# Publications

2021
[1]
H. Akrami, B. Ray Chaudhury, K. Mehlhorn, G. Shahkarami, and Q. Vermande, “Nash Social Welfare for 2-value Instances,” 2021. [Online]. Available: https://arxiv.org/abs/2106.14816. (arXiv: 2106.14816)
Abstract
We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an allocation with maximum Nash social welfare, i.e., the geometric mean of the valuations of the agents. We give a polynomial-time algorithm to find a Nash social welfare maximizing allocation when the valuation functions are integrally 2-valued, i.e., each agent has a value either $1$ or $p$ for each good, for some positive integer $p$. We then extend our algorithm to find a better approximation factor for general 2-value instances.
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@online{Akrami2106.14816, TITLE = {Nash Social Welfare for 2-value Instances}, AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Mehlhorn, Kurt and Shahkarami, Golnoosh and Vermande, Quentin}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2106.14816}, EPRINT = {2106.14816}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an allocation with maximum Nash social welfare, i.e., the geometric mean of the valuations of the agents. We give a polynomial-time algorithm to find a Nash social welfare maximizing allocation when the valuation functions are integrally 2-valued, i.e., each agent has a value either $1$ or $p$ for each good, for some positive integer $p$. We then extend our algorithm to find a better approximation factor for general 2-value instances.}, }
Endnote
%0 Report %A Akrami, Hannaneh %A Ray Chaudhury, Bhaskar %A Mehlhorn, Kurt %A Shahkarami, Golnoosh %A Vermande, Quentin %+ 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 Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Nash Social Welfare for 2-value Instances : %G eng %U http://hdl.handle.net/21.11116/0000-0008-DB45-4 %U https://arxiv.org/abs/2106.14816 %D 2021 %X We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an allocation with maximum Nash social welfare, i.e., the geometric mean of the valuations of the agents. We give a polynomial-time algorithm to find a Nash social welfare maximizing allocation when the valuation functions are integrally 2-valued, i.e., each agent has a value either $1$ or $p$ for each good, for some positive integer $p$. We then extend our algorithm to find a better approximation factor for general 2-value instances. %K Computer Science, Computer Science and Game Theory, cs.GT
[2]
I. Anagnostides, T. Gouleakis, and A. Marashian, “Robust Learning under Strong Noise via SQs,” in Proceedings of the Twenty Fourth International Conference on Artificial Intelligence and Statistics (AISTATS 2021), Virtual Conference. (Accepted/in press)
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@inproceedings{Anagnostides_AISTATS2020, TITLE = {Robust Learning under Strong Noise via {SQs}}, AUTHOR = {Anagnostides, Ioannis and Gouleakis, Themis and Marashian, Ali}, LANGUAGE = {eng}, PUBLISHER = {PMLR}, YEAR = {2021}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Twenty Fourth International Conference on Artificial Intelligence and Statistics (AISTATS 2021)}, SERIES = {Proceedings of the Machine Learning Research}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Anagnostides, Ioannis %A Gouleakis, Themis %A Marashian, Ali %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Robust Learning under Strong Noise via SQs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-DBCD-C %D 2021 %B 24th International Conference on Artificial Intelligence and Statistics %Z date of event: 2021-04-13 - 2021-04-15 %C Virtual Conference %B Proceedings of the Twenty Fourth International Conference on Artificial Intelligence and Statistics %I PMLR %B Proceedings of the Machine Learning Research
[3]
K. Axiotis, A. Backurs, K. Bringmann, C. Jin, V. Nakos, C. Tzamos, and H. Wu, “Fast and Simple Modular Subset Sum,” in Symposium on Simplicity in Algorithms (SOSA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{Axiotis_SOSA2021, 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}, ISBN = {978-1-61197-649-6}, DOI = {10.1137/1.9781611976496.6}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Symposium on Simplicity in Algorithms (SOSA 2021)}, EDITOR = {King, Valerie and Viet Le, Hung}, PAGES = {57--67}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %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/21.11116/0000-0007-56CF-0 %R 10.1137/1.9781611976496.6 %D 2021 %B SIAM Symposium on Simplicity in Algorithms %Z date of event: 2021-01-11 - 2021-01-12 %C Alexandria, VA, USA (Virtual Conference) %B Symposium on Simplicity in Algorithms %E King, Valerie; Viet Le, Hung %P 57 - 67 %I SIAM %@ 978-1-61197-649-6
[4]
R. Becker, S. Forster, A. Karrenbauer, and C. Lenzen, “Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models,” SIAM Journal on Computing, vol. 50, no. 3, 2021.
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@article{Becker2021, TITLE = {Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models}, AUTHOR = {Becker, Ruben and Forster, Sebastian and Karrenbauer, Andreas and Lenzen, Christoph}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/19M1286955}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {50}, NUMBER = {3}, PAGES = {815--856}, }
Endnote
%0 Journal Article %A Becker, Ruben %A Forster, Sebastian %A Karrenbauer, Andreas %A Lenzen, Christoph %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E543-A %R 10.1137/19M1286955 %7 2021 %D 2021 %J SIAM Journal on Computing %V 50 %N 3 %& 815 %P 815 - 856 %I SIAM %C Philadelphia %@ false
[5]
B. A. Berendsohn, L. Kozma, and D. Marx, “Finding and Counting Permutations via CSPs,” Algorithmica, vol. 148, 2021.
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@article{berendsohn2021, TITLE = {Finding and Counting Permutations via {CSPs}}, AUTHOR = {Berendsohn, Benjamin Aram and Kozma, L{\'a}szl{\'o} and Marx, D{\'a}niel}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-021-00812-z}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, VOLUME = {148}, }
Endnote
%0 Journal Article %A Berendsohn, Benjamin Aram %A Kozma, L&#225;szl&#243; %A Marx, D&#225;niel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Finding and Counting Permutations via CSPs : %G eng %U http://hdl.handle.net/21.11116/0000-0008-3403-A %R 10.1007/s00453-021-00812-z %7 2021 %D 2021 %J Algorithmica %V 148 %I Springer %C New York, NY %@ false
[6]
K. Bringmann and P. Wellnitz, “On Near-Linear-Time Algorithms for Dense Subset Sum,” in Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{Bringmann_SODA21, TITLE = {On Near-Linear-Time Algorithms for Dense Subset Sum}, AUTHOR = {Bringmann, Karl and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-61197-646-5}, DOI = {10.1137/1.9781611976465.107}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021)}, EDITOR = {Marx, D{\'a}niel}, PAGES = {1777--1796}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On Near-Linear-Time Algorithms for Dense Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8C7E-F %R 10.1137/1.9781611976465.107 %D 2021 %B 32nd Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2021-01-10 - 2021-01-13 %C Alexandria, VA, USA (Virtual Conference) %B Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms %E Marx, D&#225;niel %P 1777 - 1796 %I SIAM %@ 978-1-61197-646-5
[7]
K. Bringmann and V. Nakos, “A Fine-Grained Perspective on Approximating Subset Sum and Partition,” in Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{Bringmann_SODA21b, TITLE = {A Fine-Grained Perspective on Approximating Subset Sum and Partition}, AUTHOR = {Bringmann, Karl and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {978-1-61197-646-5}, DOI = {10.1137/1.9781611976465.108}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021)}, EDITOR = {Marx, D{\'a}niel}, PAGES = {1797--1815}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Nakos, Vasileios %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Fine-Grained Perspective on Approximating Subset Sum and Partition : %G eng %U http://hdl.handle.net/21.11116/0000-0007-90DD-D %R 10.1137/1.9781611976465.108 %D 2021 %B 32nd Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2021-01-10 - 2021-01-13 %C Alexandria, VA, USA (Virtual Conference) %B Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms %E Marx, D&#225;niel %P 1797 - 1815 %I SIAM %@ 978-1-61197-646-5
[8]
K. Bringmann and A. Nusser, “Translating Hausdorff Is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation,” in 37th International Symposium onComputational Geometry (SoCG 2021), Buffalo, NY, USA (Virtual Conference), 2021.
