Online]. Available: http://arxiv.org/abs/1804.08978. (arXiv: 1804.08978)
Abstract
A noticeable fraction of Algorithms papers in the last few decades improve the running time of well-known algorithms for fundamental problems by logarithmic factors. For example, the $O(n^2)$ dynamic programming solution to the Longest Common Subsequence problem (LCS) was improved to $O(n^2/\log^2 n)$ in several ways and using a variety of ingenious tricks. This line of research, also known as "the art of shaving log factors", lacks a tool for proving negative results. Specifically, how can we show that it is unlikely that LCS can be solved in time $O(n^2/\log^3 n)$? Perhaps the only approach for such results was suggested in a recent paper of Abboud, Hansen, Vassilevska W. and Williams (STOC'16). The authors blame the hardness of shaving logs on the hardness of solving satisfiability on Boolean formulas (Formula-SAT) faster than exhaustive search. They show that an $O(n^2/\log^{1000} n)$ algorithm for LCS would imply a major advance in circuit lower bounds. Whether this approach can lead to tighter barriers was unclear. In this paper, we push this approach to its limit and, in particular, prove that a well-known barrier from complexity theory stands in the way for shaving five additional log factors for fundamental combinatorial problems. For LCS, regular expression pattern matching, as well as the Fr\'echet distance problem from Computational Geometry, we show that an $O(n^2/\log^{7+\varepsilon} n)$ runtime would imply new Formula-SAT algorithms. Our main result is a reduction from SAT on formulas of size $s$ over $n$ variables to LCS on sequences of length $N=2^{n/2} \cdot s^{1+o(1)}$. Our reduction is essentially as efficient as possible, and it greatly improves the previously known reduction for LCS with $N=2^{n/2} \cdot s^c$, for some $c \geq 100$.
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BibTeX
@online{Abboud_arXiv1804.08978, TITLE = {Tighter Connections Between Formula-{SAT} and Shaving Logs}, AUTHOR = {Abboud, Amir and Bringmann, Karl}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1804.08978}, EPRINT = {1804.08978}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {A noticeable fraction of Algorithms papers in the last few decades improve the running time of well-known algorithms for fundamental problems by logarithmic factors. For example, the $O(n^2)$ dynamic programming solution to the Longest Common Subsequence problem (LCS) was improved to $O(n^2/\log^2 n)$ in several ways and using a variety of ingenious tricks. This line of research, also known as "the art of shaving log factors", lacks a tool for proving negative results. Specifically, how can we show that it is unlikely that LCS can be solved in time $O(n^2/\log^3 n)$? Perhaps the only approach for such results was suggested in a recent paper of Abboud, Hansen, Vassilevska W. and Williams (STOC'16). The authors blame the hardness of shaving logs on the hardness of solving satisfiability on Boolean formulas (Formula-SAT) faster than exhaustive search. They show that an $O(n^2/\log^{1000} n)$ algorithm for LCS would imply a major advance in circuit lower bounds. Whether this approach can lead to tighter barriers was unclear. In this paper, we push this approach to its limit and, in particular, prove that a well-known barrier from complexity theory stands in the way for shaving five additional log factors for fundamental combinatorial problems. For LCS, regular expression pattern matching, as well as the Fr\'echet distance problem from Computational Geometry, we show that an $O(n^2/\log^{7+\varepsilon} n)$ runtime would imply new Formula-SAT algorithms. Our main result is a reduction from SAT on formulas of size $s$ over $n$ variables to LCS on sequences of length $N=2^{n/2} \cdot s^{1+o(1)}$. Our reduction is essentially as efficient as possible, and it greatly improves the previously known reduction for LCS with $N=2^{n/2} \cdot s^c$, for some $c \geq 100$.}, }
Endnote
%0 Report %A Abboud, Amir %A Bringmann, Karl %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tighter Connections Between Formula-SAT and Shaving Logs : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3DF7-5 %U http://arxiv.org/abs/1804.08978 %D 2018 %X A noticeable fraction of Algorithms papers in the last few decades improve the running time of well-known algorithms for fundamental problems by logarithmic factors. For example, the $O(n^2)$ dynamic programming solution to the Longest Common Subsequence problem (LCS) was improved to $O(n^2/\log^2 n)$ in several ways and using a variety of ingenious tricks. This line of research, also known as "the art of shaving log factors", lacks a tool for proving negative results. Specifically, how can we show that it is unlikely that LCS can be solved in time $O(n^2/\log^3 n)$? Perhaps the only approach for such results was suggested in a recent paper of Abboud, Hansen, Vassilevska W. and Williams (STOC'16). The authors blame the hardness of shaving logs on the hardness of solving satisfiability on Boolean formulas (Formula-SAT) faster than exhaustive search. They show that an $O(n^2/\log^{1000} n)$ algorithm for LCS would imply a major advance in circuit lower bounds. Whether this approach can lead to tighter barriers was unclear. In this paper, we push this approach to its limit and, in particular, prove that a well-known barrier from complexity theory stands in the way for shaving five additional log factors for fundamental combinatorial problems. For LCS, regular expression pattern matching, as well as the Fr\'echet distance problem from Computational Geometry, we show that an $O(n^2/\log^{7+\varepsilon} n)$ runtime would imply new Formula-SAT algorithms. Our main result is a reduction from SAT on formulas of size $s$ over $n$ variables to LCS on sequences of length $N=2^{n/2} \cdot s^{1+o(1)}$. Our reduction is essentially as efficient as possible, and it greatly improves the previously known reduction for LCS with $N=2^{n/2} \cdot s^c$, for some $c \geq 100$. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[152]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “SETH-Based Lower Bounds for Subset Sum and Bicriteria Path,” 2018. [Online]. Available: http://arxiv.org/abs/1704.04546. (arXiv: 1704.04546)
Abstract
Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017).
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BibTeX
@online{Abboud_arXiv1704.04546, TITLE = {{SETH}-Based Lower Bounds for Subset Sum and Bicriteria Path}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1704.04546}, EPRINT = {1704.04546}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017).}, }
Endnote
%0 Report %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T SETH-Based Lower Bounds for Subset Sum and Bicriteria Path : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E17-3 %U http://arxiv.org/abs/1704.04546 %D 2018 %X Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017). %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[153]
A. Abboud, K. Bringmann, H. Dell, and J. Nederlof, “More Consequences of Falsifying SETH and the Orthogonal Vectors Conjecture,” in STOC’18, 50th Annual ACM SIGACT Symposium on Theory of Computing, Los Angeles, CA, USA, 2018.
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BibTeX
@inproceedings{Abboud_STOC2018, TITLE = {More Consequences of Falsifying {SETH} and the Orthogonal Vectors Conjecture}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Dell, Holger and Nederlof, Jesper}, LANGUAGE = {eng}, ISBN = {978-1-4503-5559-9}, DOI = {10.1145/3188745.3188938}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {STOC'18, 50th Annual ACM SIGACT Symposium on Theory of Computing}, PAGES = {253--266}, ADDRESS = {Los Angeles, CA, USA}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Dell, Holger %A Nederlof, Jesper %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T More Consequences of Falsifying SETH and the Orthogonal Vectors Conjecture : %G eng %U http://hdl.handle.net/21.11116/0000-0002-1707-D %R 10.1145/3188745.3188938 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 253 - 266 %I ACM %@ 978-1-4503-5559-9
[154]
A. Abboud, A. Backurs, K. Bringmann, and M. Künnemann, “Fine-Grained Complexity of Analyzing Compressed Data: Quantifying Improvements over Decompress-And-Solve,” 2018. [Online]. Available: http://arxiv.org/abs/1803.00796. (arXiv: 1803.00796)
Abstract
Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given a compression of size $n$ of data that originally has size $N$, and we want to solve a problem with time complexity $T(\cdot)$. The naive strategy of "decompress-and-solve" gives time $T(N)$, whereas "the gold standard" is time $T(n)$: to analyze the compression as efficiently as if the original data was small. We restrict our attention to data in the form of a string (text, files, genomes, etc.) and study the most ubiquitous tasks. While the challenge might seem to depend heavily on the specific compression scheme, most methods of practical relevance (Lempel-Ziv-family, dictionary methods, and others) can be unified under the elegant notion of Grammar Compressions. A vast literature, across many disciplines, established this as an influential notion for Algorithm design. We introduce a framework for proving (conditional) lower bounds in this field, allowing us to assess whether decompress-and-solve can be improved, and by how much. Our main results are: - The $O(nN\sqrt{\log{N/n}})$ bound for LCS and the $O(\min\{N \log N, nM\})$ bound for Pattern Matching with Wildcards are optimal up to $N^{o(1)}$ factors, under the Strong Exponential Time Hypothesis. (Here, $M$ denotes the uncompressed length of the compressed pattern.) - Decompress-and-solve is essentially optimal for Context-Free Grammar Parsing and RNA Folding, under the $k$-Clique conjecture. - We give an algorithm showing that decompress-and-solve is not optimal for Disjointness.
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BibTeX
@online{Abboud_arXiv1803.00796, TITLE = {Fine-Grained Complexity of Analyzing Compressed Data: Quantifying Improvements over Decompress-And-Solve}, AUTHOR = {Abboud, Amir and Backurs, Arturs and Bringmann, Karl and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1803.00796}, EPRINT = {1803.00796}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given a compression of size $n$ of data that originally has size $N$, and we want to solve a problem with time complexity $T(\cdot)$. The naive strategy of "decompress-and-solve" gives time $T(N)$, whereas "the gold standard" is time $T(n)$: to analyze the compression as efficiently as if the original data was small. We restrict our attention to data in the form of a string (text, files, genomes, etc.) and study the most ubiquitous tasks. While the challenge might seem to depend heavily on the specific compression scheme, most methods of practical relevance (Lempel-Ziv-family, dictionary methods, and others) can be unified under the elegant notion of Grammar Compressions. A vast literature, across many disciplines, established this as an influential notion for Algorithm design. We introduce a framework for proving (conditional) lower bounds in this field, allowing us to assess whether decompress-and-solve can be improved, and by how much. Our main results are: -- The $O(nN\sqrt{\log{N/n}})$ bound for LCS and the $O(\min\{N \log N, nM\})$ bound for Pattern Matching with Wildcards are optimal up to $N^{o(1)}$ factors, under the Strong Exponential Time Hypothesis. (Here, $M$ denotes the uncompressed length of the compressed pattern.) -- Decompress-and-solve is essentially optimal for Context-Free Grammar Parsing and RNA Folding, under the $k$-Clique conjecture. -- We give an algorithm showing that decompress-and-solve is not optimal for Disjointness.}, }
Endnote
%0 Report %A Abboud, Amir %A Backurs, Arturs %A Bringmann, Karl %A K&#252;nnemann, Marvin %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity of Analyzing Compressed Data: Quantifying Improvements over Decompress-And-Solve : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E38-C %U http://arxiv.org/abs/1803.00796 %D 2018 %X Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given a compression of size $n$ of data that originally has size $N$, and we want to solve a problem with time complexity $T(\cdot)$. The naive strategy of "decompress-and-solve" gives time $T(N)$, whereas "the gold standard" is time $T(n)$: to analyze the compression as efficiently as if the original data was small. We restrict our attention to data in the form of a string (text, files, genomes, etc.) and study the most ubiquitous tasks. While the challenge might seem to depend heavily on the specific compression scheme, most methods of practical relevance (Lempel-Ziv-family, dictionary methods, and others) can be unified under the elegant notion of Grammar Compressions. A vast literature, across many disciplines, established this as an influential notion for Algorithm design. We introduce a framework for proving (conditional) lower bounds in this field, allowing us to assess whether decompress-and-solve can be improved, and by how much. Our main results are: - The $O(nN\sqrt{\log{N/n}})$ bound for LCS and the $O(\min\{N \log N, nM\})$ bound for Pattern Matching with Wildcards are optimal up to $N^{o(1)}$ factors, under the Strong Exponential Time Hypothesis. (Here, $M$ denotes the uncompressed length of the compressed pattern.) - Decompress-and-solve is essentially optimal for Context-Free Grammar Parsing and RNA Folding, under the $k$-Clique conjecture. - We give an algorithm showing that decompress-and-solve is not optimal for Disjointness. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[155]
M. Abrahamsen, A. Adamaszek, K. Bringmann, V. Cohen-Addad, M. Mehr, E. Rotenberg, A. Roytman, and M. Thorup, “Fast Fencing,” in STOC’18, 50th Annual ACM SIGACT Symposium on Theory of Computing, Los Angeles, CA, USA, 2018.
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BibTeX
@inproceedings{Abrahamsen_STOC2018, TITLE = {Fast Fencing}, AUTHOR = {Abrahamsen, Mikkel and Adamaszek, Anna and Bringmann, Karl and Cohen-Addad, Vincent and Mehr, Mehran and Rotenberg, Eva and Roytman, Alan and Thorup, Mikkel}, LANGUAGE = {eng}, ISBN = {978-1-4503-5559-9}, DOI = {10.1145/3188745.3188878}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {STOC'18, 50th Annual ACM SIGACT Symposium on Theory of Computing}, PAGES = {564--573}, ADDRESS = {Los Angeles, CA, USA}, }
Endnote
%0 Conference Proceedings %A Abrahamsen, Mikkel %A Adamaszek, Anna %A Bringmann, Karl %A Cohen-Addad, Vincent %A Mehr, Mehran %A Rotenberg, Eva %A Roytman, Alan %A Thorup, Mikkel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Fast Fencing : %G eng %U http://hdl.handle.net/21.11116/0000-0002-171F-3 %R 10.1145/3188745.3188878 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 564 - 573 %I ACM %@ 978-1-4503-5559-9
[156]
M. Abrahamsen, A. Adamaszek, K. Bringmann, V. Cohen-Addad, M. Mehr, E. Rotenberg, A. Roytman, and M. Thorup, “Fast Fencing,” 2018. [Online]. Available: http://arxiv.org/abs/1804.00101. (arXiv: 1804.00101)
Abstract
We consider very natural "fence enclosure" problems studied by Capoyleas, Rote, and Woeginger and Arkin, Khuller, and Mitchell in the early 90s. Given a set $S$ of $n$ points in the plane, we aim at finding a set of closed curves such that (1) each point is enclosed by a curve and (2) the total length of the curves is minimized. We consider two main variants. In the first variant, we pay a unit cost per curve in addition to the total length of the curves. An equivalent formulation of this version is that we have to enclose $n$ unit disks, paying only the total length of the enclosing curves. In the other variant, we are allowed to use at most $k$ closed curves and pay no cost per curve. For the variant with at most $k$ closed curves, we present an algorithm that is polynomial in both $n$ and $k$. For the variant with unit cost per curve, or unit disks, we present a near-linear time algorithm. Capoyleas, Rote, and Woeginger solved the problem with at most $k$ curves in $n^{O(k)}$ time. Arkin, Khuller, and Mitchell used this to solve the unit cost per curve version in exponential time. At the time, they conjectured that the problem with $k$ curves is NP-hard for general $k$. Our polynomial time algorithm refutes this unless P equals NP.
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BibTeX
@online{Abrahamsen_arXiv1804.00101, TITLE = {Fast Fencing}, AUTHOR = {Abrahamsen, Mikkel and Adamaszek, Anna and Bringmann, Karl and Cohen-Addad, Vincent and Mehr, Mehran and Rotenberg, Eva and Roytman, Alan and Thorup, Mikkel}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1804.00101}, EPRINT = {1804.00101}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider very natural "fence enclosure" problems studied by Capoyleas, Rote, and Woeginger and Arkin, Khuller, and Mitchell in the early 90s. Given a set $S$ of $n$ points in the plane, we aim at finding a set of closed curves such that (1) each point is enclosed by a curve and (2) the total length of the curves is minimized. We consider two main variants. In the first variant, we pay a unit cost per curve in addition to the total length of the curves. An equivalent formulation of this version is that we have to enclose $n$ unit disks, paying only the total length of the enclosing curves. In the other variant, we are allowed to use at most $k$ closed curves and pay no cost per curve. For the variant with at most $k$ closed curves, we present an algorithm that is polynomial in both $n$ and $k$. For the variant with unit cost per curve, or unit disks, we present a near-linear time algorithm. Capoyleas, Rote, and Woeginger solved the problem with at most $k$ curves in $n^{O(k)}$ time. Arkin, Khuller, and Mitchell used this to solve the unit cost per curve version in exponential time. At the time, they conjectured that the problem with $k$ curves is NP-hard for general $k$. Our polynomial time algorithm refutes this unless P equals NP.}, }
Endnote
%0 Report %A Abrahamsen, Mikkel %A Adamaszek, Anna %A Bringmann, Karl %A Cohen-Addad, Vincent %A Mehr, Mehran %A Rotenberg, Eva %A Roytman, Alan %A Thorup, Mikkel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Fast Fencing : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3DFE-E %U http://arxiv.org/abs/1804.00101 %D 2018 %X We consider very natural "fence enclosure" problems studied by Capoyleas, Rote, and Woeginger and Arkin, Khuller, and Mitchell in the early 90s. Given a set $S$ of $n$ points in the plane, we aim at finding a set of closed curves such that (1) each point is enclosed by a curve and (2) the total length of the curves is minimized. We consider two main variants. In the first variant, we pay a unit cost per curve in addition to the total length of the curves. An equivalent formulation of this version is that we have to enclose $n$ unit disks, paying only the total length of the enclosing curves. In the other variant, we are allowed to use at most $k$ closed curves and pay no cost per curve. For the variant with at most $k$ closed curves, we present an algorithm that is polynomial in both $n$ and $k$. For the variant with unit cost per curve, or unit disks, we present a near-linear time algorithm. Capoyleas, Rote, and Woeginger solved the problem with at most $k$ curves in $n^{O(k)}$ time. Arkin, Khuller, and Mitchell used this to solve the unit cost per curve version in exponential time. At the time, they conjectured that the problem with $k$ curves is NP-hard for general $k$. Our polynomial time algorithm refutes this unless P equals NP. %K Computer Science, Computational Geometry, cs.CG
[157]
A. Adamaszek, A. Antoniadis, A. Kumar, and T. Mömke, “Approximating Airports and Railways,” in 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018), Caen, France, 2018.
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@inproceedings{Adamaszek_STACS2018, TITLE = {Approximating Airports and Railways}, AUTHOR = {Adamaszek, Anna and Antoniadis, Antonios and Kumar, Amit and M{\"o}mke, Tobias}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-062-0}, URL = {urn:nbn:de:0030-drops-85183}, DOI = {10.4230/LIPIcs.STACS.2018.5}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)}, EDITOR = {Niedermeier, Rolf and Vall{\'e}e, Brigitte}, PAGES = {1--13}, EID = {5}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {96}, ADDRESS = {Caen, France}, }
Endnote
%0 Conference Proceedings %A Adamaszek, Anna %A Antoniadis, Antonios %A Kumar, Amit %A M&#246;mke, Tobias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Approximating Airports and Railways : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F43-0 %R 10.4230/LIPIcs.STACS.2018.5 %U urn:nbn:de:0030-drops-85183 %D 2018 %B 35th Symposium on Theoretical Aspects of Computer Science %Z date of event: 2018-02-28 - 2018-03-03 %C Caen, France %B 35th Symposium on Theoretical Aspects of Computer Science %E Niedermeier, Rolf; Vall&#233;e, Brigitte %P 1 - 13 %Z sequence number: 5 %I Schloss Dagstuhl %@ 978-3-95977-062-0 %B Leibniz International Proceedings in Informatics %N 96 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/8518/http://drops.dagstuhl.de/doku/urheberrecht1.html
[158]
A. Adamaszek, P. Chalermsook, A. Ene, and A. Wiese, “Submodular Unsplittable Flow on Trees,” Mathematical Programming / B, vol. 172, no. 1–2, 2018.
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@article{Adamaszek2018, TITLE = {Submodular Unsplittable Flow on Trees}, AUTHOR = {Adamaszek, Anna and Chalermsook, Parinya and Ene, Alina and Wiese, Andreas}, LANGUAGE = {eng}, ISSN = {0025-5610}, DOI = {10.1007/s10107-017-1218-4}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Mathematical Programming / B}, VOLUME = {172}, NUMBER = {1-2}, PAGES = {565--589}, }
Endnote
%0 Journal Article %A Adamaszek, Anna %A Chalermsook, Parinya %A Ene, Alina %A Wiese, Andreas %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Submodular Unsplittable Flow on Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0000-73B6-1 %R 10.1007/s10107-017-1218-4 %7 2018-01-17 %D 2018 %J Mathematical Programming / B %V 172 %N 1-2 %& 565 %P 565 - 589 %I Springer %C Berlin %@ false
[159]
S. A. Amiri, K.-T. Foerster, and S. Schmid, “Walking Through Waypoints,” in LATIN 2018: Theoretical Informatics, Buenos Aires, Argentinia, 2018.
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@inproceedings{Amiri_LATIN2018, TITLE = {Walking Through Waypoints}, AUTHOR = {Amiri, Saeed Akhoondian and Foerster, Klaus-Tycho and Schmid, Stefan}, LANGUAGE = {eng}, ISBN = {978-3-319-77403-9}, DOI = {10.1007/978-3-319-77404-6_4}, PUBLISHER = {Springer}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {LATIN 2018: Theoretical Informatics}, EDITOR = {Bender, Michael A. and Farach-Colton, Mart{\'i}n and Mosteiro, Miguel A.}, PAGES = {37--51}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10807}, ADDRESS = {Buenos Aires, Argentinia}, }
Endnote
%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Foerster, Klaus-Tycho %A Schmid, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Walking Through Waypoints : %G eng %U http://hdl.handle.net/21.11116/0000-0002-5765-B %R 10.1007/978-3-319-77404-6_4 %D 2018 %B 13th Latin American Theoretical Informatics Symposium %Z date of event: 2018-04-16 - 2018-04-19 %C Buenos Aires, Argentinia %B LATIN 2018: Theoretical Informatics %E Bender, Michael A.; Farach-Colton, Mart&#237;n; Mosteiro, Miguel A. %P 37 - 51 %I Springer %@ 978-3-319-77403-9 %B Lecture Notes in Computer Science %N 10807
[160]
S. A. Amiri, P. Ossona de Mendez, R. Rabinovich, and S. Siebertz, “Distributed Domination on Graph Classes of Bounded Expansion,” in SPAA’18, 30th ACM Symposium on Parallelism in Algorithms and Architectures, Vienna, Austria, 2018.