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@inproceedings{Bringmann_SoCG2021, TITLE = {Translating {Hausdorff} Is Hard: {F}ine-Grained Lower Bounds for {Hausdorff} Distance Under Translation}, AUTHOR = {Bringmann, Karl and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-184-9}, URL = {urn:nbn:de:0030-drops-138177}, DOI = {10.4230/LIPIcs.SoCG.2021.18}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {37th International Symposium onComputational Geometry (SoCG 2021)}, EDITOR = {Buchin, Kevin and Colin de Verdi{\e}re, {\'E}rich}, PAGES = {1--17}, EID = {18}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {189}, ADDRESS = {Buffalo, NY, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Translating Hausdorff Is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation : %G eng %U http://hdl.handle.net/21.11116/0000-0008-DB6F-6 %R 10.4230/LIPIcs.SoCG.2021.18 %U urn:nbn:de:0030-drops-138177 %D 2021 %B 37th International Symposium on Computational Geometry %Z date of event: 2021-06-07 - 2021-06-11 %C Buffalo, NY, USA (Virtual Conference) %B 37th International Symposium onComputational Geometry %E Buchin, Kevin; Colin de Verdi&#232;re, &#201;rich %P 1 - 17 %Z sequence number: 18 %I Schloss Dagstuhl %@ 978-3-95977-184-9 %B Leibniz International Proceedings in Informatics %N 189 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2021/13817/https://creativecommons.org/licenses/by/4.0/legalcode
[9]
K. Bringmann and V. Nakos, “Fast n-Fold Boolean Convolution via Additive Combinatorics,” in 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Glasgow, UK (Virtual Conference), 2021.
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@inproceedings{Bringmann_ICALP2021c, TITLE = {Fast n-Fold {B}oolean Convolution via Additive Combinatorics}, AUTHOR = {Bringmann, Karl and Nakos, Vasileios}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-195-5}, URL = {urn:nbn:de:0030-drops-141108}, DOI = {10.4230/LIPIcs.ICALP.2021.41}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, EDITOR = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, PAGES = {1--17}, EID = {41}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {198}, ADDRESS = {Glasgow, UK (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Nakos, Vasileios %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fast n-Fold Boolean Convolution via Additive Combinatorics : %G eng %U http://hdl.handle.net/21.11116/0000-0008-DB8E-2 %R 10.4230/LIPIcs.ICALP.2021.41 %U urn:nbn:de:0030-drops-141108 %D 2021 %B 48th International Colloquium on Automata, Languages, and Programming %Z date of event: 2021-07-12 - 2020-07-16 %C Glasgow, UK (Virtual Conference) %B 48th International Colloquium on Automata, Languages, and Programming %E Bansal, Nikhil; Merelli, Emanuela; Worrell, James %P 1 - 17 %Z sequence number: 41 %I Schloss Dagstuhl %@ 978-3-95977-195-5 %B Leibniz International Proceedings in Informatics %N 198 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2021/14110/pdf/LIPIcs-ICALP-2021-41.pdfhttps://creativecommons.org/licenses/by/4.0/legalcode
[10]
K. Bringmann and D. Das, “A Linear-Time n0.4-Approximation for Longest Common Subsequence,” in 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Glasgow, UK (Virtual Conference), 2021.
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@inproceedings{Bringmann_ICALP2021, TITLE = {A Linear-Time $n^\{0.4\}$-Approximation for Longest Common Subsequence}, AUTHOR = {Bringmann, Karl and Das, Debarati}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-195-5}, URL = {urn:nbn:de:0030-drops-141082}, DOI = {10.4230/LIPIcs.ICALP.2021.39}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, EDITOR = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, PAGES = {1--20}, EID = {39}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {198}, ADDRESS = {Glasgow, UK (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Das, Debarati %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Linear-Time n0.4-Approximation for Longest Common Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0008-DB7B-8 %R 10.4230/LIPIcs.ICALP.2021.39 %U urn:nbn:de:0030-drops-141082 %D 2021 %B 48th International Colloquium on Automata, Languages, and Programming %Z date of event: 2021-07-12 - 2020-07-16 %C Glasgow, UK (Virtual Conference) %B 48th International Colloquium on Automata, Languages, and Programming %E Bansal, Nikhil; Merelli, Emanuela; Worrell, James %P 1 - 20 %Z sequence number: 39 %I Schloss Dagstuhl %@ 978-3-95977-195-5 %B Leibniz International Proceedings in Informatics %N 198 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2021/14108/https://creativecommons.org/licenses/by/4.0/legalcode
[11]
K. Bringmann and J. Slusallek, “Current Algorithms for Detecting Subgraphs of Bounded Treewidth Are Probably Optimal,” in 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Glasgow, UK (Virtual Conference), 2021.
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@inproceedings{Bringmann_ICALP2021b, TITLE = {Current Algorithms for Detecting Subgraphs of Bounded Treewidth Are Probably Optimal}, AUTHOR = {Bringmann, Karl and Slusallek, Jasper}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-195-5}, URL = {urn:nbn:de:0030-drops-141095}, DOI = {10.4230/LIPIcs.ICALP.2021.40}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, EDITOR = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, PAGES = {1--16}, EID = {40}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {198}, ADDRESS = {Glasgow, UK (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Slusallek, Jasper %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Current Algorithms for Detecting Subgraphs of Bounded Treewidth Are Probably Optimal : %G eng %U http://hdl.handle.net/21.11116/0000-0008-DB85-B %R 10.4230/LIPIcs.ICALP.2021.40 %U urn:nbn:de:0030-drops-141095 %D 2021 %B 48th International Colloquium on Automata, Languages, and Programming %Z date of event: 2021-07-12 - 2020-07-16 %C Glasgow, UK (Virtual Conference) %B 48th International Colloquium on Automata, Languages, and Programming %E Bansal, Nikhil; Merelli, Emanuela; Worrell, James %P 1 - 16 %Z sequence number: 40 %I Schloss Dagstuhl %@ 978-3-95977-195-5 %B Leibniz International Proceedings in Informatics %N 198 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2021/14109/https://creativecommons.org/licenses/by/4.0/legalcode
[12]
K. Bringmann and A. Nusser, “Translating Hausdorff is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation,” 2021. [Online]. Available: https://arxiv.org/abs/2101.07696. (arXiv: 2101.07696)
Abstract
Computing the similarity of two point sets is a ubiquitous task in medical imaging, geometric shape comparison, trajectory analysis, and many more settings. Arguably the most basic distance measure for this task is the Hausdorff distance, which assigns to each point from one set the closest point in the other set and then evaluates the maximum distance of any assigned pair. A drawback is that this distance measure is not translational invariant, that is, comparing two objects just according to their shape while disregarding their position in space is impossible. Fortunately, there is a canonical translational invariant version, the Hausdorff distance under translation, which minimizes the Hausdorff distance over all translations of one of the point sets. For point sets of size $n$ and $m$, the Hausdorff distance under translation can be computed in time $\tilde O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm (n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93]. As these bounds have not been improved for over 25 years, in this paper we approach the Hausdorff distance under translation from the perspective of fine-grained complexity theory. We show (i) a matching lower bound of $(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ assuming the Orthogonal Vectors Hypothesis and (ii) a matching lower bound of $n^{2-o(1)}$ for $L_2$ in the imbalanced case of $m = O(1)$ assuming the 3SUM Hypothesis.
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@online{Bringmann_2101.07696, TITLE = {Translating Hausdorff is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation}, AUTHOR = {Bringmann, Karl and Nusser, Andr{\'e}}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2101.07696}, EPRINT = {2101.07696}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Computing the similarity of two point sets is a ubiquitous task in medical imaging, geometric shape comparison, trajectory analysis, and many more settings. Arguably the most basic distance measure for this task is the Hausdorff distance, which assigns to each point from one set the closest point in the other set and then evaluates the maximum distance of any assigned pair. A drawback is that this distance measure is not translational invariant, that is, comparing two objects just according to their shape while disregarding their position in space is impossible. Fortunately, there is a canonical translational invariant version, the Hausdorff distance under translation, which minimizes the Hausdorff distance over all translations of one of the point sets. For point sets of size $n$ and $m$, the Hausdorff distance under translation can be computed in time $\tilde O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm (n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93]. As these bounds have not been improved for over 25 years, in this paper we approach the Hausdorff distance under translation from the perspective of fine-grained complexity theory. We show (i) a matching lower bound of $(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ assuming the Orthogonal Vectors Hypothesis and (ii) a matching lower bound of $n^{2-o(1)}$ for $L_2$ in the imbalanced case of $m = O(1)$ assuming the 3SUM Hypothesis.}, }
Endnote
%0 Report %A Bringmann, Karl %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Translating Hausdorff is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E242-E %U https://arxiv.org/abs/2101.07696 %D 2021 %X Computing the similarity of two point sets is a ubiquitous task in medical imaging, geometric shape comparison, trajectory analysis, and many more settings. Arguably the most basic distance measure for this task is the Hausdorff distance, which assigns to each point from one set the closest point in the other set and then evaluates the maximum distance of any assigned pair. A drawback is that this distance measure is not translational invariant, that is, comparing two objects just according to their shape while disregarding their position in space is impossible. Fortunately, there is a canonical translational invariant version, the Hausdorff distance under translation, which minimizes the Hausdorff distance over all translations of one of the point sets. For point sets of size $n$ and $m$, the Hausdorff distance under translation can be computed in time $\tilde O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm (n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93]. As these bounds have not been improved for over 25 years, in this paper we approach the Hausdorff distance under translation from the perspective of fine-grained complexity theory. We show (i) a matching lower bound of $(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ assuming the Orthogonal Vectors Hypothesis and (ii) a matching lower bound of $n^{2-o(1)}$ for $L_2$ in the imbalanced case of $m = O(1)$ assuming the 3SUM Hypothesis. %K Computer Science, Computational Geometry, cs.CG,Computer Science, Computational Complexity, cs.CC
[13]
K. Bringmann, N. Fischer, and V. Nakos, “Sparse Nonnegative Convolution is Equivalent to Dense Nonnegative Convolution,” in STOC ’21, Virtual, Italy, 2021.
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@inproceedings{Bringmann_STOC2021, TITLE = {Sparse Nonnegative Convolution is Equivalent to Dense Nonnegative Convolution}, AUTHOR = {Bringmann, Karl and Fischer, Nick and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {9781450380539}, DOI = {10.1145/3406325.3451090}, PUBLISHER = {ACM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '21}, EDITOR = {Khuller, Samir and Vassilevska Williams, Virginia}, PAGES = {1711--1724}, ADDRESS = {Virtual, Italy}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Fischer, Nick %A Nakos, Vasileios %+ 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 Sparse Nonnegative Convolution is Equivalent to Dense Nonnegative Convolution : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E23F-3 %R 10.1145/3406325.3451090 %D 2021 %B 53rd Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2021-06-21 - 2021-06-25 %C Virtual, Italy %B STOC '21 %E Khuller, Samir; Vassilevska Williams, Virginia %P 1711 - 1724 %I ACM %@ 9781450380539
[14]
K. Bringmann, N. Fischer, and V. Nakos, “Sparse Nonnegative Convolution Is Equivalent to Dense Nonnegative Convolution,” 2021. [Online]. Available: https://arxiv.org/abs/2105.05984. (arXiv: 2105.05984)
Abstract
Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications often come in the form of nonnegative convolution, where the entries of $A,B$ are nonnegative integers. The classical algorithm to compute $A\star B$ uses the Fast Fourier Transform and runs in time $O(n\log n)$. However, often $A$ and $B$ satisfy sparsity conditions, and hence one could hope for significant improvements. The ideal goal is an $O(k\log k)$-time algorithm, where $k$ is the number of non-zero elements in the output, i.e., the size of the support of $A\star B$. This problem is referred to as sparse nonnegative convolution, and has received considerable attention in the literature; the fastest algorithms to date run in time $O(k\log^2 n)$. The main result of this paper is the first $O(k\log k)$-time algorithm for sparse nonnegative convolution. Our algorithm is randomized and assumes that the length $n$ and the largest entry of $A$ and $B$ are subexponential in $k$. Surprisingly, we can phrase our algorithm as a reduction from the sparse case to the dense case of nonnegative convolution, showing that, under some mild assumptions, sparse nonnegative convolution is equivalent to dense nonnegative convolution for constant-error randomized algorithms. Specifically, if $D(n)$ is the time to convolve two nonnegative length-$n$ vectors with success probability $2/3$, and $S(k)$ is the time to convolve two nonnegative vectors with output size $k$ with success probability $2/3$, then $S(k)=O(D(k)+k(\log\log k)^2)$. Our approach uses a variety of new techniques in combination with some old machinery from linear sketching and structured linear algebra, as well as new insights on linear hashing, the most classical hash function.