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@inproceedings{Amiri_SPAA2018, TITLE = {Distributed Domination on Graph Classes of Bounded Expansion}, AUTHOR = {Amiri, Saeed Akhoondian and Ossona de Mendez, Patrice and Rabinovich, Roman and Siebertz, Sebastian}, LANGUAGE = {eng}, ISBN = {978-1-4503-5799-9}, DOI = {10.1145/3210377.3210383}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {SPAA'18, 30th ACM Symposium on Parallelism in Algorithms and Architectures}, PAGES = {143--151}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Ossona de Mendez, Patrice %A Rabinovich, Roman %A Siebertz, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Distributed Domination on Graph Classes of Bounded Expansion : %G eng %U http://hdl.handle.net/21.11116/0000-0002-7081-D %R 10.1145/3210377.3210383 %D 2018 %B 30th ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2018-07-16 - 2018-07-18 %C Vienna, Austria %B SPAA'18 %P 143 - 151 %I ACM %@ 978-1-4503-5799-9
[161]
S. A. Amiri, S. Dudycz, S. Schmid, and S. Wiederrecht, “Congestion-Free Rerouting of Flows on DAGs,” in 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), Prague, Czech Republic, 2018.
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@inproceedings{Amiri_ICALP2018, TITLE = {Congestion-Free Rerouting of Flows on {DAGs}}, AUTHOR = {Amiri, Saeed Akhoondian and Dudycz, Szymon and Schmid, Stefan and Wiederrecht, Sebastian}, LANGUAGE = {eng}, ISBN = {978-3-95977-076-7}, URL = {urn:nbn:de:0030-drops-91471}, DOI = {10.4230/LIPIcs.ICALP.2018.143}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, EDITOR = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D{\'a}niel and Sannella, Donald}, PAGES = {1--13}, EID = {143}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {107}, ADDRESS = {Prague, Czech Republic}, }
Endnote
%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Dudycz, Szymon %A Schmid, Stefan %A Wiederrecht, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Congestion-Free Rerouting of Flows on DAGs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-707F-2 %R 10.4230/LIPIcs.ICALP.2018.143 %U urn:nbn:de:0030-drops-91471 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 13 %Z sequence number: 143 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9147/http://drops.dagstuhl.de/doku/urheberrecht1.html
[162]
S. A. Amiri, K.-T. Foerster, R. Jacob, and S. Schmid, “Charting the Algorithmic Complexity of Waypoint Routing,” ACM SIGCOMM Computer Communication Review, vol. 48, no. 1, 2018.
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@article{Amiri_CCR2018, TITLE = {Charting the Algorithmic Complexity of Waypoint Routing}, AUTHOR = {Amiri, Saeed Akhoondian and Foerster, Klaus-Tycho and Jacob, Riko and Schmid, Stefan}, LANGUAGE = {eng}, ISSN = {0146-4833}, DOI = {10.1145/3211852.3211859}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM SIGCOMM Computer Communication Review}, VOLUME = {48}, NUMBER = {1}, PAGES = {42--48}, }
Endnote
%0 Journal Article %A Amiri, Saeed Akhoondian %A Foerster, Klaus-Tycho %A Jacob, Riko %A Schmid, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Charting the Algorithmic Complexity of Waypoint Routing : %G eng %U http://hdl.handle.net/21.11116/0000-0002-7083-B %R 10.1145/3211852.3211859 %7 2018 %D 2018 %J ACM SIGCOMM Computer Communication Review %V 48 %N 1 %& 42 %P 42 - 48 %I ACM %C New York, NY %@ false
[163]
A. Antoniadis and K. Schewior, “A Tight Lower Bound for Online Convex Optimization with Switching Costs,” in Approximation and Online Algorithms (WAOA 2017), Vienna, Austria, 2018.
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@inproceedings{Antoniadis_WAOA2017, TITLE = {A Tight Lower Bound for Online Convex Optimization with Switching Costs}, AUTHOR = {Antoniadis, Antonios and Schewior, Kevin}, LANGUAGE = {eng}, ISBN = {978-3-319-89440-9}, DOI = {10.1007/978-3-319-89441-6_13}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Approximation and Online Algorithms (WAOA 2017)}, EDITOR = {Solis-Oba, Roberto and Fleischer, Rudolf}, PAGES = {164--165}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10787}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Schewior, Kevin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Tight Lower Bound for Online Convex Optimization with Switching Costs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F30-5 %R 10.1007/978-3-319-89441-6_13 %D 2018 %B 15th Workshop on Approximation and Online Algorithms %Z date of event: 2017-09-07 - 2017-09-08 %C Vienna, Austria %B Approximation and Online Algorithms %E Solis-Oba, Roberto; Fleischer, Rudolf %P 164 - 165 %I Springer %@ 978-3-319-89440-9 %B Lecture Notes in Computer Science %N 10787
[164]
A. Antoniadis, K. Fleszar, R. Hoeksma, and K. Schewior, “A PTAS for Euclidean TSP with Hyperplane Neighborhoods,” 2018. [Online]. Available: http://arxiv.org/abs/1804.03953. (arXiv: 1804.03953)
Abstract
In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN is known to be APX-hard, which gives rise to studying more tractable special cases of the problem. In this paper, we focus on the fundamental special case of regions that are hyperplanes in the $d$-dimensional Euclidean space. This case contrasts the much-better understood case of so-called fat regions. While for $d=2$ an exact algorithm with running time $O(n^5)$ is known, settling the exact approximability of the problem for $d=3$ has been repeatedly posed as an open question. To date, only an approximation algorithm with guarantee exponential in $d$ is known, and NP-hardness remains open. For arbitrary fixed $d$, we develop a Polynomial Time Approximation Scheme (PTAS) that works for both the tour and path version of the problem. Our algorithm is based on approximating the convex hull of the optimal tour by a convex polytope of bounded complexity. Such polytopes are represented as solutions of a sophisticated LP formulation, which we combine with the enumeration of crucial properties of the tour. As the approximation guarantee approaches $1$, our scheme adjusts the complexity of the considered polytopes accordingly. In the analysis of our approximation scheme, we show that our search space includes a sufficiently good approximation of the optimum. To do so, we develop a novel and general sparsification technique to transform an arbitrary convex polytope into one with a constant number of vertices and, in turn, into one of bounded complexity in the above sense. Hereby, we maintain important properties of the polytope.
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@online{Antoniadis_arXiv1804.03953, TITLE = {A {PTAS} for {E}uclidean {TSP} with Hyperplane Neighborhoods}, AUTHOR = {Antoniadis, Antonios and Fleszar, Krzysztof and Hoeksma, Ruben and Schewior, Kevin}, URL = {http://arxiv.org/abs/1804.03953}, EPRINT = {1804.03953}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN is known to be APX-hard, which gives rise to studying more tractable special cases of the problem. In this paper, we focus on the fundamental special case of regions that are hyperplanes in the $d$-dimensional Euclidean space. This case contrasts the much-better understood case of so-called fat regions. While for $d=2$ an exact algorithm with running time $O(n^5)$ is known, settling the exact approximability of the problem for $d=3$ has been repeatedly posed as an open question. To date, only an approximation algorithm with guarantee exponential in $d$ is known, and NP-hardness remains open. For arbitrary fixed $d$, we develop a Polynomial Time Approximation Scheme (PTAS) that works for both the tour and path version of the problem. Our algorithm is based on approximating the convex hull of the optimal tour by a convex polytope of bounded complexity. Such polytopes are represented as solutions of a sophisticated LP formulation, which we combine with the enumeration of crucial properties of the tour. As the approximation guarantee approaches $1$, our scheme adjusts the complexity of the considered polytopes accordingly. In the analysis of our approximation scheme, we show that our search space includes a sufficiently good approximation of the optimum. To do so, we develop a novel and general sparsification technique to transform an arbitrary convex polytope into one with a constant number of vertices and, in turn, into one of bounded complexity in the above sense. Hereby, we maintain important properties of the polytope.}, }
Endnote
%0 Report %A Antoniadis, Antonios %A Fleszar, Krzysztof %A Hoeksma, Ruben %A Schewior, Kevin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T A PTAS for Euclidean TSP with Hyperplane Neighborhoods : %U http://hdl.handle.net/21.11116/0000-0002-9F37-E %U http://arxiv.org/abs/1804.03953 %D 2018 %X In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN is known to be APX-hard, which gives rise to studying more tractable special cases of the problem. In this paper, we focus on the fundamental special case of regions that are hyperplanes in the $d$-dimensional Euclidean space. This case contrasts the much-better understood case of so-called fat regions. While for $d=2$ an exact algorithm with running time $O(n^5)$ is known, settling the exact approximability of the problem for $d=3$ has been repeatedly posed as an open question. To date, only an approximation algorithm with guarantee exponential in $d$ is known, and NP-hardness remains open. For arbitrary fixed $d$, we develop a Polynomial Time Approximation Scheme (PTAS) that works for both the tour and path version of the problem. Our algorithm is based on approximating the convex hull of the optimal tour by a convex polytope of bounded complexity. Such polytopes are represented as solutions of a sophisticated LP formulation, which we combine with the enumeration of crucial properties of the tour. As the approximation guarantee approaches $1$, our scheme adjusts the complexity of the considered polytopes accordingly. In the analysis of our approximation scheme, we show that our search space includes a sufficiently good approximation of the optimum. To do so, we develop a novel and general sparsification technique to transform an arbitrary convex polytope into one with a constant number of vertices and, in turn, into one of bounded complexity in the above sense. Hereby, we maintain important properties of the polytope. %K Computer Science, Data Structures and Algorithms, cs.DS
[165]
A. Antoniadis and A. Cristi, “Near Optimal Mechanism for Energy Aware Scheduling,” in Algorithmic Game Theory (SAGT 2018), Beijing, China, 2018.
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@inproceedings{Antoniadis_SAGT2017, TITLE = {Near Optimal Mechanism for Energy Aware Scheduling}, AUTHOR = {Antoniadis, Antonios and Cristi, Andr{\'e}s}, LANGUAGE = {eng}, ISBN = {978-3-319-99659-2}, DOI = {10.1007/978-3-319-99660-8_4}, PUBLISHER = {Springer}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Algorithmic Game Theory (SAGT 2018)}, EDITOR = {Deng, Xiaotie}, PAGES = {31--42}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {11059}, ADDRESS = {Beijing, China}, }
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%0 Conference Proceedings %A Antoniadis, Antonios %A Cristi, Andr&#233;s %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Near Optimal Mechanism for Energy Aware Scheduling : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F48-B %R 10.1007/978-3-319-99660-8_4 %D 2018 %B 11th International Symposium on Algorithmic Game Theory %Z date of event: 2018-09-11 - 2018-09-14 %C Beijing, China %B Algorithmic Game Theory %E Deng, Xiaotie %P 31 - 42 %I Springer %@ 978-3-319-99659-2 %B Lecture Notes in Computer Science %N 11059
[166]
A. Antoniadis, C. Fischer, and A. Tonnis, “A Collection of Lower Bounds for Online Matching on the Line,” in LATIN 2018: Theoretical Informatics, Buenos Aires, Argentinia, 2018.
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@inproceedings{AntoniadisLATIN2018, TITLE = {A Collection of Lower Bounds for Online Matching on the Line}, AUTHOR = {Antoniadis, Antonios and Fischer, Carsten and Tonnis, Andreas}, LANGUAGE = {eng}, ISBN = {978-3-319-77403-9}, DOI = {10.1007/978-3-319-77404-6_5}, PUBLISHER = {Springer}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {LATIN 2018: Theoretical Informatics}, EDITOR = {Bender, Michael A. and Farach-Colton, Mart{\'i}n and Mosteiro, Miguel A.}, PAGES = {52--65}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10807}, ADDRESS = {Buenos Aires, Argentinia}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Fischer, Carsten %A Tonnis, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Collection of Lower Bounds for Online Matching on the Line : %G eng %U http://hdl.handle.net/21.11116/0000-0002-5763-D %R 10.1007/978-3-319-77404-6_5 %D 2018 %B 13th Latin American Theoretical Informatics Symposium %Z date of event: 2018-04-16 - 2018-04-19 %C Buenos Aires, Argentinia %B LATIN 2018: Theoretical Informatics %E Bender, Michael A.; Farach-Colton, Mart&#237;n; Mosteiro, Miguel A. %P 52 - 65 %I Springer %@ 978-3-319-77403-9 %B Lecture Notes in Computer Science %N 10807
[167]
S. Arunachalam, S. Chakraborty, M. Koucký, N. Saurabh, and R. de Wolf, “Improved Bounds on Fourier Entropy and Min-entropy,” 2018. [Online]. Available: http://arxiv.org/abs/1809.09819. (arXiv: 1809.09819)
Abstract
Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that $H(\hat{f}^2)\leq C Inf(f)$, where $H(\hat{f}^2)$ is the Shannon entropy of the Fourier distribution of $f$ and $Inf(f)$ is the total influence of $f$. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if $H_{\infty}(\hat{f}^2)\leq C Inf(f)$, where $H_{\infty}(\hat{f}^2)$ is the min-entropy of the Fourier distribution. We show $H_{\infty}(\hat{f}^2)\leq 2C_{\min}^\oplus(f)$, where $C_{\min}^\oplus(f)$ is the minimum parity certificate complexity of $f$. We also show that for every $\epsilon\geq 0$, we have $H_{\infty}(\hat{f}^2)\leq 2\log (\|\hat{f}\|_{1,\epsilon}/(1-\epsilon))$, where $\|\hat{f}\|_{1,\epsilon}$ is the approximate spectral norm of $f$. As a corollary, we verify the FMEI conjecture for the class of read-$k$ $DNF$s (for constant $k$). 2) We show that $H(\hat{f}^2)\leq 2 aUC^\oplus(f)$, where $aUC^\oplus(f)$ is the average unambiguous parity certificate complexity of $f$. This improves upon Chakraborty et al. An important consequence of the FEI conjecture is the long-standing Mansour's conjecture. We show that a weaker version of FEI already implies Mansour's conjecture: is $H(\hat{f}^2)\leq C \min\{C^0(f),C^1(f)\}$?, where $C^0(f), C^1(f)$ are the 0- and 1-certificate complexities of $f$, respectively. 3) We study what FEI implies about the structure of polynomials that 1/3-approximate a Boolean function. We pose a conjecture (which is implied by FEI): no "flat" degree-$d$ polynomial of sparsity $2^{\omega(d)}$ can 1/3-approximate a Boolean function. We prove this conjecture unconditionally for a particular class of polynomials.
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@online{Arunachalam_arXiv1809.09819, TITLE = {{Improved Bounds on Fourier Entropy and Min-entropy}}, AUTHOR = {Arunachalam, Srinivasan and Chakraborty, Sourav and Kouck{\'y}, Michal and Saurabh, Nitin and de Wolf, Ronald}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1809.09819}, EPRINT = {1809.09819}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that $H(\hat{f}^2)\leq C Inf(f)$, where $H(\hat{f}^2)$ is the Shannon entropy of the Fourier distribution of $f$ and $Inf(f)$ is the total influence of $f$. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if $H_{\infty}(\hat{f}^2)\leq C Inf(f)$, where $H_{\infty}(\hat{f}^2)$ is the min-entropy of the Fourier distribution. We show $H_{\infty}(\hat{f}^2)\leq 2C_{\min}^\oplus(f)$, where $C_{\min}^\oplus(f)$ is the minimum parity certificate complexity of $f$. We also show that for every $\epsilon\geq 0$, we have $H_{\infty}(\hat{f}^2)\leq 2\log (\|\hat{f}\|_{1,\epsilon}/(1-\epsilon))$, where $\|\hat{f}\|_{1,\epsilon}$ is the approximate spectral norm of $f$. As a corollary, we verify the FMEI conjecture for the class of read-$k$ $DNF$s (for constant $k$). 2) We show that $H(\hat{f}^2)\leq 2 aUC^\oplus(f)$, where $aUC^\oplus(f)$ is the average unambiguous parity certificate complexity of $f$. This improves upon Chakraborty et al. An important consequence of the FEI conjecture is the long-standing Mansour's conjecture. We show that a weaker version of FEI already implies Mansour's conjecture: is $H(\hat{f}^2)\leq C \min\{C^0(f),C^1(f)\}$?, where $C^0(f), C^1(f)$ are the 0- and 1-certificate complexities of $f$, respectively. 3) We study what FEI implies about the structure of polynomials that 1/3-approximate a Boolean function. We pose a conjecture (which is implied by FEI): no "flat" degree-$d$ polynomial of sparsity $2^{\omega(d)}$ can 1/3-approximate a Boolean function. We prove this conjecture unconditionally for a particular class of polynomials.}, }
Endnote
%0 Report %A Arunachalam, Srinivasan %A Chakraborty, Sourav %A Kouck&#253;, Michal %A Saurabh, Nitin %A de Wolf, Ronald %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Improved Bounds on Fourier Entropy and Min-entropy : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AA5A-A %U http://arxiv.org/abs/1809.09819 %D 2018 %X Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that $H(\hat{f}^2)\leq C Inf(f)$, where $H(\hat{f}^2)$ is the Shannon entropy of the Fourier distribution of $f$ and $Inf(f)$ is the total influence of $f$. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if $H_{\infty}(\hat{f}^2)\leq C Inf(f)$, where $H_{\infty}(\hat{f}^2)$ is the min-entropy of the Fourier distribution. We show $H_{\infty}(\hat{f}^2)\leq 2C_{\min}^\oplus(f)$, where $C_{\min}^\oplus(f)$ is the minimum parity certificate complexity of $f$. We also show that for every $\epsilon\geq 0$, we have $H_{\infty}(\hat{f}^2)\leq 2\log (\|\hat{f}\|_{1,\epsilon}/(1-\epsilon))$, where $\|\hat{f}\|_{1,\epsilon}$ is the approximate spectral norm of $f$. As a corollary, we verify the FMEI conjecture for the class of read-$k$ $DNF$s (for constant $k$). 2) We show that $H(\hat{f}^2)\leq 2 aUC^\oplus(f)$, where $aUC^\oplus(f)$ is the average unambiguous parity certificate complexity of $f$. This improves upon Chakraborty et al. An important consequence of the FEI conjecture is the long-standing Mansour's conjecture. We show that a weaker version of FEI already implies Mansour's conjecture: is $H(\hat{f}^2)\leq C \min\{C^0(f),C^1(f)\}$?, where $C^0(f), C^1(f)$ are the 0- and 1-certificate complexities of $f$, respectively. 3) We study what FEI implies about the structure of polynomials that 1/3-approximate a Boolean function. We pose a conjecture (which is implied by FEI): no "flat" degree-$d$ polynomial of sparsity $2^{\omega(d)}$ can 1/3-approximate a Boolean function. We prove this conjecture unconditionally for a particular class of polynomials. %K Computer Science, Computational Complexity, cs.CC
[168]
J. Baldus and K. Bringmann, “A Fast Implementation of Near Neighbors Queries for Fréchet Distance (GIS Cup),” 2018. [Online]. Available: http://arxiv.org/abs/1803.00806. (arXiv: 1803.00806)
Abstract
This paper describes an implementation of fast near-neighbours queries (also known as range searching) with respect to the Fr\'echet distance. The algorithm is designed to be efficient on practical data such as GPS trajectories. Our approach is to use a quadtree data structure to enumerate all curves in the database that have similar start and endpoints as the query curve. On these curves we run positive and negative filters to narrow the set of potential results. Only for those trajectories where these heuristics fail, we compute the Fr\'echet distance exactly, by running a novel recursive variant of the classic free-space diagram algorithm. Our implementation won the ACM SIGSPATIAL GIS Cup 2017.
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@online{Baldus_arXiv1803.00806, TITLE = {A Fast Implementation of Near Neighbors Queries for {F}r\'{e}chet Distance ({GIS Cup})}, AUTHOR = {Baldus, Julian and Bringmann, Karl}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1803.00806}, EPRINT = {1803.00806}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {This paper describes an implementation of fast near-neighbours queries (also known as range searching) with respect to the Fr\'echet distance. The algorithm is designed to be efficient on practical data such as GPS trajectories. Our approach is to use a quadtree data structure to enumerate all curves in the database that have similar start and endpoints as the query curve. On these curves we run positive and negative filters to narrow the set of potential results. Only for those trajectories where these heuristics fail, we compute the Fr\'echet distance exactly, by running a novel recursive variant of the classic free-space diagram algorithm. Our implementation won the ACM SIGSPATIAL GIS Cup 2017.}, }
Endnote
%0 Report %A Baldus, Julian %A Bringmann, Karl %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Fast Implementation of Near Neighbors Queries for Fr&#233;chet Distance (GIS Cup) : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E1A-E %U http://arxiv.org/abs/1803.00806 %D 2018 %X This paper describes an implementation of fast near-neighbours queries (also known as range searching) with respect to the Fr\'echet distance. The algorithm is designed to be efficient on practical data such as GPS trajectories. Our approach is to use a quadtree data structure to enumerate all curves in the database that have similar start and endpoints as the query curve. On these curves we run positive and negative filters to narrow the set of potential results. Only for those trajectories where these heuristics fail, we compute the Fr\'echet distance exactly, by running a novel recursive variant of the classic free-space diagram algorithm. Our implementation won the ACM SIGSPATIAL GIS Cup 2017. %K Computer Science, Computational Geometry, cs.CG
[169]
G. Ballard, C. Ikenmeyer, J. M. Landsberg, and N. Ryder, “The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices,” 2018. [Online]. Available: http://arxiv.org/abs/1801.00843. (arXiv: 1801.00843)
Abstract
This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12. We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of $M_{\langle n\rangle}$ for larger $n$.
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@online{Ballard_arXiv1801.00843, TITLE = {{The Geometry of Rank Decompositions of Matrix Multiplication II: $3\times 3$ Matrices}}, AUTHOR = {Ballard, Grey and Ikenmeyer, Christian and Landsberg, J. M. and Ryder, Nick}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1801.00843}, EPRINT = {1801.00843}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12. We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of $M_{\langle n\rangle}$ for larger $n$.}, }
Endnote
%0 Report %A Ballard, Grey %A Ikenmeyer, Christian %A Landsberg, J. M. %A Ryder, Nick %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3F64-9 %U http://arxiv.org/abs/1801.00843 %D 2018 %X This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12. We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of $M_{\langle n\rangle}$ for larger $n$. %K Computer Science, Computational Complexity, cs.CC,
[170]
F. Ban, V. Bhattiprolu, K. Bringmann, P. Kolev, E. Lee, and D. P. Woodruff, “A PTAS for l p-Low Rank Approximation,” 2018. [Online]. Available: http://arxiv.org/abs/1807.06101. (arXiv: 1807.06101)
Abstract
A number of recent works have studied algorithms for entrywise $\ell_p$-low rank approximation, namely, algorithms which given an $n \times d$ matrix $A$ (with $n \geq d$), output a rank-$k$ matrix $B$ minimizing $\|A-B\|_p^p=\sum_{i,j}|A_{i,j}-B_{i,j}|^p$ when $p > 0$; and $\|A-B\|_0=\sum_{i,j}[A_{i,j}\neq B_{i,j}]$ for $p=0$. On the algorithmic side, for $p \in (0,2)$, we give the first $(1+\epsilon)$-approximation algorithm running in time $n^{\text{poly}(k/\epsilon)}$. Further, for $p = 0$, we give the first almost-linear time approximation scheme for what we call the Generalized Binary $\ell_0$-Rank-$k$ problem. Our algorithm computes $(1+\epsilon)$-approximation in time $(1/\epsilon)^{2^{O(k)}/\epsilon^{2}} \cdot nd^{1+o(1)}$. On the hardness of approximation side, for $p \in (1,2)$, assuming the Small Set Expansion Hypothesis and the Exponential Time Hypothesis (ETH), we show that there exists $\delta := \delta(\alpha) > 0$ such that the entrywise $\ell_p$-Rank-$k$ problem has no $\alpha$-approximation algorithm running in time $2^{k^{\delta}}$.
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@online{Ban_arXiv1807.06101, TITLE = {A {PTAS} for $\ell_p$-Low Rank Approximation}, AUTHOR = {Ban, Frank and Bhattiprolu, Vijay and Bringmann, Karl and Kolev, Pavel and Lee, Euiwoong and Woodruff, David P.}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1807.06101}, EPRINT = {1807.06101}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {A number of recent works have studied algorithms for entrywise $\ell_p$-low rank approximation, namely, algorithms which given an $n \times d$ matrix $A$ (with $n \geq d$), output a rank-$k$ matrix $B$ minimizing $\|A-B\|_p^p=\sum_{i,j}|A_{i,j}-B_{i,j}|^p$ when $p > 0$; and $\|A-B\|_0=\sum_{i,j}[A_{i,j}\neq B_{i,j}]$ for $p=0$. On the algorithmic side, for $p \in (0,2)$, we give the first $(1+\epsilon)$-approximation algorithm running in time $n^{\text{poly}(k/\epsilon)}$. Further, for $p = 0$, we give the first almost-linear time approximation scheme for what we call the Generalized Binary $\ell_0$-Rank-$k$ problem. Our algorithm computes $(1+\epsilon)$-approximation in time $(1/\epsilon)^{2^{O(k)}/\epsilon^{2}} \cdot nd^{1+o(1)}$. On the hardness of approximation side, for $p \in (1,2)$, assuming the Small Set Expansion Hypothesis and the Exponential Time Hypothesis (ETH), we show that there exists $\delta := \delta(\alpha) > 0$ such that the entrywise $\ell_p$-Rank-$k$ problem has no $\alpha$-approximation algorithm running in time $2^{k^{\delta}}$.}, }
Endnote
%0 Report %A Ban, Frank %A Bhattiprolu, Vijay %A Bringmann, Karl %A Kolev, Pavel %A Lee, Euiwoong %A Woodruff, David P. %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A PTAS for l p-Low Rank Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9D17-4 %U http://arxiv.org/abs/1807.06101 %D 2018 %X A number of recent works have studied algorithms for entrywise $\ell_p$-low rank approximation, namely, algorithms which given an $n \times d$ matrix $A$ (with $n \geq d$), output a rank-$k$ matrix $B$ minimizing $\|A-B\|_p^p=\sum_{i,j}|A_{i,j}-B_{i,j}|^p$ when $p > 0$; and $\|A-B\|_0=\sum_{i,j}[A_{i,j}\neq B_{i,j}]$ for $p=0$. On the algorithmic side, for $p \in (0,2)$, we give the first $(1+\epsilon)$-approximation algorithm running in time $n^{\text{poly}(k/\epsilon)}$. Further, for $p = 0$, we give the first almost-linear time approximation scheme for what we call the Generalized Binary $\ell_0$-Rank-$k$ problem. Our algorithm computes $(1+\epsilon)$-approximation in time $(1/\epsilon)^{2^{O(k)}/\epsilon^{2}} \cdot nd^{1+o(1)}$. On the hardness of approximation side, for $p \in (1,2)$, assuming the Small Set Expansion Hypothesis and the Exponential Time Hypothesis (ETH), we show that there exists $\delta := \delta(\alpha) > 0$ such that the entrywise $\ell_p$-Rank-$k$ problem has no $\alpha$-approximation algorithm running in time $2^{k^{\delta}}$. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,Computer Science, Learning, cs.LG
[171]
L. Becchetti, V. Bonifaci, and E. Natale, “Pooling or Sampling: Collective Dynamics for Electrical Flow Estimation,” in AAMAS’18, 17th International Conference on Autonomous Agents and MultiAgent Systems, Stockholm, Sweden, 2018.
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@inproceedings{Becchetti_AAMAS2018, TITLE = {Pooling or Sampling: {C}ollective Dynamics for Electrical Flow Estimation}, AUTHOR = {Becchetti, Luca and Bonifaci, Vincenzo and Natale, Emanuele}, LANGUAGE = {eng}, ISBN = {978-1-4503-5649-7}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {AAMAS'18, 17th International Conference on Autonomous Agents and MultiAgent Systems}, PAGES = {1576--1584}, ADDRESS = {Stockholm, Sweden}, }
Endnote
%0 Conference Proceedings %A Becchetti, Luca %A Bonifaci, Vincenzo %A Natale, Emanuele %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Pooling or Sampling: Collective Dynamics for Electrical Flow Estimation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A953-2 %D 2018 %B 17th International Conference on Autonomous Agents and MultiAgent Systems %Z date of event: 2018-07-10 - 2018-07-15 %C Stockholm, Sweden %B AAMAS'18 %P 1576 - 1584 %I ACM %@ 978-1-4503-5649-7
[172]
L. Becchetti, A. Clementi, E. Natale, F. Pasquale, and L. Trevisan, “Finding a Bounded-Degree Expander Inside a Dense One,” 2018. [Online]. Available: http://arxiv.org/abs/1811.10316. (arXiv: 1811.10316)
Abstract
It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also an expander. As with other consequences of the MSS theorem, it is not clear how one would explicitly construct such a subgraph. We show that such a subgraph (although with quantitatively weaker expansion and near-regularity properties than those predicted by MSS) can be constructed with high probability in linear time, via a simple algorithm. Our algorithm allows a distributed implementation that runs in $\mathcal O(\log n)$ rounds and does $\bigO(n)$ total work with high probability. The analysis of the algorithm is complicated by the complex dependencies that arise between edges and between choices made in different rounds. We sidestep these difficulties by following the combinatorial approach of counting the number of possible random choices of the algorithm which lead to failure. We do so by a compression argument showing that such random choices can be encoded with a non-trivial compression. Our algorithm bears some similarity to the way agents construct a communication graph in a peer-to-peer network, and, in the bipartite case, to the way agents select servers in blockchain protocols.
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@online{Becchetti_arXiv1811.10316, TITLE = {Finding a Bounded-Degree Expander Inside a Dense One}, AUTHOR = {Becchetti, Luca and Clementi, Andrea and Natale, Emanuele and Pasquale, Francesco and Trevisan, Luca}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1811.10316}, EPRINT = {1811.10316}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also an expander. As with other consequences of the MSS theorem, it is not clear how one would explicitly construct such a subgraph. We show that such a subgraph (although with quantitatively weaker expansion and near-regularity properties than those predicted by MSS) can be constructed with high probability in linear time, via a simple algorithm. Our algorithm allows a distributed implementation that runs in $\mathcal O(\log n)$ rounds and does $\bigO(n)$ total work with high probability. The analysis of the algorithm is complicated by the complex dependencies that arise between edges and between choices made in different rounds. We sidestep these difficulties by following the combinatorial approach of counting the number of possible random choices of the algorithm which lead to failure. We do so by a compression argument showing that such random choices can be encoded with a non-trivial compression. Our algorithm bears some similarity to the way agents construct a communication graph in a peer-to-peer network, and, in the bipartite case, to the way agents select servers in blockchain protocols.}, }
Endnote
%0 Report %A Becchetti, Luca %A Clementi, Andrea %A Natale, Emanuele %A Pasquale, Francesco %A Trevisan, Luca %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Finding a Bounded-Degree Expander Inside a Dense One : %G eng %U http://hdl.handle.net/21.11116/0000-0002-B967-A %U http://arxiv.org/abs/1811.10316 %D 2018 %X It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also an expander. As with other consequences of the MSS theorem, it is not clear how one would explicitly construct such a subgraph. We show that such a subgraph (although with quantitatively weaker expansion and near-regularity properties than those predicted by MSS) can be constructed with high probability in linear time, via a simple algorithm. Our algorithm allows a distributed implementation that runs in $\mathcal O(\log n)$ rounds and does $\bigO(n)$ total work with high probability. The analysis of the algorithm is complicated by the complex dependencies that arise between edges and between choices made in different rounds. We sidestep these difficulties by following the combinatorial approach of counting the number of possible random choices of the algorithm which lead to failure. We do so by a compression argument showing that such random choices can be encoded with a non-trivial compression. Our algorithm bears some similarity to the way agents construct a communication graph in a peer-to-peer network, and, in the bipartite case, to the way agents select servers in blockchain protocols. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[173]
L. Becchetti, A. Clementi, P. Manurangsi, E. Natale, F. Pasquale, P. Raghavendra, and L. Trevisan, “Average Whenever You Meet: Opportunistic Protocols for Community Detection,” in 26th Annual European Symposium on Algorithms (ESA 2018), Helsinki, Finland, 2018.
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@inproceedings{Becchetti_ESA2018, TITLE = {Average Whenever You Meet: {O}pportunistic Protocols for Community Detection}, AUTHOR = {Becchetti, Luca and Clementi, Andrea and Manurangsi, Pasin and Natale, Emanuele and Pasquale, Francesco and Raghavendra, Prasad and Trevisan, Luca}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-081-1}, URL = {urn:nbn:de:0030-drops-94705}, DOI = {10.4230/LIPIcs.ESA.2018.7}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {26th Annual European Symposium on Algorithms (ESA 2018)}, EDITOR = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, PAGES = {1--13}, EID = {7}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {112}, ADDRESS = {Helsinki, Finland}, }
Endnote
%0 Conference Proceedings %A Becchetti, Luca %A Clementi, Andrea %A Manurangsi, Pasin %A Natale, Emanuele %A Pasquale, Francesco %A Raghavendra, Prasad %A Trevisan, Luca %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Average Whenever You Meet: Opportunistic Protocols for Community Detection : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A957-E %R 10.4230/LIPIcs.ESA.2018.7 %U urn:nbn:de:0030-drops-94705 %D 2018 %B 26th Annual European Symposium on Algorithms %Z date of event: 2018-08-20 - 2018-08-22 %C Helsinki, Finland %B 26th Annual European Symposium on Algorithms %E Azar, Yossi; Bast, Hannah; Herman, Grzegorz %P 1 - 13 %Z sequence number: 7 %I Schloss Dagstuhl %@ 978-3-95977-081-1 %B Leibniz International Proceedings in Informatics %N 112 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9470/http://drops.dagstuhl.de/doku/urheberrecht1.html
[174]
R. Becker, M. Sagraloff, V. Sharma, and C. Yap, “A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration,” Journal of Symbolic Computation, vol. 86, 2018.
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@article{Becker2017JSC, TITLE = {A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the {Pellet} Test and {Newton} Iteration}, AUTHOR = {Becker, Ruben and Sagraloff, Michael and Sharma, Vikram and Yap, Chee}, LANGUAGE = {eng}, ISSN = {0747-7171}, DOI = {10.1016/j.jsc.2017.03.009}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Journal of Symbolic Computation}, VOLUME = {86}, PAGES = {51--96}, }
Endnote
%0 Journal Article %A Becker, Ruben %A Sagraloff, Michael %A Sharma, Vikram %A Yap, Chee %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5717-8 %R 10.1016/j.jsc.2017.03.009 %7 2017-03-29 %D 2018 %J Journal of Symbolic Computation %V 86 %& 51 %P 51 - 96 %I Elsevier %C Amsterdam %@ false
[175]
A. Bhattacharya, D. Issac, R. Jaiswal, and A. Kumar, “Sampling in Space Restricted Settings,” Algorithmica, vol. 80, no. 5, 2018.
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@article{Bhattacharya2018, TITLE = {Sampling in Space Restricted Settings}, AUTHOR = {Bhattacharya, Anup and Issac, Davis and Jaiswal, Ragesh and Kumar, Amit}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-017-0335-z}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Algorithmica}, VOLUME = {80}, NUMBER = {5}, PAGES = {1439--1458}, }
Endnote
%0 Journal Article %A Bhattacharya, Anup %A Issac, Davis %A Jaiswal, Ragesh %A Kumar, Amit %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Sampling in Space Restricted Settings : %G eng %U http://hdl.handle.net/21.11116/0000-0001-2C37-1 %R 10.1007/s00453-017-0335-z %7 2017 %D 2018 %J Algorithmica %V 80 %N 5 %& 1439 %P 1439 - 1458 %I Springer-Verlag %C New York %@ false
[176]
M. Bläser, C. Ikenmeyer, G. Jindal, and V. Lysikov, “Generalized Matrix Completion and Algebraic Natural Proofs Contact Add Comment RSS-Feed,” Electronic Colloquium on Computational Complexity (ECCC): Report Series, vol. 18–064, 2018.
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@article{BlaeserCCC18_064, TITLE = {Generalized Matrix Completion and Algebraic Natural Proofs Contact Add Comment {RSS}-Feed}, AUTHOR = {Bl{\"a}ser, Markus and Ikenmeyer, Christian and Jindal, Gorav and Lysikov, Vladimir}, LANGUAGE = {eng}, ISSN = {1433-8092}, PUBLISHER = {Hasso-Plattner-Institut f{\"u}r Softwaretechnik GmbH}, ADDRESS = {Potsdam}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, JOURNAL = {Electronic Colloquium on Computational Complexity (ECCC): Report Series}, VOLUME = {18-064}, PAGES = {1--27}, }
Endnote
%0 Journal Article %A Bl&#228;ser, Markus %A Ikenmeyer, Christian %A Jindal, Gorav %A Lysikov, Vladimir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Generalized Matrix Completion and Algebraic Natural Proofs Contact Add Comment RSS-Feed : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3F5F-0 %7 2018 %D 2018 %J Electronic Colloquium on Computational Complexity (ECCC): Report Series %V 18-064 %& 1 %P 1 - 27 %I Hasso-Plattner-Institut f&#252;r Softwaretechnik GmbH %C Potsdam %@ false %U https://eccc.weizmann.ac.il/report/2018/064/
[177]
M. Bläser, C. Ikenmeyer, G. Jindal, and V. Lysikov, “Generalized Matrix Completion and Algebraic Natural Proofs,” in STOC’18, 50th Annual ACM SIGACT Symposium on Theory of Computing, Los Angeles, CA, USA, 2018.
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@inproceedings{Blaeser_STOC2018, TITLE = {Generalized Matrix Completion and Algebraic Natural Proofs}, AUTHOR = {Bl{\"a}ser, Markus and Ikenmeyer, Christian and Jindal, Gorav and Lysikov, Vladimir}, LANGUAGE = {eng}, ISBN = {978-1-4503-5559-9}, DOI = {10.1145/3188745.3188832}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {STOC'18, 50th Annual ACM SIGACT Symposium on Theory of Computing}, PAGES = {1193--1206}, ADDRESS = {Los Angeles, CA, USA}, }
Endnote
%0 Conference Proceedings %A Bl&#228;ser, Markus %A Ikenmeyer, Christian %A Jindal, Gorav %A Lysikov, Vladimir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Generalized Matrix Completion and Algebraic Natural Proofs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-17DF-A %R 10.1145/3188745.3188832 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 1193 - 1206 %I ACM %@ 978-1-4503-5559-9
[178]
M. Bläser, G. Jindal, and A. Pandey, “A Deterministic PTAS for Commutative Rank of Matrix Spaces,” Theory of Computing, vol. 14, 2018.
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@article{Blaeser_ToC18, TITLE = {A Deterministic {PTAS} for Commutative Rank of Matrix Spaces}, AUTHOR = {Bl{\"a}ser, Markus and Jindal, Gorav and Pandey, Anurag}, LANGUAGE = {eng}, ISSN = {1557-2862}, DOI = {10.4086/toc.2018.v014a003}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, JOURNAL = {Theory of Computing}, VOLUME = {14}, PAGES = {1--21}, EID = {3}, }
Endnote
%0 Journal Article %A Bl&#228;ser, Markus %A Jindal, Gorav %A Pandey, Anurag %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Deterministic PTAS for Commutative Rank of Matrix Spaces : %G eng %U http://hdl.handle.net/21.11116/0000-0002-B48E-3 %R 10.4086/toc.2018.v014a003 %7 2018 %D 2018 %J Theory of Computing %V 14 %& 1 %P 1 - 21 %Z sequence number: 3 %@ false
[179]
L. Boczkowski, E. Natale, O. Feinerman, and A. Korman, “Limits on Reliable Information Flows through Stochastic Populations,” PLoS Computational Biology, vol. 14, no. 6, 2018.
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@article{Boczkowski2018, TITLE = {Limits on Reliable Information Flows through Stochastic Populations}, AUTHOR = {Boczkowski, Lucas and Natale, Emanuele and Feinerman, Ofer and Korman, Amos}, LANGUAGE = {eng}, ISSN = {1553-734X}, DOI = {10.1371/journal.pcbi.1006195}, PUBLISHER = {Public Library of Science}, ADDRESS = {San Francisco, CA}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, JOURNAL = {PLoS Computational Biology}, VOLUME = {14}, NUMBER = {6}, EID = {e1006195}, }
Endnote
%0 Journal Article %A Boczkowski, Lucas %A Natale, Emanuele %A Feinerman, Ofer %A Korman, Amos %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Limits on Reliable Information Flows through Stochastic Populations : %G eng %U http://hdl.handle.net/21.11116/0000-0001-999D-2 %R 10.1371/journal.pcbi.1006195 %7 2018 %D 2018 %J PLoS Computational Biology %V 14 %N 6 %Z sequence number: e1006195 %I Public Library of Science %C San Francisco, CA %@ false
[180]
L. Boczkowski, O. Feinerman, A. Korman, and E. Natale, “Limits for Rumor Spreading in Stochastic Populations,” in 9th Innovations in Theoretical Computer Science (ITCS 2018), Cambridge, MA, USA, 2018.
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@inproceedings{Boczkowski_ITCS2018, TITLE = {Limits for Rumor Spreading in Stochastic Populations}, AUTHOR = {Boczkowski, Lucas and Feinerman, Ofer and Korman, Amos and Natale, Emanuele}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-060-6}, URL = {urn:nbn:de:0030-drops-83207}, DOI = {10.4230/LIPIcs.ITCS.2018.49}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {9th Innovations in Theoretical Computer Science (ITCS 2018)}, EDITOR = {Karlin, Anna R.}, PAGES = {1--21}, EID = {49}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {94}, ADDRESS = {Cambridge, MA, USA}, }
Endnote
%0 Conference Proceedings %A Boczkowski, Lucas %A Feinerman, Ofer %A Korman, Amos %A Natale, Emanuele %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Limits for Rumor Spreading in Stochastic Populations : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A962-1 %R 10.4230/LIPIcs.ITCS.2018.49 %U urn:nbn:de:0030-drops-83207 %D 2018 %B 9th Innovations in Theoretical Computer Science %Z date of event: 2018-01-11 - 2018-01-14 %C Cambridge, MA, USA %B 9th Innovations in Theoretical Computer Science %E Karlin, Anna R. %P 1 - 21 %Z sequence number: 49 %I Schloss Dagstuhl %@ 978-3-95977-060-6 %B Leibniz International Proceedings in Informatics %N 94 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/8320/http://drops.dagstuhl.de/opus/volltexte/2018/8320/
[181]
J.-D. Boissonnat, R. Dyer, and A. Ghosh, “Delaunay Triangulation of Manifolds,” Foundations of Computational Mathematics, vol. 18, no. 2, 2018.