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BibTeX
@online{Bringmann_2105.05984, TITLE = {Sparse Nonnegative Convolution Is Equivalent to Dense Nonnegative Convolution}, AUTHOR = {Bringmann, Karl and Fischer, Nick and Nakos, Vasileios}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2105.05984}, EPRINT = {2105.05984}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications often come in the form of nonnegative convolution, where the entries of $A,B$ are nonnegative integers. The classical algorithm to compute $A\star B$ uses the Fast Fourier Transform and runs in time $O(n\log n)$. However, often $A$ and $B$ satisfy sparsity conditions, and hence one could hope for significant improvements. The ideal goal is an $O(k\log k)$-time algorithm, where $k$ is the number of non-zero elements in the output, i.e., the size of the support of $A\star B$. This problem is referred to as sparse nonnegative convolution, and has received considerable attention in the literature; the fastest algorithms to date run in time $O(k\log^2 n)$. The main result of this paper is the first $O(k\log k)$-time algorithm for sparse nonnegative convolution. Our algorithm is randomized and assumes that the length $n$ and the largest entry of $A$ and $B$ are subexponential in $k$. Surprisingly, we can phrase our algorithm as a reduction from the sparse case to the dense case of nonnegative convolution, showing that, under some mild assumptions, sparse nonnegative convolution is equivalent to dense nonnegative convolution for constant-error randomized algorithms. Specifically, if $D(n)$ is the time to convolve two nonnegative length-$n$ vectors with success probability $2/3$, and $S(k)$ is the time to convolve two nonnegative vectors with output size $k$ with success probability $2/3$, then $S(k)=O(D(k)+k(\log\log k)^2)$. Our approach uses a variety of new techniques in combination with some old machinery from linear sketching and structured linear algebra, as well as new insights on linear hashing, the most classical hash function.}, }
Endnote
%0 Report %A Bringmann, Karl %A Fischer, Nick %A Nakos, Vasileios %+ 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 Sparse Nonnegative Convolution Is Equivalent to Dense Nonnegative Convolution : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E263-9 %U https://arxiv.org/abs/2105.05984 %D 2021 %X Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications often come in the form of nonnegative convolution, where the entries of $A,B$ are nonnegative integers. The classical algorithm to compute $A\star B$ uses the Fast Fourier Transform and runs in time $O(n\log n)$. However, often $A$ and $B$ satisfy sparsity conditions, and hence one could hope for significant improvements. The ideal goal is an $O(k\log k)$-time algorithm, where $k$ is the number of non-zero elements in the output, i.e., the size of the support of $A\star B$. This problem is referred to as sparse nonnegative convolution, and has received considerable attention in the literature; the fastest algorithms to date run in time $O(k\log^2 n)$. The main result of this paper is the first $O(k\log k)$-time algorithm for sparse nonnegative convolution. Our algorithm is randomized and assumes that the length $n$ and the largest entry of $A$ and $B$ are subexponential in $k$. Surprisingly, we can phrase our algorithm as a reduction from the sparse case to the dense case of nonnegative convolution, showing that, under some mild assumptions, sparse nonnegative convolution is equivalent to dense nonnegative convolution for constant-error randomized algorithms. Specifically, if $D(n)$ is the time to convolve two nonnegative length-$n$ vectors with success probability $2/3$, and $S(k)$ is the time to convolve two nonnegative vectors with output size $k$ with success probability $2/3$, then $S(k)=O(D(k)+k(\log\log k)^2)$. Our approach uses a variety of new techniques in combination with some old machinery from linear sketching and structured linear algebra, as well as new insights on linear hashing, the most classical hash function. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[15]
K. Bringmann and V. Nakos, “Fast n-fold Boolean Convolution via Additive Combinatorics,” 2021. [Online]. Available: https://arxiv.org/abs/2105.03968. (arXiv: 2105.03968)
Abstract
We consider the problem of computing the Boolean convolution (with wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq \mathbb{Z}_m$. Boolean convolution formalizes the frequent task of combining two subproblems, where the whole problem has a solution of size $k$ if for some $i$ the first subproblem has a solution of size~$i$ and the second subproblem has a solution of size $k-i$. Our problem formalizes a natural generalization, namely combining solutions of $n$ subproblems subject to a modular constraint. This simultaneously generalises Modular Subset Sum and Boolean Convolution (Sumset Computation). Although nearly optimal algorithms are known for special cases of this problem, not even tiny improvements are known for the general case. We almost resolve the computational complexity of this problem, shaving essentially a factor of $n$ from the running time of previous algorithms. Specifically, we present a \emph{deterministic} algorithm running in \emph{almost} linear time with respect to the input plus output size $k$. We also present a \emph{Las Vegas} algorithm running in \emph{nearly} linear expected time with respect to the input plus output size $k$. Previously, no deterministic or randomized $o(nk)$ algorithm was known. At the heart of our approach lies a careful usage of Kneser's theorem from Additive Combinatorics, and a new deterministic almost linear output-sensitive algorithm for non-negative sparse convolution. In total, our work builds a solid toolbox that could be of independent interest.