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@article{Boissonnat2017, TITLE = {Delaunay Triangulation of Manifolds}, AUTHOR = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit}, LANGUAGE = {eng}, ISSN = {1615-3375}, DOI = {10.1007/s10208-017-9344-1}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Foundations of Computational Mathematics}, VOLUME = {18}, NUMBER = {2}, PAGES = {399--431}, }
Endnote
%0 Journal Article %A Boissonnat, Jean-Daniel %A Dyer, Ramsay %A Ghosh, Arijit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Delaunay Triangulation of Manifolds : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-7945-0 %R 10.1007/s10208-017-9344-1 %7 2017-02-01 %D 2018 %J Foundations of Computational Mathematics %V 18 %N 2 %& 399 %P 399 - 431 %I Springer %C New York, NY %@ false
[182]
K. Bringmann and M. Künnemann, “Multivariate Fine-Grained Complexity of Longest Common Subsequence,” 2018. [Online]. Available: http://arxiv.org/abs/1803.00938. (arXiv: 1803.00938)
Abstract
We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent, no $O(n^{2-\varepsilon})$-time algorithm is known. Recent work indeed shows that such an algorithm would refute the Strong Exponential Time Hypothesis (SETH) [Abboud, Backurs, Vassilevska Williams + Bringmann, K\"unnemann FOCS'15]. Despite the quadratic-time barrier, for over 40 years an enduring scientific interest continued to produce fast algorithms for LCS and its variations. Particular attention was put into identifying and exploiting input parameters that yield strongly subquadratic time algorithms for special cases of interest, e.g., differential file comparison. This line of research was successfully pursued until 1990, at which time significant improvements came to a halt. In this paper, using the lens of fine-grained complexity, our goal is to (1) justify the lack of further improvements and (2) determine whether some special cases of LCS admit faster algorithms than currently known. To this end, we provide a systematic study of the multivariate complexity of LCS, taking into account all parameters previously discussed in the literature: the input size $n:=\max\{|x|,|y|\}$, the length of the shorter string $m:=\min\{|x|,|y|\}$, the length $L$ of an LCS of $x$ and $y$, the numbers of deletions $\delta := m-L$ and $\Delta := n-L$, the alphabet size, as well as the numbers of matching pairs $M$ and dominant pairs $d$. For any class of instances defined by fixing each parameter individually to a polynomial in terms of the input size, we prove a SETH-based lower bound matching one of three known algorithms. Specifically, we determine the optimal running time for LCS under SETH as $(n+\min\{d, \delta \Delta, \delta m\})^{1\pm o(1)}$. [...]
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@online{Bringmann_arXiv1803.00938, TITLE = {Multivariate Fine-Grained Complexity of Longest Common Subsequence}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1803.00938}, EPRINT = {1803.00938}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent, no $O(n^{2-\varepsilon})$-time algorithm is known. Recent work indeed shows that such an algorithm would refute the Strong Exponential Time Hypothesis (SETH) [Abboud, Backurs, Vassilevska Williams + Bringmann, K\"unnemann FOCS'15]. Despite the quadratic-time barrier, for over 40 years an enduring scientific interest continued to produce fast algorithms for LCS and its variations. Particular attention was put into identifying and exploiting input parameters that yield strongly subquadratic time algorithms for special cases of interest, e.g., differential file comparison. This line of research was successfully pursued until 1990, at which time significant improvements came to a halt. In this paper, using the lens of fine-grained complexity, our goal is to (1) justify the lack of further improvements and (2) determine whether some special cases of LCS admit faster algorithms than currently known. To this end, we provide a systematic study of the multivariate complexity of LCS, taking into account all parameters previously discussed in the literature: the input size $n:=\max\{|x|,|y|\}$, the length of the shorter string $m:=\min\{|x|,|y|\}$, the length $L$ of an LCS of $x$ and $y$, the numbers of deletions $\delta := m-L$ and $\Delta := n-L$, the alphabet size, as well as the numbers of matching pairs $M$ and dominant pairs $d$. For any class of instances defined by fixing each parameter individually to a polynomial in terms of the input size, we prove a SETH-based lower bound matching one of three known algorithms. Specifically, we determine the optimal running time for LCS under SETH as $(n+\min\{d, \delta \Delta, \delta m\})^{1\pm o(1)}$. [...]}, }
Endnote
%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Multivariate Fine-Grained Complexity of Longest Common Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E02-8 %U http://arxiv.org/abs/1803.00938 %D 2018 %X We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent, no $O(n^{2-\varepsilon})$-time algorithm is known. Recent work indeed shows that such an algorithm would refute the Strong Exponential Time Hypothesis (SETH) [Abboud, Backurs, Vassilevska Williams + Bringmann, K\"unnemann FOCS'15]. Despite the quadratic-time barrier, for over 40 years an enduring scientific interest continued to produce fast algorithms for LCS and its variations. Particular attention was put into identifying and exploiting input parameters that yield strongly subquadratic time algorithms for special cases of interest, e.g., differential file comparison. This line of research was successfully pursued until 1990, at which time significant improvements came to a halt. In this paper, using the lens of fine-grained complexity, our goal is to (1) justify the lack of further improvements and (2) determine whether some special cases of LCS admit faster algorithms than currently known. To this end, we provide a systematic study of the multivariate complexity of LCS, taking into account all parameters previously discussed in the literature: the input size $n:=\max\{|x|,|y|\}$, the length of the shorter string $m:=\min\{|x|,|y|\}$, the length $L$ of an LCS of $x$ and $y$, the numbers of deletions $\delta := m-L$ and $\Delta := n-L$, the alphabet size, as well as the numbers of matching pairs $M$ and dominant pairs $d$. For any class of instances defined by fixing each parameter individually to a polynomial in terms of the input size, we prove a SETH-based lower bound matching one of three known algorithms. Specifically, we determine the optimal running time for LCS under SETH as $(n+\min\{d, \delta \Delta, \delta m\})^{1\pm o(1)}$. [...] %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[183]
K. Bringmann and M. Künnemann, “Multivariate Fine-Grained Complexity of Longest Common Subsequence,” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), New Orleans, LA, USA, 2018.
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@inproceedings{Bringmann_SODA18, TITLE = {Multivariate Fine-Grained Complexity of Longest Common Subsequence}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, ISBN = {978-1-61197-503-1}, DOI = {10.1137/1.9781611975031.79}, PUBLISHER = {SIAM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)}, EDITOR = {Czumaj, Artur}, PAGES = {1216--1235}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Multivariate Fine-Grained Complexity of Longest Common Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0000-3F0E-C %R 10.1137/1.9781611975031.79 %D 2018 %B Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2018-01-07 - 2018-01-10 %C New Orleans, LA, USA %B Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %E Czumaj, Artur %P 1216 - 1235 %I SIAM %@ 978-1-61197-503-1
[184]
K. Bringmann, T. Husfeldt, and M. Magnusson, “Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth,” 2018. [Online]. Available: http://arxiv.org/abs/1805.07135. (arXiv: 1805.07135)
Abstract
We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\cdot \binom{k+\lceil\log n\rceil}{k} \cdot 2^k k^2 \log n)$, where $k$ is the treewidth of the graph. For every $\epsilon>0$, this bound is $n^{1+\epsilon}\exp O(k)$, which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) in the regime of non-constant treewidth can be improved by revisiting the analysis of orthogonal range searching, improving bounds of the form $\log^d n$ to $\binom{d+\lceil\log n\rceil}{d}$, as originally observed by Monier (J. Alg. 1980). We also investigate the parameterization by vertex cover number.
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@online{Bringmann_arXiv1805.07135, TITLE = {Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth}, AUTHOR = {Bringmann, Karl and Husfeldt, Thore and Magnusson, M{\aa}ns}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1805.07135}, EPRINT = {1805.07135}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\cdot \binom{k+\lceil\log n\rceil}{k} \cdot 2^k k^2 \log n)$, where $k$ is the treewidth of the graph. For every $\epsilon>0$, this bound is $n^{1+\epsilon}\exp O(k)$, which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) in the regime of non-constant treewidth can be improved by revisiting the analysis of orthogonal range searching, improving bounds of the form $\log^d n$ to $\binom{d+\lceil\log n\rceil}{d}$, as originally observed by Monier (J. Alg. 1980). We also investigate the parameterization by vertex cover number.}, }
Endnote
%0 Report %A Bringmann, Karl %A Husfeldt, Thore %A Magnusson, M&#229;ns %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0002-173B-3 %U http://arxiv.org/abs/1805.07135 %D 2018 %X We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\cdot \binom{k+\lceil\log n\rceil}{k} \cdot 2^k k^2 \log n)$, where $k$ is the treewidth of the graph. For every $\epsilon>0$, this bound is $n^{1+\epsilon}\exp O(k)$, which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) in the regime of non-constant treewidth can be improved by revisiting the analysis of orthogonal range searching, improving bounds of the form $\log^d n$ to $\binom{d+\lceil\log n\rceil}{d}$, as originally observed by Monier (J. Alg. 1980). We also investigate the parameterization by vertex cover number. %K Computer Science, Data Structures and Algorithms, cs.DS
[185]
K. Bringmann, S. Cabello, and M. T. M. Emmerich, “Maximum Volume Subset Selection for Anchored Boxes,” 2018. [Online]. Available: http://arxiv.org/abs/1803.00849. (arXiv: 1803.00849)
Abstract
Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each box has a corner at the origin and the other corner in the positive quadrant of $\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of selecting $k$ boxes in $B$ that maximize the volume of the union of the selected boxes. This research is motivated by applications in skyline queries for databases and in multicriteria optimization, where the problem is known as the hypervolume subset selection problem. It is known that the problem can be solved in polynomial time in the plane, while the best known running time in any dimension $d \ge 3$ is $\Omega\big(\binom{n}{k}\big)$. We show that: - The problem is NP-hard already in 3 dimensions. - In 3 dimensions, we break the bound $\Omega\big(\binom{n}{k}\big)$, by providing an $n^{O(\sqrt{k})}$ algorithm. - For any constant dimension $d$, we present an efficient polynomial-time approximation scheme.
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@online{Bringmann_arXiv1803.00849, TITLE = {Maximum Volume Subset Selection for Anchored Boxes}, AUTHOR = {Bringmann, Karl and Cabello, Sergio and Emmerich, Michael T. M.}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1803.00849}, EPRINT = {1803.00849}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each box has a corner at the origin and the other corner in the positive quadrant of $\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of selecting $k$ boxes in $B$ that maximize the volume of the union of the selected boxes. This research is motivated by applications in skyline queries for databases and in multicriteria optimization, where the problem is known as the hypervolume subset selection problem. It is known that the problem can be solved in polynomial time in the plane, while the best known running time in any dimension $d \ge 3$ is $\Omega\big(\binom{n}{k}\big)$. We show that: -- The problem is NP-hard already in 3 dimensions. -- In 3 dimensions, we break the bound $\Omega\big(\binom{n}{k}\big)$, by providing an $n^{O(\sqrt{k})}$ algorithm. -- For any constant dimension $d$, we present an efficient polynomial-time approximation scheme.}, }
Endnote
%0 Report %A Bringmann, Karl %A Cabello, Sergio %A Emmerich, Michael T. M. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Maximum Volume Subset Selection for Anchored Boxes : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E08-2 %U http://arxiv.org/abs/1803.00849 %D 2018 %X Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each box has a corner at the origin and the other corner in the positive quadrant of $\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of selecting $k$ boxes in $B$ that maximize the volume of the union of the selected boxes. This research is motivated by applications in skyline queries for databases and in multicriteria optimization, where the problem is known as the hypervolume subset selection problem. It is known that the problem can be solved in polynomial time in the plane, while the best known running time in any dimension $d \ge 3$ is $\Omega\big(\binom{n}{k}\big)$. We show that: - The problem is NP-hard already in 3 dimensions. - In 3 dimensions, we break the bound $\Omega\big(\binom{n}{k}\big)$, by providing an $n^{O(\sqrt{k})}$ algorithm. - For any constant dimension $d$, we present an efficient polynomial-time approximation scheme. %K Computer Science, Computational Geometry, cs.CG,Computer Science, Data Structures and Algorithms, cs.DS
[186]
K. Bringmann and P. Wellnitz, “Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars,” 2018. [Online]. Available: http://arxiv.org/abs/1803.00804. (arXiv: 1803.00804)
Abstract
Tree-adjoining grammars are a generalization of context-free grammars that are well suited to model human languages and are thus popular in computational linguistics. In the tree-adjoining grammar recognition problem, given a grammar $\Gamma$ and a string $s$ of length $n$, the task is to decide whether $s$ can be obtained from $\Gamma$. Rajasekaran and Yooseph's parser (JCSS'98) solves this problem in time $O(n^{2\omega})$, where $\omega < 2.373$ is the matrix multiplication exponent. The best algorithms avoiding fast matrix multiplication take time $O(n^6)$. The first evidence for hardness was given by Satta (J. Comp. Linguist.'94): For a more general parsing problem, any algorithm that avoids fast matrix multiplication and is significantly faster than $O(|\Gamma| n^6)$ in the case of $|\Gamma| = \Theta(n^{12})$ would imply a breakthrough for Boolean matrix multiplication. Following an approach by Abboud et al. (FOCS'15) for context-free grammar recognition, in this paper we resolve many of the disadvantages of the previous lower bound. We show that, even on constant-size grammars, any improvement on Rajasekaran and Yooseph's parser would imply a breakthrough for the $k$-Clique problem. This establishes tree-adjoining grammar parsing as a practically relevant problem with the unusual running time of $n^{2\omega}$, up to lower order factors.
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@online{Bringmann_arXiv1803.00804, TITLE = {Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars}, AUTHOR = {Bringmann, Karl and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1803.00804}, EPRINT = {1803.00804}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Tree-adjoining grammars are a generalization of context-free grammars that are well suited to model human languages and are thus popular in computational linguistics. In the tree-adjoining grammar recognition problem, given a grammar $\Gamma$ and a string $s$ of length $n$, the task is to decide whether $s$ can be obtained from $\Gamma$. Rajasekaran and Yooseph's parser (JCSS'98) solves this problem in time $O(n^{2\omega})$, where $\omega < 2.373$ is the matrix multiplication exponent. The best algorithms avoiding fast matrix multiplication take time $O(n^6)$. The first evidence for hardness was given by Satta (J. Comp. Linguist.'94): For a more general parsing problem, any algorithm that avoids fast matrix multiplication and is significantly faster than $O(|\Gamma| n^6)$ in the case of $|\Gamma| = \Theta(n^{12})$ would imply a breakthrough for Boolean matrix multiplication. Following an approach by Abboud et al. (FOCS'15) for context-free grammar recognition, in this paper we resolve many of the disadvantages of the previous lower bound. We show that, even on constant-size grammars, any improvement on Rajasekaran and Yooseph's parser would imply a breakthrough for the $k$-Clique problem. This establishes tree-adjoining grammar parsing as a practically relevant problem with the unusual running time of $n^{2\omega}$, up to lower order factors.}, }
Endnote
%0 Report %A Bringmann, Karl %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E2A-C %U http://arxiv.org/abs/1803.00804 %D 2018 %X Tree-adjoining grammars are a generalization of context-free grammars that are well suited to model human languages and are thus popular in computational linguistics. In the tree-adjoining grammar recognition problem, given a grammar $\Gamma$ and a string $s$ of length $n$, the task is to decide whether $s$ can be obtained from $\Gamma$. Rajasekaran and Yooseph's parser (JCSS'98) solves this problem in time $O(n^{2\omega})$, where $\omega < 2.373$ is the matrix multiplication exponent. The best algorithms avoiding fast matrix multiplication take time $O(n^6)$. The first evidence for hardness was given by Satta (J. Comp. Linguist.'94): For a more general parsing problem, any algorithm that avoids fast matrix multiplication and is significantly faster than $O(|\Gamma| n^6)$ in the case of $|\Gamma| = \Theta(n^{12})$ would imply a breakthrough for Boolean matrix multiplication. Following an approach by Abboud et al. (FOCS'15) for context-free grammar recognition, in this paper we resolve many of the disadvantages of the previous lower bound. We show that, even on constant-size grammars, any improvement on Rajasekaran and Yooseph's parser would imply a breakthrough for the $k$-Clique problem. This establishes tree-adjoining grammar parsing as a practically relevant problem with the unusual running time of $n^{2\omega}$, up to lower order factors. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[187]
K. Bringmann, M. Künnemann, and A. Nusser, “Fréchet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability,” 2018. [Online]. Available: http://arxiv.org/abs/1810.10982. (arXiv: 1810.10982)
Abstract
The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length $n$ in the plane, the fastest known algorithm runs in time $\tilde{\cal O}(n^{5})$ [Ben Avraham, Kaplan, Sharir '15]. This is achieved by constructing an arrangement of disks of size ${\cal O}(n^{4})$, and then traversing its faces while updating reachability in a directed grid graph of size $N := {\cal O}(n^2)$, which can be done in time $\tilde{\cal O}(\sqrt{N})$ per update [Diks, Sankowski '07]. The contribution of this paper is two-fold. First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than $\tilde{\cal O}(\sqrt{N})$, we improve this part of the algorithm: We observe that an offline variant of dynamic $s$-$t$-reachability in directed grid graphs suffices, and we solve this variant in amortized time $\tilde{\cal O}(N^{1/3})$ per update, resulting in an improved running time of $\tilde{\cal O}(n^{4.66...})$ for the discrete Fr\'echet distance under translation. Second, we provide evidence that constructing the arrangement of size ${\cal O}(n^{4})$ is necessary in the worst case, by proving a conditional lower bound of $n^{4 - o(1)}$ on the running time for the discrete Fr\'echet distance under translation, assuming the Strong Exponential Time Hypothesis.
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@online{Bringmann_arXiv1810.10982, TITLE = {Fr{\'e}chet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1810.10982}, EPRINT = {1810.10982}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length $n$ in the plane, the fastest known algorithm runs in time $\tilde{\cal O}(n^{5})$ [Ben Avraham, Kaplan, Sharir '15]. This is achieved by constructing an arrangement of disks of size ${\cal O}(n^{4})$, and then traversing its faces while updating reachability in a directed grid graph of size $N := {\cal O}(n^2)$, which can be done in time $\tilde{\cal O}(\sqrt{N})$ per update [Diks, Sankowski '07]. The contribution of this paper is two-fold. First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than $\tilde{\cal O}(\sqrt{N})$, we improve this part of the algorithm: We observe that an offline variant of dynamic $s$-$t$-reachability in directed grid graphs suffices, and we solve this variant in amortized time $\tilde{\cal O}(N^{1/3})$ per update, resulting in an improved running time of $\tilde{\cal O}(n^{4.66...})$ for the discrete Fr\'echet distance under translation. Second, we provide evidence that constructing the arrangement of size ${\cal O}(n^{4})$ is necessary in the worst case, by proving a conditional lower bound of $n^{4 -- o(1)}$ on the running time for the discrete Fr\'echet distance under translation, assuming the Strong Exponential Time Hypothesis.}, }
Endnote
%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fr&#233;chet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E35-1 %U http://arxiv.org/abs/1810.10982 %D 2018 %X The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length $n$ in the plane, the fastest known algorithm runs in time $\tilde{\cal O}(n^{5})$ [Ben Avraham, Kaplan, Sharir '15]. This is achieved by constructing an arrangement of disks of size ${\cal O}(n^{4})$, and then traversing its faces while updating reachability in a directed grid graph of size $N := {\cal O}(n^2)$, which can be done in time $\tilde{\cal O}(\sqrt{N})$ per update [Diks, Sankowski '07]. The contribution of this paper is two-fold. First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than $\tilde{\cal O}(\sqrt{N})$, we improve this part of the algorithm: We observe that an offline variant of dynamic $s$-$t$-reachability in directed grid graphs suffices, and we solve this variant in amortized time $\tilde{\cal O}(N^{1/3})$ per update, resulting in an improved running time of $\tilde{\cal O}(n^{4.66...})$ for the discrete Fr\'echet distance under translation. Second, we provide evidence that constructing the arrangement of size ${\cal O}(n^{4})$ is necessary in the worst case, by proving a conditional lower bound of $n^{4 - o(1)}$ on the running time for the discrete Fr\'echet distance under translation, assuming the Strong Exponential Time Hypothesis. %K Computer Science, Data Structures and Algorithms, cs.DS
[188]
K. Bringmann and B. Ray Chaudhury, “Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS,” 2018. [Online]. Available: http://arxiv.org/abs/1810.01238. (arXiv: 1810.01238)
Abstract
We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a sketch size and streaming space usage of $\mathcal{O}(L^{|\Sigma| - 1} \log L)$. We also prove matching unconditional lower bounds. As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an $\mathcal{O}(\textrm{min}\{nm, n + m^{{\lvert \Sigma \rvert}}\})$-time algorithm for this problem, on strings $x,y$ of length $n,m$, with $n \ge m$. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis.
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@online{Bringmann_arXiv1810.01238, TITLE = {Sketching, Streaming, and Fine-Grained Complexity of (Weighted) {LCS}}, AUTHOR = {Bringmann, Karl and Ray Chaudhury, Bhaskar}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1810.01238}, EPRINT = {1810.01238}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a sketch size and streaming space usage of $\mathcal{O}(L^{|\Sigma| - 1} \log L)$. We also prove matching unconditional lower bounds. As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an $\mathcal{O}(\textrm{min}\{nm, n + m^{{\lvert \Sigma \rvert}}\})$-time algorithm for this problem, on strings $x,y$ of length $n,m$, with $n \ge m$. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis.}, }
Endnote
%0 Report %A Bringmann, Karl %A Ray Chaudhury, Bhaskar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS : %G eng %U http://hdl.handle.net/21.11116/0000-0002-57B9-C %U http://arxiv.org/abs/1810.01238 %D 2018 %X We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a sketch size and streaming space usage of $\mathcal{O}(L^{|\Sigma| - 1} \log L)$. We also prove matching unconditional lower bounds. As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an $\mathcal{O}(\textrm{min}\{nm, n + m^{{\lvert \Sigma \rvert}}\})$-time algorithm for this problem, on strings $x,y$ of length $n,m$, with $n \ge m$. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis. %K Computer Science, Data Structures and Algorithms, cs.DS,
[189]
K. Bringmann and B. Ray Chaudhury, “Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS,” in 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018), Ahmedabad, India, 2018.
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@inproceedings{Bringmann_FSTTCS2018, TITLE = {Sketching, Streaming, and Fine-Grained Complexity of (Weighted) {LCS}}, AUTHOR = {Bringmann, Karl and Ray Chaudhury, Bhaskar}, LANGUAGE = {eng}, ISSN = {1868-896}, ISBN = {978-3-95977-093-4}, URL = {urn:nbn:de:0030-drops-99390}, DOI = {10.4230/LIPIcs.FSTTCS.2018.40}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, EDITOR = {Ganguly, Sumit and Pandya, Paritosh}, PAGES = {1--16}, EID = {40}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {122}, ADDRESS = {Ahmedabad, India}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Ray Chaudhury, Bhaskar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9D0B-2 %R 10.4230/LIPIcs.FSTTCS.2018.40 %U urn:nbn:de:0030-drops-99390 %D 2018 %B 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science %Z date of event: 2018-12-11 - 2018-12-13 %C Ahmedabad, India %B 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science %E Ganguly, Sumit; Pandya, Paritosh %P 1 - 16 %Z sequence number: 40 %I Schloss Dagstuhl %@ 978-3-95977-093-4 %B Leibniz International Proceedings in Informatics %N 122 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9939/http://drops.dagstuhl.de/doku/urheberrecht1.html
[190]
K. Bringmann, C. Ikenmeyer, and J. Zuiddam, “On Algebraic Branching Programs of Small Width,” Journal of the ACM, vol. 65, no. 5, 2018.
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@article{Bringmann_JACM2018, TITLE = {On Algebraic Branching Programs of Small Width}, AUTHOR = {Bringmann, Karl and Ikenmeyer, Christian and Zuiddam, Jeroen}, LANGUAGE = {eng}, ISSN = {0004-5411}, DOI = {10.1145/3209663}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Journal of the ACM}, VOLUME = {65}, NUMBER = {5}, PAGES = {1--29}, EID = {32}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Ikenmeyer, Christian %A Zuiddam, Jeroen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Algebraic Branching Programs of Small Width : %G eng %U http://hdl.handle.net/21.11116/0000-0002-1B53-3 %R 10.1145/3209663 %7 2018 %D 2018 %J Journal of the ACM %V 65 %N 5 %& 1 %P 1 - 29 %Z sequence number: 32 %I ACM %C New York, NY %@ false
[191]
K. Bringmann and S. Krinninger, “A Note on Hardness of Diameter Approximation,” Information Processing Letters, vol. 133, 2018.
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@article{Bringmann2018, TITLE = {A Note on Hardness of Diameter Approximation}, AUTHOR = {Bringmann, Karl and Krinninger, Sebastian}, LANGUAGE = {eng}, ISSN = {0020-0190}, DOI = {10.1016/j.ipl.2017.12.010}, PUBLISHER = {Elsevier}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Information Processing Letters}, VOLUME = {133}, PAGES = {10--15}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Krinninger, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Note on Hardness of Diameter Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0001-2C44-2 %R 10.1016/j.ipl.2017.12.010 %7 2018 %D 2018 %J Information Processing Letters %V 133 %& 10 %P 10 - 15 %I Elsevier %@ false
[192]
K. Bringmann, P. Gawrychowski, S. Mozes, and O. Weimann, “Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can),” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), New Orleans, LA, USA, 2018.
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@inproceedings{Bringmann_SODA18b, TITLE = {Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless {APSP} can)}, AUTHOR = {Bringmann, Karl and Gawrychowski, Pawe{\l} and Mozes, Shay and Weimann, Oren}, LANGUAGE = {eng}, ISBN = {978-1-61197-503-1}, DOI = {10.1137/1.9781611975031.77}, PUBLISHER = {SIAM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)}, EDITOR = {Czumaj, Artur}, PAGES = {1190--1206}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Gawrychowski, Pawe&#322; %A Mozes, Shay %A Weimann, Oren %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can) : %G eng %U http://hdl.handle.net/21.11116/0000-0000-3F13-5 %R 10.1137/1.9781611975031.77 %D 2018 %B Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2018-01-07 - 2018-01-10 %C New Orleans, LA, USA %B Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %E Czumaj, Artur %P 1190 - 1206 %I SIAM %@ 978-1-61197-503-1
[193]
K. Bringmann, T. Friedrich, and A. Krohmer, “De-anonymization of Heterogeneous Random Graphs in Quasilinear Time,” Algorithmica, vol. 80, no. 11, 2018.
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@article{bringmann_deanonymization_2018, TITLE = {De-anonymization of Heterogeneous Random Graphs in Quasilinear Time}, AUTHOR = {Bringmann, Karl and Friedrich, Tobias and Krohmer, Anton}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-017-0395-0}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York, NY}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Algorithmica}, VOLUME = {80}, NUMBER = {11}, PAGES = {3397--3427}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Friedrich, Tobias %A Krohmer, Anton %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T De-anonymization of Heterogeneous Random Graphs in Quasilinear Time : %G eng %U http://hdl.handle.net/21.11116/0000-0001-F6A3-1 %R 10.1007/s00453-017-0395-0 %7 2017-11-15 %D 2018 %J Algorithmica %V 80 %N 11 %& 3397 %P 3397 - 3427 %I Springer-Verlag %C New York, NY %@ false
[194]
J. Bund, C. Lenzen, and M. Medina, “Small Hazard-free Transducers,” 2018. [Online]. Available: http://arxiv.org/abs/1811.12369. (arXiv: 1811.12369)
Abstract
Recently, an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions has been shown. This raises the question: which classes of functions permit efficient hazard-free circuits? Our main result is as follows. A \emph{transducer} is a finite state machine that transcribes, symbol by symbol, an input string of length $n$ into an output string of length $n$. We prove that any function arising from a transducer with $s$ states, that is input symbols which are encoded by $\ell$ bits, has a hazard-free circuit of size $2^{\BO(s+\ell)}\cdot n$ and depth $\BO(\ell+ s\cdot \log n)$; in particular, if $s, \ell\in \BO(1)$, size and depth are asymptotically optimal. We utilize our main result to derive efficient circuits for \emph{$k$-recoverable addition}. Informally speaking, a code is \emph{$k$-recoverable} if it does not increase uncertainty regarding the encoded value, so long as it is guaranteed that it is from $\{x,x+1,\ldots,x+k\}$ for some $x\in \NN_0$. We provide an asymptotically optimal $k$-recoverable code. We also realize a transducer with $\BO(k)$ states that adds two codewords from this $k$-recoverable code. Combined with our main result, we obtain a hazard-free adder circuit of size $2^{\BO(k)}n$ and depth $\BO(k\log n)$ with respect to this code, i.e., a $k$-recoverable adder circuit that adds two codewords of $n$ bits each. In other words, $k$-recoverable addition is fixed-parameter tractable with respect to $k$.
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@online{Bund_arXiv1811.12369, TITLE = {Small Hazard-free Transducers}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1811.12369}, EPRINT = {1811.12369}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Recently, an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions has been shown. This raises the question: which classes of functions permit efficient hazard-free circuits? Our main result is as follows. A \emph{transducer} is a finite state machine that transcribes, symbol by symbol, an input string of length $n$ into an output string of length $n$. We prove that any function arising from a transducer with $s$ states, that is input symbols which are encoded by $\ell$ bits, has a hazard-free circuit of size $2^{\BO(s+\ell)}\cdot n$ and depth $\BO(\ell+ s\cdot \log n)$; in particular, if $s, \ell\in \BO(1)$, size and depth are asymptotically optimal. We utilize our main result to derive efficient circuits for \emph{$k$-recoverable addition}. Informally speaking, a code is \emph{$k$-recoverable} if it does not increase uncertainty regarding the encoded value, so long as it is guaranteed that it is from $\{x,x+1,\ldots,x+k\}$ for some $x\in \NN_0$. We provide an asymptotically optimal $k$-recoverable code. We also realize a transducer with $\BO(k)$ states that adds two codewords from this $k$-recoverable code. Combined with our main result, we obtain a hazard-free adder circuit of size $2^{\BO(k)}n$ and depth $\BO(k\log n)$ with respect to this code, i.e., a $k$-recoverable adder circuit that adds two codewords of $n$ bits each. In other words, $k$-recoverable addition is fixed-parameter tractable with respect to $k$.}, }
Endnote
%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Small Hazard-free Transducers : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9FAD-9 %U http://arxiv.org/abs/1811.12369 %D 2018 %X Recently, an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions has been shown. This raises the question: which classes of functions permit efficient hazard-free circuits? Our main result is as follows. A \emph{transducer} is a finite state machine that transcribes, symbol by symbol, an input string of length $n$ into an output string of length $n$. We prove that any function arising from a transducer with $s$ states, that is input symbols which are encoded by $\ell$ bits, has a hazard-free circuit of size $2^{\BO(s+\ell)}\cdot n$ and depth $\BO(\ell+ s\cdot \log n)$; in particular, if $s, \ell\in \BO(1)$, size and depth are asymptotically optimal. We utilize our main result to derive efficient circuits for \emph{$k$-recoverable addition}. Informally speaking, a code is \emph{$k$-recoverable} if it does not increase uncertainty regarding the encoded value, so long as it is guaranteed that it is from $\{x,x+1,\ldots,x+k\}$ for some $x\in \NN_0$. We provide an asymptotically optimal $k$-recoverable code. We also realize a transducer with $\BO(k)$ states that adds two codewords from this $k$-recoverable code. Combined with our main result, we obtain a hazard-free adder circuit of size $2^{\BO(k)}n$ and depth $\BO(k\log n)$ with respect to this code, i.e., a $k$-recoverable adder circuit that adds two codewords of $n$ bits each. In other words, $k$-recoverable addition is fixed-parameter tractable with respect to $k$. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[195]
J. Bund, C. Lenzen, and M. Medina, “Optimal Metastability-containing Sorting Networks,” in Proceedings of the 2018 Design, Automation & Test in Europe (DATE 2018), Dresden, Germany, 2018.
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@inproceedings{Bund_DATE2018, TITLE = {Optimal Metastability-containing Sorting Networks}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, ISBN = {978-3-9819263-1-6}, DOI = {10.23919/DATE.2018.8342063}, PUBLISHER = {IEEE}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Proceedings of the 2018 Design, Automation \& Test in Europe (DATE 2018)}, PAGES = {521--526}, ADDRESS = {Dresden, Germany}, }
Endnote
%0 Conference Proceedings %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-containing Sorting Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3F69-4 %R 10.23919/DATE.2018.8342063 %D 2018 %B Design, Automation & Test in Europe Conference & Exhibition %Z date of event: 2018-03-19 - 2018-03-23 %C Dresden, Germany %B Proceedings of the 2018 Design, Automation & Test in Europe %P 521 - 526 %I IEEE %@ 978-3-9819263-1-6
[196]
J. Bund, C. Lenzen, and M. Medina, “Optimal Metastability-Containing Sorting Networks,” 2018. [Online]. Available: http://arxiv.org/abs/1801.07549. (arXiv: 1801.07549)
Abstract
When setup/hold times of bistable elements are violated, they may become metastable, i.e., enter a transient state that is neither digital 0 nor 1. In general, metastability cannot be avoided, a problem that manifests whenever taking discrete measurements of analog values. Metastability of the output then reflects uncertainty as to whether a measurement should be rounded up or down to the next possible measurement outcome. Surprisingly, Lenzen and Medina (ASYNC 2016) showed that metastability can be contained, i.e., measurement values can be correctly sorted without resolving metastability first. However, both their work and the state of the art by Bund et al. (DATE 2017) leave open whether such a solution can be as small and fast as standard sorting networks. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Concretely, for 10-channel sorting networks and 16-bit wide inputs, we improve by 48.46% in delay and by 71.58% in area over Bund et al. Our simulations indicate that straightforward transistor-level optimization is likely to result in performance on par with standard (non-containing) solutions.
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@online{Bund_arXiv1801.07549, TITLE = {Optimal Metastability-Containing Sorting Networks}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1801.07549}, EPRINT = {1801.07549}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {When setup/hold times of bistable elements are violated, they may become metastable, i.e., enter a transient state that is neither digital 0 nor 1. In general, metastability cannot be avoided, a problem that manifests whenever taking discrete measurements of analog values. Metastability of the output then reflects uncertainty as to whether a measurement should be rounded up or down to the next possible measurement outcome. Surprisingly, Lenzen and Medina (ASYNC 2016) showed that metastability can be contained, i.e., measurement values can be correctly sorted without resolving metastability first. However, both their work and the state of the art by Bund et al. (DATE 2017) leave open whether such a solution can be as small and fast as standard sorting networks. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Concretely, for 10-channel sorting networks and 16-bit wide inputs, we improve by 48.46% in delay and by 71.58% in area over Bund et al. Our simulations indicate that straightforward transistor-level optimization is likely to result in performance on par with standard (non-containing) solutions.}, }
Endnote
%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-Containing Sorting Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-1801-2 %U http://arxiv.org/abs/1801.07549 %D 2018 %X When setup/hold times of bistable elements are violated, they may become metastable, i.e., enter a transient state that is neither digital 0 nor 1. In general, metastability cannot be avoided, a problem that manifests whenever taking discrete measurements of analog values. Metastability of the output then reflects uncertainty as to whether a measurement should be rounded up or down to the next possible measurement outcome. Surprisingly, Lenzen and Medina (ASYNC 2016) showed that metastability can be contained, i.e., measurement values can be correctly sorted without resolving metastability first. However, both their work and the state of the art by Bund et al. (DATE 2017) leave open whether such a solution can be as small and fast as standard sorting networks. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Concretely, for 10-channel sorting networks and 16-bit wide inputs, we improve by 48.46% in delay and by 71.58% in area over Bund et al. Our simulations indicate that straightforward transistor-level optimization is likely to result in performance on par with standard (non-containing) solutions. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[197]
P. Chalermsook, A. Schmid, and S. Uniyal, “A Tight Extremal Bound on the Lovász Cactus Number in Planar Graphs,” 2018. [Online]. Available: http://arxiv.org/abs/1804.03485. (arXiv: 1804.03485)
Abstract
A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph $G$ contains a cactus subgraph $C$ where $C$ contains at least a $\frac{1}{6}$ fraction of the triangular faces of $G$. We also show that this ratio cannot be improved by showing a tight lower bound. Together with an algorithm for linear matroid parity, our bound implies two approximation algorithms for computing "dense planar structures" inside any graph: (i) A $\frac{1}{6}$ approximation algorithm for, given any graph $G$, finding a planar subgraph with a maximum number of triangular faces; this improves upon the previous $\frac{1}{11}$-approximation; (ii) An alternate (and arguably more illustrative) proof of the $\frac{4}{9}$ approximation algorithm for finding a planar subgraph with a maximum number of edges. Our bound is obtained by analyzing a natural local search strategy and heavily exploiting the exchange arguments. Therefore, this suggests the power of local search in handling problems of this kind.
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@online{Chalermsook_arXiv1804.03485, TITLE = {A Tight Extremal Bound on the {Lov\'{a}sz} Cactus Number in Planar Graphs}, AUTHOR = {Chalermsook, Parinya and Schmid, Andreas and Uniyal, Sumedha}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1804.03485}, EPRINT = {1804.03485}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph $G$ contains a cactus subgraph $C$ where $C$ contains at least a $\frac{1}{6}$ fraction of the triangular faces of $G$. We also show that this ratio cannot be improved by showing a tight lower bound. Together with an algorithm for linear matroid parity, our bound implies two approximation algorithms for computing "dense planar structures" inside any graph: (i) A $\frac{1}{6}$ approximation algorithm for, given any graph $G$, finding a planar subgraph with a maximum number of triangular faces; this improves upon the previous $\frac{1}{11}$-approximation; (ii) An alternate (and arguably more illustrative) proof of the $\frac{4}{9}$ approximation algorithm for finding a planar subgraph with a maximum number of edges. Our bound is obtained by analyzing a natural local search strategy and heavily exploiting the exchange arguments. Therefore, this suggests the power of local search in handling problems of this kind.}, }
Endnote
%0 Report %A Chalermsook, Parinya %A Schmid, Andreas %A Uniyal, Sumedha %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Tight Extremal Bound on the Lov&#225;sz Cactus Number in Planar Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5D0-0 %U http://arxiv.org/abs/1804.03485 %D 2018 %X A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph $G$ contains a cactus subgraph $C$ where $C$ contains at least a $\frac{1}{6}$ fraction of the triangular faces of $G$. We also show that this ratio cannot be improved by showing a tight lower bound. Together with an algorithm for linear matroid parity, our bound implies two approximation algorithms for computing "dense planar structures" inside any graph: (i) A $\frac{1}{6}$ approximation algorithm for, given any graph $G$, finding a planar subgraph with a maximum number of triangular faces; this improves upon the previous $\frac{1}{11}$-approximation; (ii) An alternate (and arguably more illustrative) proof of the $\frac{4}{9}$ approximation algorithm for finding a planar subgraph with a maximum number of edges. Our bound is obtained by analyzing a natural local search strategy and heavily exploiting the exchange arguments. Therefore, this suggests the power of local search in handling problems of this kind. %K Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Combinatorics, math.CO
[198]
P. Chalermsook, S. Das, G. Even, B. Laekhanukit, and D. Vaz, “Survivable Network Design for Group Connectivity in Low-Treewidth Graphs,” 2018. [Online]. Available: http://arxiv.org/abs/1802.10403. (arXiv: 1802.10403)
Abstract
In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph $H$ that connects the root to every group. We consider a fault-tolerant variant of GST, which we call Restricted (Rooted) Group SNDP. In this setting, each group $S_i$ has a demand $k_i\in[k],k\in\mathbb N$, and we wish to find a min-cost $H\subseteq G$ such that, for each group $S_i$, there is a vertex in $S_i$ connected to the root via $k_i$ (vertex or edge) disjoint paths. While GST admits $O(\log^2 n\log h)$ approximation, its high connectivity variants are Label-Cover hard, and for the vertex-weighted version, the hardness holds even when $k=2$. Previously, positive results were known only for the edge-weighted version when $k=2$ [Gupta et al., SODA 2010; Khandekar et al., Theor. Comput. Sci., 2012] and for a relaxed variant where the disjoint paths may end at different vertices in a group [Chalermsook et al., SODA 2015]. Our main result is an $O(\log n\log h)$ approximation for Restricted Group SNDP that runs in time $n^{f(k, w)}$, where $w$ is the treewidth of $G$. This nearly matches the lower bound when $k$ and $w$ are constant. The key to achieving this result is a non-trivial extension of the framework in [Chalermsook et al., SODA 2017], which embeds all feasible solutions to the problem into a dynamic program (DP) table. However, finding the optimal solution in the DP table remains intractable. We formulate a linear program relaxation for the DP and obtain an approximate solution via randomized rounding. This framework also allows us to systematically construct DP tables for high-connectivity problems. As a result, we present new exact algorithms for several variants of survivable network design problems in low-treewidth graphs.