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BibTeX
@online{Bringmann_2105.03968, TITLE = {Fast $n$-fold {B}oolean Convolution via Additive Combinatorics}, AUTHOR = {Bringmann, Karl and Nakos, Vasileios}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2105.03968}, EPRINT = {2105.03968}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the problem of computing the Boolean convolution (with wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq \mathbb{Z}_m$. Boolean convolution formalizes the frequent task of combining two subproblems, where the whole problem has a solution of size $k$ if for some $i$ the first subproblem has a solution of size~$i$ and the second subproblem has a solution of size $k-i$. Our problem formalizes a natural generalization, namely combining solutions of $n$ subproblems subject to a modular constraint. This simultaneously generalises Modular Subset Sum and Boolean Convolution (Sumset Computation). Although nearly optimal algorithms are known for special cases of this problem, not even tiny improvements are known for the general case. We almost resolve the computational complexity of this problem, shaving essentially a factor of $n$ from the running time of previous algorithms. Specifically, we present a \emph{deterministic} algorithm running in \emph{almost} linear time with respect to the input plus output size $k$. We also present a \emph{Las Vegas} algorithm running in \emph{nearly} linear expected time with respect to the input plus output size $k$. Previously, no deterministic or randomized $o(nk)$ algorithm was known. At the heart of our approach lies a careful usage of Kneser's theorem from Additive Combinatorics, and a new deterministic almost linear output-sensitive algorithm for non-negative sparse convolution. In total, our work builds a solid toolbox that could be of independent interest.}, }
Endnote
%0 Report %A Bringmann, Karl %A Nakos, Vasileios %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fast n-fold Boolean Convolution via Additive Combinatorics : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E25B-3 %U https://arxiv.org/abs/2105.03968 %D 2021 %X We consider the problem of computing the Boolean convolution (with wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq \mathbb{Z}_m$. Boolean convolution formalizes the frequent task of combining two subproblems, where the whole problem has a solution of size $k$ if for some $i$ the first subproblem has a solution of size~$i$ and the second subproblem has a solution of size $k-i$. Our problem formalizes a natural generalization, namely combining solutions of $n$ subproblems subject to a modular constraint. This simultaneously generalises Modular Subset Sum and Boolean Convolution (Sumset Computation). Although nearly optimal algorithms are known for special cases of this problem, not even tiny improvements are known for the general case. We almost resolve the computational complexity of this problem, shaving essentially a factor of $n$ from the running time of previous algorithms. Specifically, we present a \emph{deterministic} algorithm running in \emph{almost} linear time with respect to the input plus output size $k$. We also present a \emph{Las Vegas} algorithm running in \emph{nearly} linear expected time with respect to the input plus output size $k$. Previously, no deterministic or randomized $o(nk)$ algorithm was known. At the heart of our approach lies a careful usage of Kneser's theorem from Additive Combinatorics, and a new deterministic almost linear output-sensitive algorithm for non-negative sparse convolution. In total, our work builds a solid toolbox that could be of independent interest. %K Computer Science, Data Structures and Algorithms, cs.DS
[16]
K. Bringmann, V. Cohen-Addad, and D. Das, “A Linear-Time n0.4-Approximation for Longest Common Subsequence,” 2021. [Online]. Available: https://arxiv.org/abs/2106.08195. (arXiv: 2106.08195)
Abstract
We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found despite an extensive effort. The lack of progress on the problem has recently been explained by Abboud, Backurs, and Vassilevska Williams [FOCS'15] and Bringmann and K\"unnemann [FOCS'15] who proved that there is no subquadratic algorithm unless the Strong Exponential Time Hypothesis fails. This has led the community to look for subquadratic approximation algorithms for the problem. Yet, unlike the edit distance problem for which a constant-factor approximation in almost-linear time is known, very little progress has been made on LCS, making it a notoriously difficult problem also in the realm of approximation. For the general setting, only a naive $O(n^{\varepsilon/2})$-approximation algorithm with running time $\tilde{O}(n^{2-\varepsilon})$ has been known, for any constant $0 < \varepsilon \le 1$. Recently, a breakthrough result by Hajiaghayi, Seddighin, Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a $O(n^{0.497956})$-approximation in expectation; improving upon the naive $O(\sqrt{n})$-approximation for the first time. In this paper, we provide an algorithm that in time $O(n^{2-\varepsilon})$ computes an $\tilde{O}(n^{2\varepsilon/5})$-approximation with high probability, for any $0 < \varepsilon \le 1$. Our result (1) gives an $\tilde{O}(n^{0.4})$-approximation in linear time, improving upon the bound of Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose approximation scales with any subquadratic running time $O(n^{2-\varepsilon})$, improving upon the naive bound of $O(n^{\varepsilon/2})$ for any $\varepsilon$, and (3) instead of only in expectation, succeeds with high probability.
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BibTeX
@online{Bringmann_2106.08195, TITLE = {A Linear-Time $n^\{0.4\}$-Approximation for Longest Common Subsequence}, AUTHOR = {Bringmann, Karl and Cohen-Addad, Vincent and Das, Debarati}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2106.08195}, EPRINT = {2106.08195}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found despite an extensive effort. The lack of progress on the problem has recently been explained by Abboud, Backurs, and Vassilevska Williams [FOCS'15] and Bringmann and K\"unnemann [FOCS'15] who proved that there is no subquadratic algorithm unless the Strong Exponential Time Hypothesis fails. This has led the community to look for subquadratic approximation algorithms for the problem. Yet, unlike the edit distance problem for which a constant-factor approximation in almost-linear time is known, very little progress has been made on LCS, making it a notoriously difficult problem also in the realm of approximation. For the general setting, only a naive $O(n^{\varepsilon/2})$-approximation algorithm with running time $\tilde{O}(n^{2-\varepsilon})$ has been known, for any constant $0 < \varepsilon \le 1$. Recently, a breakthrough result by Hajiaghayi, Seddighin, Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a $O(n^{0.497956})$-approximation in expectation; improving upon the naive $O(\sqrt{n})$-approximation for the first time. In this paper, we provide an algorithm that in time $O(n^{2-\varepsilon})$ computes an $\tilde{O}(n^{2\varepsilon/5})$-approximation with high probability, for any $0 < \varepsilon \le 1$. Our result (1) gives an $\tilde{O}(n^{0.4})$-approximation in linear time, improving upon the bound of Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose approximation scales with any subquadratic running time $O(n^{2-\varepsilon})$, improving upon the naive bound of $O(n^{\varepsilon/2})$ for any $\varepsilon$, and (3) instead of only in expectation, succeeds with high probability.}, }
Endnote
%0 Report %A Bringmann, Karl %A Cohen-Addad, Vincent %A Das, Debarati %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Linear-Time n0.4-Approximation for Longest Common Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E267-5 %U https://arxiv.org/abs/2106.08195 %D 2021 %X We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found despite an extensive effort. The lack of progress on the problem has recently been explained by Abboud, Backurs, and Vassilevska Williams [FOCS'15] and Bringmann and K\"unnemann [FOCS'15] who proved that there is no subquadratic algorithm unless the Strong Exponential Time Hypothesis fails. This has led the community to look for subquadratic approximation algorithms for the problem. Yet, unlike the edit distance problem for which a constant-factor approximation in almost-linear time is known, very little progress has been made on LCS, making it a notoriously difficult problem also in the realm of approximation. For the general setting, only a naive $O(n^{\varepsilon/2})$-approximation algorithm with running time $\tilde{O}(n^{2-\varepsilon})$ has been known, for any constant $0 < \varepsilon \le 1$. Recently, a breakthrough result by Hajiaghayi, Seddighin, Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a $O(n^{0.497956})$-approximation in expectation; improving upon the naive $O(\sqrt{n})$-approximation for the first time. In this paper, we provide an algorithm that in time $O(n^{2-\varepsilon})$ computes an $\tilde{O}(n^{2\varepsilon/5})$-approximation with high probability, for any $0 < \varepsilon \le 1$. Our result (1) gives an $\tilde{O}(n^{0.4})$-approximation in linear time, improving upon the bound of Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose approximation scales with any subquadratic running time $O(n^{2-\varepsilon})$, improving upon the naive bound of $O(n^{\varepsilon/2})$ for any $\varepsilon$, and (3) instead of only in expectation, succeeds with high probability. %K Computer Science, Data Structures and Algorithms, cs.DS,
[17]
K. Bringmann and J. Slusallek, “Current Algorithms for Detecting Subgraphs of Bounded Treewidth are Probably Optimal,” 2021. [Online]. Available: https://arxiv.org/abs/2105.05062. (arXiv: 2105.05062)
Abstract
The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via color-coding that runs in time $O(n^{tw(H)+1})$ [Alon, Yuster, Zwick'95], where $n$ is the number of vertices of the host graph $G$. While there are pattern graphs known for which Subgraph Isomorphism can be solved in an improved running time of $O(n^{tw(H)+1-\varepsilon})$ or even faster (e.g. for $k$-cliques), it is not known whether such improvements are possible for all patterns. The only known lower bound rules out time $n^{o(tw(H) / \log(tw(H)))}$ for any class of patterns of unbounded treewidth assuming the Exponential Time Hypothesis [Marx'07]. In this paper, we demonstrate the existence of maximally hard pattern graphs $H$ that require time $n^{tw(H)+1-o(1)}$. Specifically, under the Strong Exponential Time Hypothesis (SETH), a standard assumption from fine-grained complexity theory, we prove the following asymptotic statement for large treewidth $t$: For any $\varepsilon > 0$ there exists $t \ge 3$ and a pattern graph $H$ of treewidth $t$ such that Subgraph Isomorphism on pattern $H$ has no algorithm running in time $O(n^{t+1-\varepsilon})$. Under the more recent 3-uniform Hyperclique hypothesis, we even obtain tight lower bounds for each specific treewidth $t \ge 3$: For any $t \ge 3$ there exists a pattern graph $H$ of treewidth $t$ such that for any $\varepsilon>0$ Subgraph Isomorphism on pattern $H$ has no algorithm running in time $O(n^{t+1-\varepsilon})$. In addition to these main results, we explore (1) colored and uncolored problem variants (and why they are equivalent for most cases), (2) Subgraph Isomorphism for $tw < 3$, (3) Subgraph Isomorphism parameterized by pathwidth, and (4) a weighted problem variant.
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BibTeX
@online{Bringmann_2105.05062, TITLE = {Current Algorithms for Detecting Subgraphs of Bounded Treewidth are Probably Optimal}, AUTHOR = {Bringmann, Karl and Slusallek, Jasper}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2105.05062}, EPRINT = {2105.05062}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via color-coding that runs in time $O(n^{tw(H)+1})$ [Alon, Yuster, Zwick'95], where $n$ is the number of vertices of the host graph $G$. While there are pattern graphs known for which Subgraph Isomorphism can be solved in an improved running time of $O(n^{tw(H)+1-\varepsilon})$ or even faster (e.g. for $k$-cliques), it is not known whether such improvements are possible for all patterns. The only known lower bound rules out time $n^{o(tw(H) / \log(tw(H)))}$ for any class of patterns of unbounded treewidth assuming the Exponential Time Hypothesis [Marx'07]. In this paper, we demonstrate the existence of maximally hard pattern graphs $H$ that require time $n^{tw(H)+1-o(1)}$. Specifically, under the Strong Exponential Time Hypothesis (SETH), a standard assumption from fine-grained complexity theory, we prove the following asymptotic statement for large treewidth $t$: For any $\varepsilon > 0$ there exists $t \ge 3$ and a pattern graph $H$ of treewidth $t$ such that Subgraph Isomorphism on pattern $H$ has no algorithm running in time $O(n^{t+1-\varepsilon})$. Under the more recent 3-uniform Hyperclique hypothesis, we even obtain tight lower bounds for each specific treewidth $t \ge 3$: For any $t \ge 3$ there exists a pattern graph $H$ of treewidth $t$ such that for any $\varepsilon>0$ Subgraph Isomorphism on pattern $H$ has no algorithm running in time $O(n^{t+1-\varepsilon})$. In addition to these main results, we explore (1) colored and uncolored problem variants (and why they are equivalent for most cases), (2) Subgraph Isomorphism for $tw < 3$, (3) Subgraph Isomorphism parameterized by pathwidth, and (4) a weighted problem variant.}, }
Endnote
%0 Report %A Bringmann, Karl %A Slusallek, Jasper %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Current Algorithms for Detecting Subgraphs of Bounded Treewidth are Probably Optimal : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E25F-F %U https://arxiv.org/abs/2105.05062 %D 2021 %X The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via color-coding that runs in time $O(n^{tw(H)+1})$ [Alon, Yuster, Zwick'95], where $n$ is the number of vertices of the host graph $G$. While there are pattern graphs known for which Subgraph Isomorphism can be solved in an improved running time of $O(n^{tw(H)+1-\varepsilon})$ or even faster (e.g. for $k$-cliques), it is not known whether such improvements are possible for all patterns. The only known lower bound rules out time $n^{o(tw(H) / \log(tw(H)))}$ for any class of patterns of unbounded treewidth assuming the Exponential Time Hypothesis [Marx'07]. In this paper, we demonstrate the existence of maximally hard pattern graphs $H$ that require time $n^{tw(H)+1-o(1)}$. Specifically, under the Strong Exponential Time Hypothesis (SETH), a standard assumption from fine-grained complexity theory, we prove the following asymptotic statement for large treewidth $t$: For any $\varepsilon > 0$ there exists $t \ge 3$ and a pattern graph $H$ of treewidth $t$ such that Subgraph Isomorphism on pattern $H$ has no algorithm running in time $O(n^{t+1-\varepsilon})$. Under the more recent 3-uniform Hyperclique hypothesis, we even obtain tight lower bounds for each specific treewidth $t \ge 3$: For any $t \ge 3$ there exists a pattern graph $H$ of treewidth $t$ such that for any $\varepsilon>0$ Subgraph Isomorphism on pattern $H$ has no algorithm running in time $O(n^{t+1-\varepsilon})$. In addition to these main results, we explore (1) colored and uncolored problem variants (and why they are equivalent for most cases), (2) Subgraph Isomorphism for $tw < 3$, (3) Subgraph Isomorphism parameterized by pathwidth, and (4) a weighted problem variant. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,
[18]
K. Bringmann, A. Cassis, N. Fischer, and M. Künnemann, “Fine-Grained Completeness for Optimization in P,” 2021. [Online]. Available: https://arxiv.org/abs/2107.01721. (arXiv: 2107.01721)
Abstract
We initiate the study of fine-grained completeness theorems for exact and approximate optimization in the polynomial-time regime. Inspired by the first completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova, Williams, TALG 2019) as well as the classic class MaxSNP and MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis, JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain a number of natural optimization problems in P, including Maximum Inner Product, general forms of nearest neighbor search and optimization variants of the $k$-XOR problem. Specifically, we define MaxSP as the class of problems definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) : \phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free first-order property over a given relational structure (with MinSP defined analogously). On $m$-sized structures, we can solve each such problem in time $O(m^{k+\ell-1})$. Our results are: - We determine (a sparse variant of) the Maximum/Minimum Inner Product problem as complete under *deterministic* fine-grained reductions: A strongly subquadratic algorithm for Maximum/Minimum Inner Product would beat the baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by a polynomial factor. - This completeness transfers to approximation: Maximum/Minimum Inner Product is also complete in the sense that a strongly subquadratic $c$-approximation would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019), we obtain the perhaps surprising consequence that refuting the OV Hypothesis is *equivalent* to giving a $O(1)$-approximation for all MinSP problems in faster-than-$O(m^{k+\ell-1})$ time.