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@online{Chalermsook_arXiv1802.10403, TITLE = {Survivable Network Design for Group Connectivity in Low-Treewidth Graphs}, AUTHOR = {Chalermsook, Parinya and Das, Syamantak and Even, Guy and Laekhanukit, Bundit and Vaz, Daniel}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1802.10403}, EPRINT = {1802.10403}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph $H$ that connects the root to every group. We consider a fault-tolerant variant of GST, which we call Restricted (Rooted) Group SNDP. In this setting, each group $S_i$ has a demand $k_i\in[k],k\in\mathbb N$, and we wish to find a min-cost $H\subseteq G$ such that, for each group $S_i$, there is a vertex in $S_i$ connected to the root via $k_i$ (vertex or edge) disjoint paths. While GST admits $O(\log^2 n\log h)$ approximation, its high connectivity variants are Label-Cover hard, and for the vertex-weighted version, the hardness holds even when $k=2$. Previously, positive results were known only for the edge-weighted version when $k=2$ [Gupta et al., SODA 2010; Khandekar et al., Theor. Comput. Sci., 2012] and for a relaxed variant where the disjoint paths may end at different vertices in a group [Chalermsook et al., SODA 2015]. Our main result is an $O(\log n\log h)$ approximation for Restricted Group SNDP that runs in time $n^{f(k, w)}$, where $w$ is the treewidth of $G$. This nearly matches the lower bound when $k$ and $w$ are constant. The key to achieving this result is a non-trivial extension of the framework in [Chalermsook et al., SODA 2017], which embeds all feasible solutions to the problem into a dynamic program (DP) table. However, finding the optimal solution in the DP table remains intractable. We formulate a linear program relaxation for the DP and obtain an approximate solution via randomized rounding. This framework also allows us to systematically construct DP tables for high-connectivity problems. As a result, we present new exact algorithms for several variants of survivable network design problems in low-treewidth graphs.}, }
Endnote
%0 Report %A Chalermsook, Parinya %A Das, Syamantak %A Even, Guy %A Laekhanukit, Bundit %A Vaz, Daniel %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Survivable Network Design for Group Connectivity in Low-Treewidth Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A84E-A %U http://arxiv.org/abs/1802.10403 %D 2018 %X In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph $H$ that connects the root to every group. We consider a fault-tolerant variant of GST, which we call Restricted (Rooted) Group SNDP. In this setting, each group $S_i$ has a demand $k_i\in[k],k\in\mathbb N$, and we wish to find a min-cost $H\subseteq G$ such that, for each group $S_i$, there is a vertex in $S_i$ connected to the root via $k_i$ (vertex or edge) disjoint paths. While GST admits $O(\log^2 n\log h)$ approximation, its high connectivity variants are Label-Cover hard, and for the vertex-weighted version, the hardness holds even when $k=2$. Previously, positive results were known only for the edge-weighted version when $k=2$ [Gupta et al., SODA 2010; Khandekar et al., Theor. Comput. Sci., 2012] and for a relaxed variant where the disjoint paths may end at different vertices in a group [Chalermsook et al., SODA 2015]. Our main result is an $O(\log n\log h)$ approximation for Restricted Group SNDP that runs in time $n^{f(k, w)}$, where $w$ is the treewidth of $G$. This nearly matches the lower bound when $k$ and $w$ are constant. The key to achieving this result is a non-trivial extension of the framework in [Chalermsook et al., SODA 2017], which embeds all feasible solutions to the problem into a dynamic program (DP) table. However, finding the optimal solution in the DP table remains intractable. We formulate a linear program relaxation for the DP and obtain an approximate solution via randomized rounding. This framework also allows us to systematically construct DP tables for high-connectivity problems. As a result, we present new exact algorithms for several variants of survivable network design problems in low-treewidth graphs. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Discrete Mathematics, cs.DM
[199]
P. Chalermsook, S. Das, G. Even, B. Laekhanukit, and D. Vaz, “Survivable Network Design for Group Connectivity in Low-Treewidth Graphs,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018), Princeton, NJ, USA, 2018.
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@inproceedings{Chalermsook_APPROXRANDOM18, TITLE = {Survivable Network Design for Group Connectivity in Low-Treewidth Graphs}, AUTHOR = {Chalermsook, Parinya and Das, Syamantak and Even, Guy and Laekhanukit, Bundit and Vaz, Daniel}, LANGUAGE = {eng}, ISBN = {978-3-95977-085-9}, URL = {urn:nbn:de:0030-drops-94127}, DOI = {10.4230/LIPIcs.APPROX-RANDOM.2018.8}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)}, EDITOR = {Blais, Eric and Jansen, Klaus and Rolim, Jos{\'e} D. P. and Steurer, David}, PAGES = {1--19}, EID = {8}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {116}, ADDRESS = {Princeton, NJ, USA}, }
Endnote
%0 Conference Proceedings %A Chalermsook, Parinya %A Das, Syamantak %A Even, Guy %A Laekhanukit, Bundit %A Vaz, Daniel %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Survivable Network Design for Group Connectivity in Low-Treewidth Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A832-8 %R 10.4230/LIPIcs.APPROX-RANDOM.2018.8 %U urn:nbn:de:0030-drops-94127 %D 2018 %B 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems / 22nd International Workshop on Randomization and Computation %Z date of event: 2018-08-20 - 2018-08-22 %C Princeton, NJ, USA %B Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques %E Blais, Eric; Jansen, Klaus; Rolim, Jos&#233; D. P.; Steurer, David %P 1 - 19 %Z sequence number: 8 %I Schloss Dagstuhl %@ 978-3-95977-085-9 %B Leibniz International Proceedings in Informatics %N 116 %U http://drops.dagstuhl.de/opus/volltexte/2018/9412/http://drops.dagstuhl.de/doku/urheberrecht1.html
[200]
P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Multi-Finger Binary Search Trees,” in 29th International Symposium on Algorithms and Computation (ISAAC 2018), Jiaoxi, Yilan, Taiwan, 2018.
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@inproceedings{Chalermsook_ISAAC2018b, TITLE = {Multi-Finger Binary Search Trees}, AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, L{\a}sz{\o} and Mehlhorn, Kurt and Saranurak, Thatchaphol}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-094-1}, URL = {urn:nbn:de:0030-drops-100032}, DOI = {10.4230/LIPIcs.ISAAC.2018.55}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {29th International Symposium on Algorithms and Computation (ISAAC 2018)}, EDITOR = {Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou}, PAGES = {1--26}, EID = {55}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {123}, ADDRESS = {Jiaoxi, Yilan, Taiwan}, }
Endnote
%0 Conference Proceedings %A Chalermsook, Parinya %A Goswami, Mayank %A Kozma, L&#224;sz&#242; %A Mehlhorn, Kurt %A Saranurak, Thatchaphol %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Multi-Finger Binary Search Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AADE-5 %R 10.4230/LIPIcs.ISAAC.2018.55 %U urn:nbn:de:0030-drops-100032 %D 2018 %B 29th International Symposium on Algorithms and Computation %Z date of event: 2018-12-16 - 2018-12-19 %C Jiaoxi, Yilan, Taiwan %B 29th International Symposium on Algorithms and Computation %E Hsu, Wen-Lian; Lee, Der-Tsai; Liao, Chung-Shou %P 1 - 26 %Z sequence number: 55 %I Schloss Dagstuhl %@ 978-3-95977-094-1 %B Leibniz International Proceedings in Informatics %N 123 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/10003/http://drops.dagstuhl.de/doku/urheberrecht1.html
[201]
L. S. Chandran, Y. K. Cheung, and D. Issac, “Spanning Tree Congestion and Computation of Generalized Györi-Lovász Partition,” in 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), Prague, Czech Republic, 2018.
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@inproceedings{stc-gyo-lov-2018-chandran, TITLE = {Spanning Tree Congestion and Computation of Generalized {Gy{\"o}ri-Lov{\'a}sz} Partition}, AUTHOR = {Chandran, L. Sunil and Cheung, Yun Kuen and Issac, Davis}, LANGUAGE = {eng}, ISBN = {978-3-95977-076-7}, URL = {urn:nbn:de:0030-drops-90361}, DOI = {10.4230/LIPIcs.ICALP.2018.32}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, EDITOR = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D{\'a}niel and Sannella, Donald}, PAGES = {1--14}, EID = {32}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {107}, ADDRESS = {Prague, Czech Republic}, }
Endnote
%0 Conference Proceedings %A Chandran, L. Sunil %A Cheung, Yun Kuen %A Issac, Davis %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Spanning Tree Congestion and Computation of Generalized Gy&#246;ri-Lov&#225;sz Partition : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E67-9 %R 10.4230/LIPIcs.ICALP.2018.32 %U urn:nbn:de:0030-drops-90361 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 14 %Z sequence number: 32 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9036/http://drops.dagstuhl.de/doku/urheberrecht1.html
[202]
L. S. Chandran, A. Das, D. Issac, and E. J. van Leeuwen, “Algorithms and Bounds for Very Strong Rainbow Coloring,” in LATIN 2018: Theoretical Informatics, Buenos Aires, Argentinia, 2018.
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@inproceedings{Chandran_LATIN2018, TITLE = {Algorithms and Bounds for Very Strong Rainbow Coloring}, AUTHOR = {Chandran, L. Sunil and Das, Anita and Issac, Davis and van Leeuwen, Erik Jan}, LANGUAGE = {eng}, ISBN = {978-3-319-77403-9}, DOI = {10.1007/978-3-319-77404-6_46}, PUBLISHER = {Springer}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {LATIN 2018: Theoretical Informatics}, EDITOR = {Bender, Michael A. and Farach-Colton, Mart{\'i}n and Mosteiro, Miguel A.}, PAGES = {625--639}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10807}, ADDRESS = {Buenos Aires, Argentinia}, }
Endnote
%0 Conference Proceedings %A Chandran, L. Sunil %A Das, Anita %A Issac, Davis %A van Leeuwen, Erik Jan %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Algorithms and Bounds for Very Strong Rainbow Coloring : %G eng %U http://hdl.handle.net/21.11116/0000-0002-576A-6 %R 10.1007/978-3-319-77404-6_46 %D 2018 %B 13th Latin American Theoretical Informatics Symposium %Z date of event: 2018-04-16 - 2018-04-19 %C Buenos Aires, Argentinia %B LATIN 2018: Theoretical Informatics %E Bender, Michael A.; Farach-Colton, Mart&#237;n; Mosteiro, Miguel A. %P 625 - 639 %I Springer %@ 978-3-319-77403-9 %B Lecture Notes in Computer Science %N 10807
[203]
T. M. Chan, T. C. van Dijk, K. Fleszar, J. Spoerhase, and A. Wolff, “Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity,” in 29th International Symposium on Algorithms and Computation (ISAAC 2018), Jiaoxi, Yilan, Taiwan, 2018.
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@inproceedings{Chan_ISAAC2018b, TITLE = {Stabbing Rectangles by Line Segments -- How Decomposition Reduces the Shallow-Cell Complexity}, AUTHOR = {Chan, Timothy M. and van Dijk, Thomas C. and Fleszar, Krzysztof and Spoerhase, Joachim and Wolff, Alexander}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-094-1}, URL = {urn:nbn:de:0030-drops-100094}, DOI = {10.4230/LIPIcs.ISAAC.2018.61}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {29th International Symposium on Algorithms and Computation (ISAAC 2018)}, EDITOR = {Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou}, PAGES = {1--13}, EID = {61}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {123}, ADDRESS = {Jiaoxi, Yilan, Taiwan}, }
Endnote
%0 Conference Proceedings %A Chan, Timothy M. %A van Dijk, Thomas C. %A Fleszar, Krzysztof %A Spoerhase, Joachim %A Wolff, Alexander %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ADEA-4 %R 10.4230/LIPIcs.ISAAC.2018.61 %U urn:nbn:de:0030-drops-100094 %D 2018 %B 29th International Symposium on Algorithms and Computation %Z date of event: 2018-12-16 - 2018-12-19 %C Jiaoxi, Yilan, Taiwan %B 29th International Symposium on Algorithms and Computation %E Hsu, Wen-Lian; Lee, Der-Tsai; Liao, Chung-Shou %P 1 - 13 %Z sequence number: 61 %I Schloss Dagstuhl %@ 978-3-95977-094-1 %B Leibniz International Proceedings in Informatics %N 123 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/10009/http://drops.dagstuhl.de/doku/urheberrecht1.html
[204]
Y. K. Cheung, “Steiner Point Removal - Distant Terminals Don’t (Really) Bother,” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), New Orleans, LA, USA, 2018.
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@inproceedings{Cheung_SODA18, TITLE = {{S}teiner Point Removal -- Distant Terminals Don't (Really) Bother}, AUTHOR = {Cheung, Yun Kuen}, LANGUAGE = {eng}, ISBN = {978-1-61197-503-1}, DOI = {10.1137/1.9781611975031.89}, PUBLISHER = {SIAM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)}, EDITOR = {Czumaj, Artur}, PAGES = {1353--1360}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Cheung, Yun Kuen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Steiner Point Removal - Distant Terminals Don't (Really) Bother : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AA8C-1 %R 10.1137/1.9781611975031.89 %D 2018 %B Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2018-01-07 - 2018-01-10 %C New Orleans, LA, USA %B Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %E Czumaj, Artur %P 1353 - 1360 %I SIAM %@ 978-1-61197-503-1
[205]
Y. K. Cheung, R. Cole, and Y. Tao, “Parallel Stochastic Asynchronous Coordinate Descent: Tight Bounds on the Possible Parallelism,” 2018. [Online]. Available: http://arxiv.org/abs/1811.05087. (arXiv: 1811.05087)
Abstract
Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar duration, then linear speedup is possible with up to $\Theta(\sqrt n/L_{\mathsf{res}})$ processors, where $L_{\mathsf{res}}$ is a suitable Lipschitz parameter. This paper shows the bound is tight for essentially all possible values of $L_{\mathsf{res}}$.
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@online{corr/abs-1811-05087, TITLE = {Parallel Stochastic Asynchronous Coordinate Descent: {T}ight Bounds on the Possible Parallelism}, AUTHOR = {Cheung, Yun Kuen and Cole, Richard and Tao, Yixin}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1811.05087}, EPRINT = {1811.05087}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar duration, then linear speedup is possible with up to $\Theta(\sqrt n/L_{\mathsf{res}})$ processors, where $L_{\mathsf{res}}$ is a suitable Lipschitz parameter. This paper shows the bound is tight for essentially all possible values of $L_{\mathsf{res}}$.}, }
Endnote
%0 Report %A Cheung, Yun Kuen %A Cole, Richard %A Tao, Yixin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Parallel Stochastic Asynchronous Coordinate Descent: Tight Bounds on the Possible Parallelism : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAF2-D %U http://arxiv.org/abs/1811.05087 %D 2018 %X Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar duration, then linear speedup is possible with up to $\Theta(\sqrt n/L_{\mathsf{res}})$ processors, where $L_{\mathsf{res}}$ is a suitable Lipschitz parameter. This paper shows the bound is tight for essentially all possible values of $L_{\mathsf{res}}$. %K Mathematics, Optimization and Control, math.OC,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[206]
Y. K. Cheung, “Multiplicative Weights Updates with Constant Step-Size in Graphical Constant-Sum Games,” in Advances in Neural Information Processing Systems 31 (NIPS 2018), Montréal, Canada, 2018.
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@inproceedings{NeurIPS/Cheung18, TITLE = {Multiplicative Weights Updates with Constant Step-Size in Graphical Constant-Sum Games}, AUTHOR = {Cheung, Yun Kuen}, LANGUAGE = {eng}, PUBLISHER = {Curran Associates}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 31 (NIPS 2018)}, EDITOR = {Bengio, S. and Wallach, H. and Larochelle, H. and Grauman, K. and Cesa-Bianchi, N. and Garnett, R.}, PAGES = {3532--3542}, ADDRESS = {Montr{\'e}al, Canada}, }
Endnote
%0 Conference Proceedings %A Cheung, Yun Kuen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Multiplicative Weights Updates with Constant Step-Size in Graphical Constant-Sum Games : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AB07-6 %D 2018 %B Thirty-second Conference on Neural Information Processing Systems %Z date of event: 2018-12-02 - 2018-12-08 %C Montr&#233;al, Canada %B Advances in Neural Information Processing Systems 31 %E Bengio, S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R. %P 3532 - 3542 %I Curran Associates %U http://papers.nips.cc/paper/7612-multiplicative-weights-updates-with-constant-step-size-in-graphical-constant-sum-games.pdf
[207]
Y. K. Cheung, R. Cole, and Y. Tao, “Dynamics of Distributed Updating in Fisher Markets,” in ACM EC’18, Nineteenth ACM Conference on Economics and Computation, Ithaca, NY, USA, 2018.
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@inproceedings{EC/CCT18, TITLE = {Dynamics of Distributed Updating in {F}isher Markets}, AUTHOR = {Cheung, Yun Kuen and Cole, Richard and Tao, Yixin}, LANGUAGE = {eng}, ISBN = {978-1-4503-5829-3}, DOI = {10.1145/3219166.3219189}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {ACM EC'18, Nineteenth ACM Conference on Economics and Computation}, PAGES = {351--368}, ADDRESS = {Ithaca, NY, USA}, }
Endnote
%0 Conference Proceedings %A Cheung, Yun Kuen %A Cole, Richard %A Tao, Yixin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Dynamics of Distributed Updating in Fisher Markets : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAE9-8 %R 10.1145/3219166.3219189 %D 2018 %B Nineteenth ACM Conference on Economics and Computation %Z date of event: 2018-06-18 - 2018-06-22 %C Ithaca, NY, USA %B ACM EC'18 %P 351 - 368 %I ACM %@ 978-1-4503-5829-3
[208]
Y. K. Cheung and R. Cole, “Amortized Analysis of Asynchronous Price Dynamics,” in 26th Annual European Symposium on Algorithms (ESA 2018), Helsinki, Finland, 2018.
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@inproceedings{Cheung_ESA2018, TITLE = {Amortized Analysis of Asynchronous Price Dynamics}, AUTHOR = {Cheung, Yun Kuen and Cole, Richard}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-081-1}, URL = {urn:nbn:de:0030-drops-94812}, DOI = {10.4230/LIPIcs.ESA.2018.18}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {26th Annual European Symposium on Algorithms (ESA 2018)}, EDITOR = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, PAGES = {1--15}, EID = {18}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {112}, ADDRESS = {Helsinki, Finland}, }
Endnote
%0 Conference Proceedings %A Cheung, Yun Kuen %A Cole, Richard %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Amortized Analysis of Asynchronous Price Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAEE-3 %R 10.4230/LIPIcs.ESA.2018.18 %U urn:nbn:de:0030-drops-94812 %D 2018 %B 26th Annual European Symposium on Algorithms %Z date of event: 2018-08-20 - 2018-08-22 %C Helsinki, Finland %B 26th Annual European Symposium on Algorithms %E Azar, Yossi; Bast, Hannah; Herman, Grzegorz %P 1 - 15 %Z sequence number: 18 %I Schloss Dagstuhl %@ 978-3-95977-081-1 %B Leibniz International Proceedings in Informatics %N 112 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9481/http://drops.dagstuhl.de/doku/urheberrecht1.html
[209]
Y. K. Cheung, R. Cole, and Y. Tao, “(Near) Optimal Parallelism Bound for Fully Asynchronous Coordinate Descent with Linear Speedup,” 2018. [Online]. Available: http://arxiv.org/abs/1811.03254. (arXiv: 1811.03254)
Abstract
When solving massive optimization problems in areas such as machine learning, it is a common practice to seek speedup via massive parallelism. However, especially in an asynchronous environment, there are limits on the possible parallelism. Accordingly, we seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions $F:\mathbb{R}^n \rightarrow \mathbb{R}$ of the form $$F(x) = f(x) ~+~ \sum_{k=1}^n \Psi_k(x_k),$$ where $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a smooth convex function, and each $\Psi_k:\mathbb{R} \rightarrow \mathbb{R}$ is a univariate and possibly non-smooth convex function. Our approach is to quantify the shortfall in progress compared to the standard sequential stochastic gradient descent. This leads to a truly simple yet optimal analysis of the standard stochastic ACD in a partially asynchronous environment, which already generalizes and improves on the bounds in prior work. We also give a considerably more involved analysis for general asynchronous environments in which the only constraint is that each update can overlap with at most $q$ others, where $q$ is at most the number of processors times the ratio in the lengths of the longest and shortest updates. The main technical challenge is to demonstrate linear speedup in the latter environment. This stems from the subtle interplay of asynchrony and randomization. This improves Liu and Wright's (SIOPT'15) lower bound on the maximum degree of parallelism almost quadratically, and we show that our new bound is almost optimal.
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@online{corr/abs-1811-03254, TITLE = {(Near) Optimal Parallelism Bound for Fully Asynchronous Coordinate Descent with Linear Speedup}, AUTHOR = {Cheung, Yun Kuen and Cole, Richard and Tao, Yixin}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1811.03254}, EPRINT = {1811.03254}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {When solving massive optimization problems in areas such as machine learning, it is a common practice to seek speedup via massive parallelism. However, especially in an asynchronous environment, there are limits on the possible parallelism. Accordingly, we seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions $F:\mathbb{R}^n \rightarrow \mathbb{R}$ of the form $$F(x) = f(x) ~+~ \sum_{k=1}^n \Psi_k(x_k),$$ where $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a smooth convex function, and each $\Psi_k:\mathbb{R} \rightarrow \mathbb{R}$ is a univariate and possibly non-smooth convex function. Our approach is to quantify the shortfall in progress compared to the standard sequential stochastic gradient descent. This leads to a truly simple yet optimal analysis of the standard stochastic ACD in a partially asynchronous environment, which already generalizes and improves on the bounds in prior work. We also give a considerably more involved analysis for general asynchronous environments in which the only constraint is that each update can overlap with at most $q$ others, where $q$ is at most the number of processors times the ratio in the lengths of the longest and shortest updates. The main technical challenge is to demonstrate linear speedup in the latter environment. This stems from the subtle interplay of asynchrony and randomization. This improves Liu and Wright's (SIOPT'15) lower bound on the maximum degree of parallelism almost quadratically, and we show that our new bound is almost optimal.}, }
Endnote
%0 Report %A Cheung, Yun Kuen %A Cole, Richard %A Tao, Yixin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T (Near) Optimal Parallelism Bound for Fully Asynchronous Coordinate Descent with Linear Speedup : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAF5-A %U http://arxiv.org/abs/1811.03254 %D 2018 %X When solving massive optimization problems in areas such as machine learning, it is a common practice to seek speedup via massive parallelism. However, especially in an asynchronous environment, there are limits on the possible parallelism. Accordingly, we seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions $F:\mathbb{R}^n \rightarrow \mathbb{R}$ of the form $$F(x) = f(x) ~+~ \sum_{k=1}^n \Psi_k(x_k),$$ where $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a smooth convex function, and each $\Psi_k:\mathbb{R} \rightarrow \mathbb{R}$ is a univariate and possibly non-smooth convex function. Our approach is to quantify the shortfall in progress compared to the standard sequential stochastic gradient descent. This leads to a truly simple yet optimal analysis of the standard stochastic ACD in a partially asynchronous environment, which already generalizes and improves on the bounds in prior work. We also give a considerably more involved analysis for general asynchronous environments in which the only constraint is that each update can overlap with at most $q$ others, where $q$ is at most the number of processors times the ratio in the lengths of the longest and shortest updates. The main technical challenge is to demonstrate linear speedup in the latter environment. This stems from the subtle interplay of asynchrony and randomization. This improves Liu and Wright's (SIOPT'15) lower bound on the maximum degree of parallelism almost quadratically, and we show that our new bound is almost optimal. %K Mathematics, Optimization and Control, math.OC,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[210]
Y. K. Cheung, M. Hoefer, and P. Nakhe, “Tracing Equilibrium in Dynamic Markets via Distributed Adaptation,” 2018. [Online]. Available: http://arxiv.org/abs/1804.08017. (arXiv: 1804.08017)
Abstract
Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest.