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@online{Bringmann_2107.01721, TITLE = {Fine-Grained Completeness for Optimization in P}, AUTHOR = {Bringmann, Karl and Cassis, Alejandro and Fischer, Nick and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2107.01721}, EPRINT = {2107.01721}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We initiate the study of fine-grained completeness theorems for exact and approximate optimization in the polynomial-time regime. Inspired by the first completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova, Williams, TALG 2019) as well as the classic class MaxSNP and MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis, JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain a number of natural optimization problems in P, including Maximum Inner Product, general forms of nearest neighbor search and optimization variants of the $k$-XOR problem. Specifically, we define MaxSP as the class of problems definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) : \phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free first-order property over a given relational structure (with MinSP defined analogously). On $m$-sized structures, we can solve each such problem in time $O(m^{k+\ell-1})$. Our results are: -- We determine (a sparse variant of) the Maximum/Minimum Inner Product problem as complete under *deterministic* fine-grained reductions: A strongly subquadratic algorithm for Maximum/Minimum Inner Product would beat the baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by a polynomial factor. -- This completeness transfers to approximation: Maximum/Minimum Inner Product is also complete in the sense that a strongly subquadratic $c$-approximation would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019), we obtain the perhaps surprising consequence that refuting the OV Hypothesis is *equivalent* to giving a $O(1)$-approximation for all MinSP problems in faster-than-$O(m^{k+\ell-1})$ time.}, }
Endnote
%0 Report %A Bringmann, Karl %A Cassis, Alejandro %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 External Organizations %T Fine-Grained Completeness for Optimization in P : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E26A-2 %U https://arxiv.org/abs/2107.01721 %D 2021 %X We initiate the study of fine-grained completeness theorems for exact and approximate optimization in the polynomial-time regime. Inspired by the first completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova, Williams, TALG 2019) as well as the classic class MaxSNP and MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis, JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain a number of natural optimization problems in P, including Maximum Inner Product, general forms of nearest neighbor search and optimization variants of the $k$-XOR problem. Specifically, we define MaxSP as the class of problems definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) : \phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free first-order property over a given relational structure (with MinSP defined analogously). On $m$-sized structures, we can solve each such problem in time $O(m^{k+\ell-1})$. Our results are: - We determine (a sparse variant of) the Maximum/Minimum Inner Product problem as complete under *deterministic* fine-grained reductions: A strongly subquadratic algorithm for Maximum/Minimum Inner Product would beat the baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by a polynomial factor. - This completeness transfers to approximation: Maximum/Minimum Inner Product is also complete in the sense that a strongly subquadratic $c$-approximation would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019), we obtain the perhaps surprising consequence that refuting the OV Hypothesis is *equivalent* to giving a $O(1)$-approximation for all MinSP problems in faster-than-$O(m^{k+\ell-1})$ time. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[19]
K. Bringmann, M. Künnemann, and A. Nusser, “Discrete Fréchet Distance under Translation: Conditional Hardness and an Improved Algorithm,” ACM Transactions on Algorithms, vol. 17, no. 3, 2021.
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@article{Bringmann2021, TITLE = {Discrete {F}r\'{e}chet Distance under Translation: {C}onditional Hardness and an Improved Algorithm}, AUTHOR = {Bringmann, Karl and K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3460656}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {17}, NUMBER = {3}, PAGES = {1--42}, EID = {25}, }
Endnote
%0 Journal Article %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 Discrete Fr&#233;chet Distance under Translation: Conditional Hardness and an Improved Algorithm : %G eng %U http://hdl.handle.net/21.11116/0000-0009-2A8B-C %R 10.1145/3460656 %7 2021 %D 2021 %J ACM Transactions on Algorithms %V 17 %N 3 %& 1 %P 1 - 42 %Z sequence number: 25 %I ACM %C New York, NY %@ false
[20]
P. Charalampopoulos, T. Kociumaka, and P. Wellnitz, “Faster Approximate Pattern Matching: A Unified Approach,” in FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science, Durham, NC, USA (Virtual Conference), 2021.
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@inproceedings{Charalampopoulos_FOCS2020, TITLE = {Faster Approximate Pattern Matching: {A} Unified Approach}, AUTHOR = {Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-7281-9621-3}, DOI = {10.1109/FOCS46700.2020}, PUBLISHER = {IEEE}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science}, PAGES = {978--989}, ADDRESS = {Durham, NC, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Charalampopoulos, Panagiotis %A Kociumaka, Tomasz %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Approximate Pattern Matching: A Unified Approach : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8C66-9 %R 10.1109/FOCS46700.2020 %D 2021 %B 61st Annual IEEE Symposium on Foundations of Computer Science %Z date of event: 2020-11-16 - 2020-11-19 %C Durham, NC, USA (Virtual Conference) %B FOCS 2020 %P 978 - 989 %I IEEE %@ 978-1-7281-9621-3
[21]
M. Cheraghchi and V. Nakos, “Combinatorial Group Testing and Sparse Recovery Schemes with Near-Optimal Decoding Time,” in FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science, Durham, NC, USA (Virtual Conference), 2021.