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@online{Cheung_arXiv1804.08017, TITLE = {Tracing Equilibrium in Dynamic Markets via Distributed Adaptation}, AUTHOR = {Cheung, Yun Kuen and Hoefer, Martin and Nakhe, Paresh}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1804.08017}, EPRINT = {1804.08017}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest.}, }
Endnote
%0 Report %A Cheung, Yun Kuen %A Hoefer, Martin %A Nakhe, Paresh %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Tracing Equilibrium in Dynamic Markets via Distributed Adaptation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AE08-2 %U http://arxiv.org/abs/1804.08017 %D 2018 %X Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest. %K Computer Science, Computer Science and Game Theory, cs.GT
[211]
L. Chiantini, J. D. Hauenstein, C. Ikenmeyer, J. M. Landsberg, and G. Ottaviani, “Polynomials and the Exponent of Matrix Multiplication,” Bulletin of the London Mathematical Society, vol. 50, no. 3, 2018.
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@article{Chaintini2018, TITLE = {Polynomials and the Exponent of Matrix Multiplication}, AUTHOR = {Chiantini, Luca and Hauenstein, Jonathan D. and Ikenmeyer, Christian and Landsberg, Joseph M. and Ottaviani, Giorgio}, LANGUAGE = {eng}, ISSN = {0024-6093}, DOI = {10.1112/blms.12147}, PUBLISHER = {London Mathematical Society}, ADDRESS = {London}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Bulletin of the London Mathematical Society}, VOLUME = {50}, NUMBER = {3}, PAGES = {369--389}, }
Endnote
%0 Journal Article %A Chiantini, Luca %A Hauenstein, Jonathan D. %A Ikenmeyer, Christian %A Landsberg, Joseph M. %A Ottaviani, Giorgio %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Polynomials and the Exponent of Matrix Multiplication : %G eng %U http://hdl.handle.net/21.11116/0000-0001-88D0-A %R 10.1112/blms.12147 %7 2018 %D 2018 %J Bulletin of the London Mathematical Society %V 50 %N 3 %& 369 %P 369 - 389 %I London Mathematical Society %C London %@ false
[212]
A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter Triangulations Have Good Quality,” in EuroCG 18 Extended Abstracts, Berlin, Germany, 2018.
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@inproceedings{Choudhary-coxeter, TITLE = {Coxeter Triangulations Have Good Quality}, AUTHOR = {Choudhary, Aruni and Kachanovich, Siargey and Wintraecken, Mathijs}, LANGUAGE = {eng}, URL = {https://conference.imp.fu-berlin.de/eurocg18/download/eurocg_proc.pdf}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {EuroCG 18 Extended Abstracts}, PAGES = {37--42}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Choudhary, Aruni %A Kachanovich, Siargey %A Wintraecken, Mathijs %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Coxeter Triangulations Have Good Quality : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5C4-E %D 2018 %B 34th European Workshop on Computational Geometry %Z date of event: 2018-03-21 - 2018-03-23 %C Berlin, Germany %B EuroCG 18 Extended Abstracts %P 37 - 42 %U https://conference.imp.fu-berlin.de/eurocg18/download/eurocg_proc.pdf
[213]
A. Clementi, L. Gualà, E. Natale, F. Pasquale, G. Scornavacca, and L. Trevisan, “Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise,” 2018. [Online]. Available: http://arxiv.org/abs/1807.05626. (arXiv: 1807.05626)
Abstract
Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An $\Omega(\epsilon^{-2} n)$ lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where $\epsilon$ is a parameter that measures the amount of noise). In such model, we prove a new $\Theta(\epsilon^{-2} n \log n)$ bound for Broadcast and a $\Theta(\epsilon^{-2} \log n)$ bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast.
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@online{Clementi_arXiv1807.05626, TITLE = {Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise}, AUTHOR = {Clementi, Andrea and Gual{\a}, Luciano and Natale, Emanuele and Pasquale, Francesco and Scornavacca, Giacomo and Trevisan, Luca}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1807.05626}, EPRINT = {1807.05626}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An $\Omega(\epsilon^{-2} n)$ lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where $\epsilon$ is a parameter that measures the amount of noise). In such model, we prove a new $\Theta(\epsilon^{-2} n \log n)$ bound for Broadcast and a $\Theta(\epsilon^{-2} \log n)$ bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast.}, }
Endnote
%0 Report %A Clementi, Andrea %A Gual&#224;, Luciano %A Natale, Emanuele %A Pasquale, Francesco %A Scornavacca, Giacomo %A Trevisan, Luca %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise : %G eng %U http://hdl.handle.net/21.11116/0000-0002-B985-7 %U http://arxiv.org/abs/1807.05626 %D 2018 %X Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An $\Omega(\epsilon^{-2} n)$ lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where $\epsilon$ is a parameter that measures the amount of noise). In such model, we prove a new $\Theta(\epsilon^{-2} n \log n)$ bound for Broadcast and a $\Theta(\epsilon^{-2} \log n)$ bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[214]
A. Clementi, M. Ghaffari, L. Gualà, E. Natale, F. Pasquale, and G. Scornavacca, “A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors,” in 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Liverpool, UK, 2018.
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@inproceedings{Clementi_MFCS2018, TITLE = {A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors}, AUTHOR = {Clementi, Andrea and Ghaffari, Mohsen and Gual{\a}, Luciano and Natale, Emanuele and Pasquale, Francesco and Scornavacca, Giacomo}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-086-6}, URL = {urn:nbn:de:0030-drops-96107}, DOI = {10.4230/LIPIcs.MFCS.2018.28}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, EDITOR = {Potapov, Igor and Spirakis, Paul and Worrell, James}, PAGES = {1--15}, EID = {28}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {117}, ADDRESS = {Liverpool, UK}, }
Endnote
%0 Conference Proceedings %A Clementi, Andrea %A Ghaffari, Mohsen %A Gual&#224;, Luciano %A Natale, Emanuele %A Pasquale, Francesco %A Scornavacca, Giacomo %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A96C-7 %R 10.4230/LIPIcs.MFCS.2018.28 %U urn:nbn:de:0030-drops-96107 %D 2018 %B 43rd International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2018-08-27 - 2018-08-31 %C Liverpool, UK %B 43rd International Symposium on Mathematical Foundations of Computer Science %E Potapov, Igor; Spirakis, Paul; Worrell, James %P 1 - 15 %Z sequence number: 28 %I Schloss Dagstuhl %@ 978-3-95977-086-6 %B Leibniz International Proceedings in Informatics %N 117 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9610/http://drops.dagstuhl.de/doku/urheberrecht1.html
[215]
C. Croitoru and K. Mehlhorn, “On Testing Substitutability,” 2018. [Online]. Available: http://arxiv.org/abs/1805.07642. (arXiv: 1805.07642)
Abstract
The papers~\cite{hatfimmokomi11} and~\cite{azizbrilharr13} propose algorithms for testing whether the choice function induced by a (strict) preference list of length $N$ over a universe $U$ is substitutable. The running time of these algorithms is $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that $N$ may be exponential in the size $|U|$ of the universe.
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@online{Croitoru_arXiv1805.07642, TITLE = {On Testing Substitutability}, AUTHOR = {Croitoru, Cosmina and Mehlhorn, Kurt}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1805.07642}, EPRINT = {1805.07642}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The papers~\cite{hatfimmokomi11} and~\cite{azizbrilharr13} propose algorithms for testing whether the choice function induced by a (strict) preference list of length $N$ over a universe $U$ is substitutable. The running time of these algorithms is $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that $N$ may be exponential in the size $|U|$ of the universe.}, }
Endnote
%0 Report %A Croitoru, Cosmina %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On Testing Substitutability : %G eng %U http://hdl.handle.net/21.11116/0000-0002-05FA-F %U http://arxiv.org/abs/1805.07642 %D 2018 %X The papers~\cite{hatfimmokomi11} and~\cite{azizbrilharr13} propose algorithms for testing whether the choice function induced by a (strict) preference list of length $N$ over a universe $U$ is substitutable. The running time of these algorithms is $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that $N$ may be exponential in the size $|U|$ of the universe. %K Computer Science, Data Structures and Algorithms, cs.DS,econ.EM
[216]
C. Croitoru and K. Mehlhorn, “On Testing Substitutability,” Information Processing Letters, vol. 138, 2018.
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@article{Croitoru_2018, TITLE = {On Testing Substitutability}, AUTHOR = {Croitoru, Cosmina and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {0020-0190}, DOI = {10.1016/j.ipl.2018.05.006}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Information Processing Letters}, VOLUME = {138}, PAGES = {19--21}, }
Endnote
%0 Journal Article %A Croitoru, Cosmina %A Mehlhorn, Kurt %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On Testing Substitutability : %G eng %U http://hdl.handle.net/21.11116/0000-0001-EE14-D %R 10.1016/j.ipl.2018.05.006 %7 2018 %D 2018 %J Information Processing Letters %V 138 %& 19 %P 19 - 21 %I Elsevier %C Amsterdam %@ false
[217]
E. Cruciani, E. Natale, A. Nusser, and G. Scornavacca, “Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks,” Bulletin of the EATCS, vol. 125, 2018.
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@article{Cruciani_EATCS2018, TITLE = {Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks}, AUTHOR = {Cruciani, Emilio and Natale, Emanuele and Nusser, Andr{\'e} and Scornavacca, Giacomo}, LANGUAGE = {eng}, ISSN = {0252-9742}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Bulletin of the EATCS}, VOLUME = {125}, EID = {542}, }
Endnote
%0 Journal Article %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A48F-4 %7 2018 %D 2018 %J Bulletin of the EATCS %O EATCS %V 125 %Z sequence number: 542 %@ false
[218]
E. Cruciani, E. Natale, A. Nusser, and G. Scornavacca, “Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks,” 2018. [Online]. Available: http://arxiv.org/abs/1804.07223. (arXiv: 1804.07223)
Abstract
Consider the following process on a network: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. This process is known as the 2-Choices dynamics and is arguably the most basic non-trivial opinion dynamics modeling voting behavior on social networks. Despite its apparent simplicity, 2-Choices has been analytically characterized only on networks with a strong expansion property -- under assumptions on the initial configuration that establish it as a fast majority consensus protocol. In this work, we aim at contributing to the understanding of the 2-Choices dynamics by considering its behavior on a class of networks with core-periphery structure, a well-known topological assumption in social networks. In a nutshell, assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. Then, depending on the strength of the cut between the core and the periphery, a phase-transition phenomenon occurs: Either the core's opinion rapidly spreads among the rest of the network, or a metastability phase takes place, in which both opinions coexist in the network for superpolynomial time. The interest of our result is twofold. On the one hand, by looking at the 2-Choices dynamics as a simplistic model of competition among opinions in social networks, our theorem sheds light on the influence of the core on the rest of the network, as a function of the core's connectivity towards the latter. On the other hand, to the best of our knowledge, we provide the first analytical result which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network. Finally, we validate our theoretical predictions with extensive experiments on real networks.
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@online{Cruciano_arXiv1804.07223, TITLE = {Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks}, AUTHOR = {Cruciani, Emilio and Natale, Emanuele and Nusser, Andr{\'e} and Scornavacca, Giacomo}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1804.07223}, EPRINT = {1804.07223}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Consider the following process on a network: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. This process is known as the 2-Choices dynamics and is arguably the most basic non-trivial opinion dynamics modeling voting behavior on social networks. Despite its apparent simplicity, 2-Choices has been analytically characterized only on networks with a strong expansion property -- under assumptions on the initial configuration that establish it as a fast majority consensus protocol. In this work, we aim at contributing to the understanding of the 2-Choices dynamics by considering its behavior on a class of networks with core-periphery structure, a well-known topological assumption in social networks. In a nutshell, assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. Then, depending on the strength of the cut between the core and the periphery, a phase-transition phenomenon occurs: Either the core's opinion rapidly spreads among the rest of the network, or a metastability phase takes place, in which both opinions coexist in the network for superpolynomial time. The interest of our result is twofold. On the one hand, by looking at the 2-Choices dynamics as a simplistic model of competition among opinions in social networks, our theorem sheds light on the influence of the core on the rest of the network, as a function of the core's connectivity towards the latter. On the other hand, to the best of our knowledge, we provide the first analytical result which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network. Finally, we validate our theoretical predictions with extensive experiments on real networks.}, }
Endnote
%0 Report %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A446-6 %U http://arxiv.org/abs/1804.07223 %D 2018 %X Consider the following process on a network: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. This process is known as the 2-Choices dynamics and is arguably the most basic non-trivial opinion dynamics modeling voting behavior on social networks. Despite its apparent simplicity, 2-Choices has been analytically characterized only on networks with a strong expansion property -- under assumptions on the initial configuration that establish it as a fast majority consensus protocol. In this work, we aim at contributing to the understanding of the 2-Choices dynamics by considering its behavior on a class of networks with core-periphery structure, a well-known topological assumption in social networks. In a nutshell, assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. Then, depending on the strength of the cut between the core and the periphery, a phase-transition phenomenon occurs: Either the core's opinion rapidly spreads among the rest of the network, or a metastability phase takes place, in which both opinions coexist in the network for superpolynomial time. The interest of our result is twofold. On the one hand, by looking at the 2-Choices dynamics as a simplistic model of competition among opinions in social networks, our theorem sheds light on the influence of the core on the rest of the network, as a function of the core's connectivity towards the latter. On the other hand, to the best of our knowledge, we provide the first analytical result which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network. Finally, we validate our theoretical predictions with extensive experiments on real networks. %K cs.SI, Physics, Physics and Society, physics.soc-ph
[219]
E. Cruciani, E. Natale, A. Nusser, and G. Scornavacca, “Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks,” in AAMAS’18, 17th International Conference on Autonomous Agents and MultiAgent Systems, Stockholm, Sweden, 2018.
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@inproceedings{Cruciani_AAMAS2018, TITLE = {Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks}, AUTHOR = {Cruciani, Emilio and Natale, Emanuele and Nusser, Andr{\'e} and Scornavacca, Giacomo}, LANGUAGE = {eng}, ISBN = {978-1-4503-5649-7}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {AAMAS'18, 17th International Conference on Autonomous Agents and MultiAgent Systems}, PAGES = {777--785}, ADDRESS = {Stockholm, Sweden}, }
Endnote
%0 Conference Proceedings %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A47E-8 %D 2018 %B 17th International Conference on Autonomous Agents and MultiAgent Systems %Z date of event: 2018-07-10 - 2018-07-15 %C Stockholm, Sweden %B AAMAS'18 %P 777 - 785 %I ACM %@ 978-1-4503-5649-7
[220]
E. Cruciani, E. Natale, and G. Scornavacca, “On the Metastability of Quadratic Majority Dynamics on Clustered Graphs and its Biological Implications,” Bulletin of the EATCS, vol. 125, 2018.
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@article{Cruciani_EATCS2018b, TITLE = {On the Metastability of Quadratic Majority Dynamics on Clustered Graphs and its Biological Implications}, AUTHOR = {Cruciani, Emilio and Natale, Emanuele and Scornavacca, Giacomo}, LANGUAGE = {eng}, ISSN = {0252-9742}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Bulletin of the EATCS}, VOLUME = {125}, EID = {535}, }
Endnote
%0 Journal Article %A Cruciani, Emilio %A Natale, Emanuele %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Metastability of Quadratic Majority Dynamics on Clustered Graphs and its Biological Implications : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A94B-C %7 2018 %D 2018 %J Bulletin of the EATCS %O EATCS %V 125 %Z sequence number: 535 %@ false
[221]
E. Cruciani, E. Natale, A. Nusser, and G. Scornavacca, “On the Emergent Behavior of the 2-Choices Dynamics,” in Proceedings of the 19th Italian Conference on Theoretical Computer Science (ICTCS 2018), Urbino, Italy, 2018.
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@inproceedings{Cruciano_ICTCS2018, TITLE = {On the Emergent Behavior of the 2-Choices Dynamics}, AUTHOR = {Cruciani, Emilio and Natale, Emanuele and Nusser, Andr{\'e} and Scornavacca, Giacomo}, LANGUAGE = {eng}, URL = {urn:nbn:de:0074-2243-4}, PUBLISHER = {CEUR-WS}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 19th Italian Conference on Theoretical Computer Science (ICTCS 2018)}, EDITOR = {Aldini, Alessandro and Bernardo, Marco}, SERIES = {CEUR Workshop Proceedings}, VOLUME = {2243}, ADDRESS = {Urbino, Italy}, }
Endnote
%0 Conference Proceedings %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Emergent Behavior of the 2-Choices Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A44E-E %D 2018 %B 19th Italian Conference on Theoretical Computer Science %Z date of event: 2018-09-18 - 2018-09-20 %C Urbino, Italy %B Proceedings of the 19th Italian Conference on Theoretical Computer Science %E Aldini, Alessandro; Bernardo, Marco %I CEUR-WS %B CEUR Workshop Proceedings %N 2243 %U http://ceur-ws.org/Vol-2243/paper4.pdf
[222]
M. Cygan, S. Kratsch, and J. Nederlof, “Fast Hamiltonicity Checking Via Bases of Perfect Matchings,” Journal of the ACM, vol. 65, no. 3, 2018.
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@article{Cygan2018, TITLE = {Fast {Hamiltonicity} Checking Via Bases of Perfect Matchings}, AUTHOR = {Cygan, Marek and Kratsch, Stefan and Nederlof, Jesper}, LANGUAGE = {eng}, ISSN = {0004-5411}, DOI = {10.1145/3148227}, PUBLISHER = {Association for Computing Machinery, Inc.}, ADDRESS = {New York, NY}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Journal of the ACM}, VOLUME = {65}, NUMBER = {3}, EID = {12}, }
Endnote
%0 Journal Article %A Cygan, Marek %A Kratsch, Stefan %A Nederlof, Jesper %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Fast Hamiltonicity Checking Via Bases of Perfect Matchings : %G eng %U http://hdl.handle.net/21.11116/0000-0001-7AE5-4 %R 10.1145/3148227 %7 2018 %D 2018 %J Journal of the ACM %V 65 %N 3 %Z sequence number: 12 %I Association for Computing Machinery, Inc. %C New York, NY %@ false
[223]
M. Cygan, G. Kortsarz, and B. Laekhanukit, “On Subexponential Running Times for Approximating Directed Steiner Tree and Related Problems,” 2018. [Online]. Available: http://arxiv.org/abs/1811.00710. (arXiv: 1811.00710)
Abstract
This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0<d<1. What is the best possible running time for achieving such approximation? This question was answered implicitly in the work of Moshkovitz [Theory of Computing, 2015]: Assuming both the Projection Games Conjecture (PGC) and the Exponential-Time Hypothesis (ETH), any ((1-d) ln n)-approximation algorithm for Set-Cover must run in time >= 2^{n^{c d}}, for some constant 0<d<1. We study the questions along this line. First, we show that under ETH and PGC any ((1-d) \ln n)-approximation for Set-Cover requires 2^{n^{d}}-time. This (almost) matches the running time of 2^{O(n^d)} for approximating Set-Cover to a factor (1-d) ln n by Cygan et al. [IPL, 2009]. Our result is tight up to the constant multiplying the n^{d} terms in the exponent. This lower bound applies to all of its generalizations, e.g., Group Steiner Tree (GST), Directed Steiner (DST), Covering Steiner Tree (CST), Connected Polymatroid (CP). We also show that in almost exponential time, these problems reduce to Set-Cover: We show (1-d)ln n approximation algorithms for all these problems that run in time 2^{n^{d \log n } poly(m). We also study log^{2-d}n approximation for GST. Chekuri-Pal [FOCS, 2005] showed that GST admits (log^{2-d}n)-approximation in time exp(2^{log^{d+o(1)}n}), for any 0 < d < 1. We show the lower bound of GST: any (log^{2-d}n)-approximation for GST must run in time >= exp((1+o(1)){log^{d-c}n}), for any c>0, unless the ETH is false. Our result follows by analyzing the work of Halperin and Krauthgamer [STOC, 2003]. The same lower and upper bounds hold for CST.
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@online{Cygan_arXiv1811.00710, TITLE = {{On Subexponential Running Times for Approximating Directed Steiner Tree and Related Problems}}, AUTHOR = {Cygan, Marek and Kortsarz, Guy and Laekhanukit, Bundit}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1811.00710}, EPRINT = {1811.00710}, EPRINTTYPE = {arXiv}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, ABSTRACT = {This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0<d<1. What is the best possible running time for achieving such approximation? This question was answered implicitly in the work of Moshkovitz [Theory of Computing, 2015]: Assuming both the Projection Games Conjecture (PGC) and the Exponential-Time Hypothesis (ETH), any ((1-d) ln n)-approximation algorithm for Set-Cover must run in time >= 2^{n^{c d}}, for some constant 0<d<1. We study the questions along this line. First, we show that under ETH and PGC any ((1-d) \ln n)-approximation for Set-Cover requires 2^{n^{d}}-time. This (almost) matches the running time of 2^{O(n^d)} for approximating Set-Cover to a factor (1-d) ln n by Cygan et al. [IPL, 2009]. Our result is tight up to the constant multiplying the n^{d} terms in the exponent. This lower bound applies to all of its generalizations, e.g., Group Steiner Tree (GST), Directed Steiner (DST), Covering Steiner Tree (CST), Connected Polymatroid (CP). We also show that in almost exponential time, these problems reduce to Set-Cover: We show (1-d)ln n approximation algorithms for all these problems that run in time 2^{n^{d \log n } poly(m). We also study log^{2-d}n approximation for GST. Chekuri-Pal [FOCS, 2005] showed that GST admits (log^{2-d}n)-approximation in time exp(2^{log^{d+o(1)}n}), for any 0 < d < 1. We show the lower bound of GST: any (log^{2-d}n)-approximation for GST must run in time >= exp((1+o(1)){log^{d-c}n}), for any c>0, unless the ETH is false. Our result follows by analyzing the work of Halperin and Krauthgamer [STOC, 2003]. The same lower and upper bounds hold for CST.}, }
Endnote
%0 Report %A Cygan, Marek %A Kortsarz, Guy %A Laekhanukit, Bundit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On Subexponential Running Times for Approximating Directed Steiner Tree and Related Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A85B-B %U http://arxiv.org/abs/1811.00710 %D 2018 %X This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0<d<1. What is the best possible running time for achieving such approximation? This question was answered implicitly in the work of Moshkovitz [Theory of Computing, 2015]: Assuming both the Projection Games Conjecture (PGC) and the Exponential-Time Hypothesis (ETH), any ((1-d) ln n)-approximation algorithm for Set-Cover must run in time >= 2^{n^{c d}}, for some constant 0<d<1. We study the questions along this line. First, we show that under ETH and PGC any ((1-d) \ln n)-approximation for Set-Cover requires 2^{n^{d}}-time. This (almost) matches the running time of 2^{O(n^d)} for approximating Set-Cover to a factor (1-d) ln n by Cygan et al. [IPL, 2009]. Our result is tight up to the constant multiplying the n^{d} terms in the exponent. This lower bound applies to all of its generalizations, e.g., Group Steiner Tree (GST), Directed Steiner (DST), Covering Steiner Tree (CST), Connected Polymatroid (CP). We also show that in almost exponential time, these problems reduce to Set-Cover: We show (1-d)ln n approximation algorithms for all these problems that run in time 2^{n^{d \log n } poly(m). We also study log^{2-d}n approximation for GST. Chekuri-Pal [FOCS, 2005] showed that GST admits (log^{2-d}n)-approximation in time exp(2^{log^{d+o(1)}n}), for any 0 < d < 1. We show the lower bound of GST: any (log^{2-d}n)-approximation for GST must run in time >= exp((1+o(1)){log^{d-c}n}), for any c>0, unless the ETH is false. Our result follows by analyzing the work of Halperin and Krauthgamer [STOC, 2003]. The same lower and upper bounds hold for CST. %K Computer Science, Data Structures and Algorithms, cs.DS
[224]
R. David, C. S. Karthik, and B. Laekhanukit, “On the Complexity of Closest Pair via Polar-Pair of Point-Sets,” in 34th International Symposium on Computational Geometry (SoCG 2018), Budapest, Hungary, 2018.
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@inproceedings{David_SoCG2018, TITLE = {On the Complexity of Closest Pair via Polar-Pair of Point-Sets}, AUTHOR = {David, Roee and Karthik, C. S. and Laekhanukit, Bundit}, LANGUAGE = {eng}, ISBN = {978-3-95977-066-8}, URL = {urn:nbn:de:0030-drops-87412}, DOI = {10.4230/LIPIcs.SoCG.2018.28}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {34th International Symposium on Computational Geometry (SoCG 2018)}, EDITOR = {Speckmann, Bettina and T{\'o}th, Csaba D.}, PAGES = {1--15}, EID = {28}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {99}, ADDRESS = {Budapest, Hungary}, }
Endnote
%0 Conference Proceedings %A David, Roee %A Karthik, C. S. %A Laekhanukit, Bundit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Complexity of Closest Pair via Polar-Pair of Point-Sets : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A827-5 %R 10.4230/LIPIcs.SoCG.2018.28 %U urn:nbn:de:0030-drops-87412 %D 2018 %B 34th International Symposium on Computational Geometry %Z date of event: 2018-06-11 - 2018-06-14 %C Budapest, Hungary %B 34th International Symposium on Computational Geometry %E Speckmann, Bettina; T&#243;th, Csaba D. %P 1 - 15 %Z sequence number: 28 %I Schloss Dagstuhl %@ 978-3-95977-066-8 %B Leibniz International Proceedings in Informatics %N 99 %U http://drops.dagstuhl.de/opus/volltexte/2018/8741/http://drops.dagstuhl.de/doku/urheberrecht1.html
[225]
T. Eden, R. Levi, and D. Ron, “Testing Bounded Arboricity,” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), New Orleans, LA, USA, 2018.
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@inproceedings{Eden_SODA18, TITLE = {Testing Bounded Arboricity}, AUTHOR = {Eden, Talya and Levi, Reut and Ron, Dana}, LANGUAGE = {eng}, ISBN = {978-1-61197-503-1}, DOI = {10.1137/1.9781611975031.136}, PUBLISHER = {SIAM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)}, EDITOR = {Czumaj, Artur}, PAGES = {2081--2092}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Eden, Talya %A Levi, Reut %A Ron, Dana %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Testing Bounded Arboricity : %G eng %U http://hdl.handle.net/21.11116/0000-0004-B7C0-4 %R 10.1137/1.9781611975031.136 %D 2018 %B Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2018-01-07 - 2018-01-10 %C New Orleans, LA, USA %B Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %E Czumaj, Artur %P 2081 - 2092 %I SIAM %@ 978-1-61197-503-1
[226]
G. Even, M. Medina, and D. Rawitz, “Online Generalized Caching with Varying Weights and Costs,” in SPAA’18, 30th ACM Symposium on Parallelism in Algorithms and Architectures, Vienna, Austria, 2018.
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@inproceedings{Even_SPAA2018, TITLE = {Online Generalized Caching with Varying Weights and Costs}, AUTHOR = {Even, Guy and Medina, Moti and Rawitz, Dror}, LANGUAGE = {eng}, ISBN = {978-1-4503-5799-9}, DOI = {10.1145/3210377.3210404}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {SPAA'18, 30th ACM Symposium on Parallelism in Algorithms and Architectures}, PAGES = {205--2012}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Even, Guy %A Medina, Moti %A Rawitz, Dror %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Online Generalized Caching with Varying Weights and Costs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ABEA-6 %R 10.1145/3210377.3210404 %D 2018 %B 30th ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2018-07-16 - 2018-07-18 %C Vienna, Austria %B SPAA'18 %P 205 - 2012 %I ACM %@ 978-1-4503-5799-9
[227]
G. Even, M. Ghaffari, and M. Medina, “Distributed Set Cover Approximation: Primal-Dual with Optimal Locality,” in 32nd International Symposium on Distributed Computing (DISC 2018), New Orleans, LA, USA, 2018.
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@inproceedings{Even_DISC2018, TITLE = {Distributed Set Cover Approximation: {P}rimal-Dual with Optimal Locality}, AUTHOR = {Even, Guy and Ghaffari, Mohsen and Medina, Moti}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-092-7}, URL = {urn:nbn:de:0030-drops-98114}, DOI = {10.4230/LIPIcs.DISC.2018.22}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {32nd International Symposium on Distributed Computing (DISC 2018)}, EDITOR = {Schmid, Ulrich and Widder, Josef}, PAGES = {1--14}, EID = {22}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {121}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Even, Guy %A Ghaffari, Mohsen %A Medina, Moti %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Distributed Set Cover Approximation: Primal-Dual with Optimal Locality : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AC02-A %R 10.4230/LIPIcs.DISC.2018.22 %U urn:nbn:de:0030-drops-98114 %D 2018 %B 32nd International Symposium on Distributed Computing %Z date of event: 2018-10-15 - 2018-10-19 %C New Orleans, LA, USA %B 32nd International Symposium on Distributed Computing %E Schmid, Ulrich; Widder, Josef %P 1 - 14 %Z sequence number: 22 %I Schloss Dagstuhl %@ 978-3-95977-092-7 %B Leibniz International Proceedings in Informatics %N 121 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9811/http://drops.dagstuhl.de/doku/urheberrecht1.html
[228]
H. Fichtenberger, R. Levi, Y. Vasudev, and M. Wötzel, “A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error,” in 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), Prague, Czech Republic, 2018.
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@inproceedings{FLVW18, TITLE = {A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error}, AUTHOR = {Fichtenberger, Hendrik and Levi, Reut and Vasudev, Yadu and W{\"o}tzel, Maximilian}, LANGUAGE = {eng}, ISBN = {978-3-95977-076-7}, URL = {urn:nbn:de:0030-drops-90563}, DOI = {10.4230/LIPIcs.ICALP.2018.52}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, EDITOR = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D{\'a}niel and Sannella, Donald}, PAGES = {1--14}, EID = {52}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {107}, ADDRESS = {Prague, Czech Republic}, }
Endnote
%0 Conference Proceedings %A Fichtenberger, Hendrik %A Levi, Reut %A Vasudev, Yadu %A W&#246;tzel, Maximilian %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Sublinear Tester for Outerplanarity (and Other Forbidden Minors) With One-Sided Error : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E86A-2 %R 10.4230/LIPIcs.ICALP.2018.52 %U urn:nbn:de:0030-drops-90563 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 14 %Z sequence number: 52 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9056/http://drops.dagstuhl.de/doku/urheberrecht1.html
[229]
K. Fleszar, M. Mnich, and J. Spoerhase, “New Algorithms for Maximum Disjoint Paths Based on Tree-likeness,” Mathematical Programming / A, vol. 171, no. 1–2, 2018.
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@article{edge-disjoint-paths-mapr-17, TITLE = {New Algorithms for Maximum Disjoint Paths Based on Tree-likeness}, AUTHOR = {Fleszar, Krzysztof and Mnich, Matthias and Spoerhase, Joachim}, LANGUAGE = {eng}, ISSN = {0025-5610}, DOI = {10.1007/s10107-017-1199-3}, PUBLISHER = {North-Holland}, ADDRESS = {Heidelberg}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Mathematical Programming / A}, VOLUME = {171}, NUMBER = {1-2}, PAGES = {433--461}, }
Endnote
%0 Journal Article %A Fleszar, Krzysztof %A Mnich, Matthias %A Spoerhase, Joachim %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T New Algorithms for Maximum Disjoint Paths Based on Tree-likeness : %G eng %U http://hdl.handle.net/21.11116/0000-0000-B54C-F %R 10.1007/s10107-017-1199-3 %7 2017 %D 2018 %J Mathematical Programming / A %V 171 %N 1-2 %& 433 %P 433 - 461 %I North-Holland %C Heidelberg %@ false
[230]
S. Friedrichs and C. Lenzen, “Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford,” Journal of the ACM, vol. 65, no. 6, 2018.
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@article{FriedrichsJACM2018, TITLE = {Parallel Metric Tree Embedding based on an Algebraic View on {Moore}-{Bellman}-{Ford}}, AUTHOR = {Friedrichs, Stephan and Lenzen, Christoph}, LANGUAGE = {eng}, ISSN = {0004-5411}, DOI = {10.1145/3231591}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {Journal of the ACM}, VOLUME = {65}, NUMBER = {6}, EID = {43}, }
Endnote
%0 Journal Article %A Friedrichs, Stephan %A Lenzen, Christoph %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford : %G eng %U http://hdl.handle.net/21.11116/0000-0002-8892-F %R 10.1145/3231591 %7 2018 %D 2018 %J Journal of the ACM %V 65 %N 6 %Z sequence number: 43 %I ACM %C New York, NY %@ false
[231]
S. Friedrichs, M. Függer, and C. Lenzen, “Metastability-Containing Circuits,” IEEE Transactions on Computers, vol. 67, no. 8, 2018.
Abstract
Communication across unsynchronized clock domains is inherently vulnerable to metastable upsets; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Traditionally, a possibly metastable input is stored in synchronizers, decreasing the odds of maintained metastability over time. This approach costs time, and does not guarantee success. We propose a fundamentally different approach: It is possible to \emph{contain} metastability by logical masking, so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in---and uncertainty about---the output. We present a synchronizer-free, fault-tolerant clock synchronization algorithm as application, synchronizing clock domains and thus enabling metastability-free communication. At the heart of our approach lies a model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results while at the same time reproducing established impossibility results regarding avoidance, resolution, and detection of metastability. Furthermore, we fully classify which functions can be computed by synchronous circuits with standard registers, and show that masking registers are computationally strictly more powerful.
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@article{Friedrichs_Fuegger_Lenzen2018, TITLE = {Metastability-Containing Circuits}, AUTHOR = {Friedrichs, Stephan and F{\"u}gger, Matthias and Lenzen, Christoph}, LANGUAGE = {eng}, ISSN = {0018-9340}, DOI = {10.1109/TC.2018.2808185}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, ABSTRACT = {Communication across unsynchronized clock domains is inherently vulnerable to metastable upsets; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Traditionally, a possibly metastable input is stored in synchronizers, decreasing the odds of maintained metastability over time. This approach costs time, and does not guarantee success. We propose a fundamentally different approach: It is possible to \emph{contain} metastability by logical masking, so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in---and uncertainty about---the output. We present a synchronizer-free, fault-tolerant clock synchronization algorithm as application, synchronizing clock domains and thus enabling metastability-free communication. At the heart of our approach lies a model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results while at the same time reproducing established impossibility results regarding avoidance, resolution, and detection of metastability. Furthermore, we fully classify which functions can be computed by synchronous circuits with standard registers, and show that masking registers are computationally strictly more powerful.}, JOURNAL = {IEEE Transactions on Computers}, VOLUME = {67}, NUMBER = {8}, PAGES = {1167--1183}, }
Endnote
%0 Journal Article %A Friedrichs, Stephan %A F&#252;gger, Matthias %A Lenzen, Christoph %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Metastability-Containing Circuits : %G eng %U http://hdl.handle.net/21.11116/0000-0001-E5A0-7 %R 10.1109/TC.2018.2808185 %7 2018 %D 2018 %X Communication across unsynchronized clock domains is inherently vulnerable to metastable upsets; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Traditionally, a possibly metastable input is stored in synchronizers, decreasing the odds of maintained metastability over time. This approach costs time, and does not guarantee success. We propose a fundamentally different approach: It is possible to \emph{contain} metastability by logical masking, so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in---and uncertainty about---the output. We present a synchronizer-free, fault-tolerant clock synchronization algorithm as application, synchronizing clock domains and thus enabling metastability-free communication. At the heart of our approach lies a model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results while at the same time reproducing established impossibility results regarding avoidance, resolution, and detection of metastability. Furthermore, we fully classify which functions can be computed by synchronous circuits with standard registers, and show that masking registers are computationally strictly more powerful. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC %J IEEE Transactions on Computers %V 67 %N 8 %& 1167 %P 1167 - 1183 %I IEEE %C Piscataway, NJ %@ false
[232]
M. Függer, A. Kinali, C. Lenzen, and B. Wiederhake, “Fast All-Digital Clock Frequency Adaptation Circuit for Voltage Droop Tolerance,” in 24th IEEE International Symposium on Asynchronous Circuits and Systems, Vienna, Austria, 2018.
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@inproceedings{Fuegger_ASYNC2018, TITLE = {Fast All-Digital Clock Frequency Adaptation Circuit for Voltage Droop Tolerance}, AUTHOR = {F{\"u}gger, Matthias and Kinali, Attila and Lenzen, Christoph and Wiederhake, Ben}, LANGUAGE = {eng}, ISBN = {978-1-5386-5883-3}, DOI = {10.1109/ASYNC.2018.00025}, PUBLISHER = {IEEE}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {24th IEEE International Symposium on Asynchronous Circuits and Systems}, PAGES = {68--77}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A F&#252;gger, Matthias %A Kinali, Attila %A Lenzen, Christoph %A Wiederhake, Ben %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fast All-Digital Clock Frequency Adaptation Circuit for Voltage Droop Tolerance : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9FA4-2 %R 10.1109/ASYNC.2018.00025 %D 2018 %B 24th IEEE International Symposium on Asynchronous Circuits and Systems %Z date of event: 2018-05-13 - 2018-05-16 %C Vienna, Austria %B 24th IEEE International Symposium on Asynchronous Circuits and Systems %P 68 - 77 %I IEEE %@ 978-1-5386-5883-3
[233]
J. Garg, M. Hoefer, and K. Mehlhorn, “Approximating the Nash Social Welfare with Budget-Additive Valuations,” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), New Orleans, LA, USA, 2018.
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@inproceedings{GargHoeferMehlhornSODA18, TITLE = {Approximating the {Nash} Social Welfare with Budget-Additive Valuations}, AUTHOR = {Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISBN = {978-1-61197-503-1}, DOI = {10.1137/1.9781611975031.150}, PUBLISHER = {SIAM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)}, EDITOR = {Czumaj, Artur}, PAGES = {2326--2340}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Garg, Jugal %A Hoefer, Martin %A Mehlhorn, Kurt %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Approximating the Nash Social Welfare with Budget-Additive Valuations : %G eng %U http://hdl.handle.net/21.11116/0000-0000-37F9-A %R 10.1137/1.9781611975031.150 %D 2018 %B Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2018-01-07 - 2018-01-10 %C New Orleans, LA, USA %B Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms %E Czumaj, Artur %P 2326 - 2340 %I SIAM %@ 978-1-61197-503-1
[234]
M. Ghaffari, A. Karrenbauer, F. Kuhn, C. Lenzen, and B. Patt-Shamir, “Near-Optimal Distributed Maximum Flow,” SIAM Journal on Computing, vol. 47, no. 6, 2018.
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@article{GKKLP2018, TITLE = {Near-Optimal Distributed Maximum Flow}, AUTHOR = {Ghaffari, Mohsen and Karrenbauer, Andreas and Kuhn, Fabian and Lenzen, Christoph and Patt-Shamir, Boaz}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/17M113277X}, PUBLISHER = {Society for Industrial and Applied Mathematics.}, ADDRESS = {Philadelphia, PA}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {47}, NUMBER = {6}, PAGES = {2078--2117}, }
Endnote
%0 Journal Article %A Ghaffari, Mohsen %A Karrenbauer, Andreas %A Kuhn, Fabian %A Lenzen, Christoph %A Patt-Shamir, Boaz %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Near-Optimal Distributed Maximum Flow : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A3A9-7 %R 10.1137/17M113277X %7 2018 %D 2018 %J SIAM Journal on Computing %V 47 %N 6 %& 2078 %P 2078 - 2117 %I Society for Industrial and Applied Mathematics. %C Philadelphia, PA %@ false
[235]
F. Grandoni, T. Mömke, A. Wiese, and H. Zhou, “A(5/3+ε)-Approximation for Unsplittable Flow on a Path: Placing Small Tasks into Boxes,” in STOC’18, 50th Annual ACM SIGACT Symposium on Theory of Computing, Los Angeles, CA, USA, 2018.
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@inproceedings{DBLP:conf/stoc/0001MW018, TITLE = {A {(5/3} + {$$\epsilon$$})-approximation for unsplittable flow on a path: {P}lacing small tasks into boxes}, AUTHOR = {Grandoni, Fabrizio and M{\"o}mke, Tobias and Wiese, Andreas and Zhou, Hang}, LANGUAGE = {eng}, ISBN = {978-1-4503-5559-9}, DOI = {10.1145/3188745.3188894}, PUBLISHER = {ACM}, YEAR = {2018}, MARGINALMARK = {$\bullet$}, DATE = {2018}, BOOKTITLE = {STOC'18, 50th Annual ACM SIGACT Symposium on Theory of Computing}, PAGES = {607--619}, ADDRESS = {Los Angeles, CA, USA}, }
Endnote
%0 Conference Proceedings %A Grandoni, Fabrizio %A M&#246;mke, Tobias %A Wiese, Andreas %A Zhou, Hang %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A(5/3+&#949;)-Approximation for Unsplittable Flow on a Path: Placing Small Tasks into Boxes : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5F3-9 %R 10.1145/3188745.3188894 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 607 - 619 %I ACM %@ 978-1-4503-5559-9
[236]
F. Grandoni, B. Laekhanukit, and S. Li, “O(log 2 k/ log log k)-Approximation Algorithm for Directed Steiner Tree: A Tight Quasi-Polynomial-Time Algorithm,” 2018. [Online]. Available: http://arxiv.org/abs/1811.03020. (arXiv: 1811.03020)
Abstract
In the Directed Steiner Tree (DST) problem we are given an $n$-vertex directed edge-weighted graph, a root $r$, and a collection of $k$ terminal nodes. Our goal is to find a minimum-cost arborescence that contains a directed path from $r$ to every terminal. We present an $O(\log^2 k/\log\log{k})$-approximation algorithm for DST that runs in quasi-polynomial-time. By adjusting the parameters in the hardness result of Halperin and Krauthgamer, we show the matching lower bound of $\Omega(\log^2{k}/\log\log{k})$ for the class of quasi-polynomial-time algorithms. This is the first improvement on the DST problem since the classical quasi-polynomial-time $O(\log^3 k)$ approximation algorithm by Charikar et al. (The paper erroneously claims an $O(\log^2k)$ approximation due to a mistake in prior work.) Our approach is based on two main ingredients. First, we derive an approximation preserving reduction to the Label-Consistent Subtree (LCST) problem. The LCST instance has quasi-polynomial size and logarithmic height. We remark that, in contrast, Zelikovsky's heigh-reduction theorem used in all prior work on DST achieves a reduction to a tree instance of the related Group Steiner Tree (GST) problem of similar height, however losing a logarithmic factor in the approximation ratio. Our second ingredient is an LP-rounding algorithm to approximately solve LCST instances, which is inspired by the framework devel