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@inproceedings{Cheraghchi_FOCS2020, TITLE = {Combinatorial Group Testing and Sparse Recovery Schemes with Near-Optimal Decoding Time}, AUTHOR = {Cheraghchi, Mahdi and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {978-1-7281-9621-3}, DOI = {10.1109/FOCS46700.2020}, PUBLISHER = {IEEE}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science}, PAGES = {1203--1213}, ADDRESS = {Durham, NC, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Cheraghchi, Mahdi %A Nakos, Vasileios %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Combinatorial Group Testing and Sparse Recovery Schemes with Near-Optimal Decoding Time : %G eng %U http://hdl.handle.net/21.11116/0000-0007-56C6-9 %R 10.1109/FOCS46700.2020 %D 2021 %B 61st Annual IEEE Symposium on Foundations of Computer Science %Z date of event: 2020-11-16 - 2020-11-19 %C Durham, NC, USA (Virtual Conference) %B FOCS 2020 %P 1203 - 1213 %I IEEE %@ 978-1-7281-9621-3
[22]
C. Coupette and C. Lenzen, “A Breezing Proof of the KMW Bound,” in Symposium on Simplicity in Algorithms (SOSA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{Coupette_SOSA2020, TITLE = {A Breezing Proof of the {KMW} Bound}, AUTHOR = {Coupette, Corinna and Lenzen, Christoph}, LANGUAGE = {eng}, ISBN = {978-1-61197-649-6}, DOI = {10.1137/1.9781611976496.21}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Symposium on Simplicity in Algorithms (SOSA 2021)}, EDITOR = {King, Valerie and Viet Le, Hung}, PAGES = {184--195}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Coupette, Corinna %A Lenzen, Christoph %+ Algorithms and Complexity, 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/21.11116/0000-0007-7A44-4 %R 10.1137/1.9781611976496.21 %D 2021 %B SIAM Symposium on Simplicity in Algorithms %Z date of event: 2021-01-11 - 2021-01-12 %C Alexandria, VA, USA (Virtual Conference) %B Symposium on Simplicity in Algorithms %E King, Valerie; Viet Le, Hung %P 184 - 195 %I SIAM %@ 978-1-61197-649-6
[23]
C. Coupette, J. Beckedorf, D. Hartung, M. Bommarito, and D. M. Katz, “Measuring Law Over Time: A Network Analytical Framework with an Application to Statutes and Regulations in the United States and Germany,” Frontiers in Physics, vol. 9, 2021.
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@article{Coupette2021, TITLE = {Measuring Law Over Time: {A} Network Analytical Framework with an Application to Statutes and Regulations in the {United States} and {Germany}}, AUTHOR = {Coupette, Corinna and Beckedorf, Janis and Hartung, Dirk and Bommarito, Michael and Katz, Daniel Martin}, LANGUAGE = {eng}, ISSN = {2296-424X}, DOI = {10.3389/fphy.2021.658463}, PUBLISHER = {Frontiers Media}, ADDRESS = {Lausanne}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Frontiers in Physics}, VOLUME = {9}, EID = {658463}, }
Endnote
%0 Journal Article %A Coupette, Corinna %A Beckedorf, Janis %A Hartung, Dirk %A Bommarito, Michael %A Katz, Daniel Martin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Measuring Law Over Time: A Network Analytical Framework with an Application to Statutes and Regulations in the United States and Germany : %G eng %U http://hdl.handle.net/21.11116/0000-0008-D8FA-B %R 10.3389/fphy.2021.658463 %7 2021 %D 2021 %J Frontiers in Physics %V 9 %Z sequence number: 658463 %I Frontiers Media %C Lausanne %@ false
[24]
C. Coupette and J. Vreeken, “Graph Similarity Description: How Are These Graphs Similar?,” in KDD ’21, 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Virtual Event, Singapore, 2021.
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@inproceedings{Coupette_KDD2021, TITLE = {Graph Similarity Description: {H}ow Are These Graphs Similar?}, AUTHOR = {Coupette, Corinna and Vreeken, Jilles}, LANGUAGE = {eng}, ISBN = {978-1-4503-8332-5}, DOI = {10.1145/3447548.3467257}, PUBLISHER = {ACM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {KDD '21, 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining}, EDITOR = {Zhu, Fieda and Ooi, Beng, Chin and Miao, Chunyan and Cong, Gao and Tang, Jiliang and Derr, Tyler}, PAGES = {185--195}, ADDRESS = {Virtual Event, Singapore}, }
Endnote
%0 Conference Proceedings %A Coupette, Corinna %A Vreeken, Jilles %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Graph Similarity Description: How Are These Graphs Similar? : %G eng %U http://hdl.handle.net/21.11116/0000-0009-652C-5 %R 10.1145/3447548.3467257 %D 2021 %B 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining %Z date of event: 2021-08-14 - 2021-08-18 %C Virtual Event, Singapore %B KDD '21 %E Zhu, Fieda; Ooi, Beng, Chin; Miao, Chunyan; Cong, Gao; Tang, Jiliang; Derr, Tyler %P 185 - 195 %I ACM %@ 978-1-4503-8332-5
[25]
E. Cruciani, E. Natale, A. Nusser, and G. Scornavacca, “Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks,” Distributed Computing, vol. Early Access, 2021.
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@article{Cruciani_DC2021, 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 = {0178-2770}, DOI = {10.1007/s00446-021-00396-5}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Distributed Computing}, VOLUME = {Early Access}, }
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/21.11116/0000-0008-BA11-3 %R 10.1007/s00446-021-00396-5 %7 2021 %D 2021 %J Distributed Computing %V Early Access %I Springer International %C Berlin %@ false
[26]
O. Darwish, A. Elmasry, and J. Katajainen, “Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls,” ACM Transactions on Algorithms, vol. 17, no. 2, 2021.
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@article{Darwish2021, TITLE = {Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls}, AUTHOR = {Darwish, Omar and Elmasry, Amr and Katajainen, Jyrki}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3452938}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {17}, NUMBER = {2}, EID = {18}, }
Endnote
%0 Journal Article %A Darwish, Omar %A Elmasry, Amr %A Katajainen, Jyrki %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls : %G eng %U http://hdl.handle.net/21.11116/0000-0008-D8F2-3 %R 10.1145/3452938 %7 2021 %D 2021 %J ACM Transactions on Algorithms %V 17 %N 2 %Z sequence number: 18 %I ACM %C New York, NY %@ false
[27]
N. R. Dayama, M. Shiripour, A. Oulasvirta, E. Ivanko, and A. Karrenbauer, “Foraging-based Optimization of Menu Systems,” International Journal of Human-Computer Studies, vol. 151, 2021.
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@article{Dayama2021, TITLE = {Foraging-based Optimization of Menu Systems}, AUTHOR = {Dayama, Niraj Ramesh and Shiripour, Morteza and Oulasvirta, Antti and Ivanko, Evgeny and Karrenbauer, Andreas}, LANGUAGE = {eng}, ISSN = {1071-5819}, DOI = {10.1016/j.ijhcs.2021.102624}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, JOURNAL = {International Journal of Human-Computer Studies}, VOLUME = {151}, EID = {102624}, }
Endnote
%0 Journal Article %A Dayama, Niraj Ramesh %A Shiripour, Morteza %A Oulasvirta, Antti %A Ivanko, Evgeny %A Karrenbauer, Andreas %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Foraging-based Optimization of Menu Systems : %G eng %U http://hdl.handle.net/21.11116/0000-0008-9D57-6 %R 10.1016/j.ijhcs.2021.102624 %7 2021 %D 2021 %J International Journal of Human-Computer Studies %V 151 %Z sequence number: 102624 %I Elsevier %C Amsterdam %@ false
[28]
A. Driemel, A. Nusser, J. M. Phillips, and I. Psarros, “The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances,” Discrete & Computational Geometry, 2021.
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@article{Driemel21, TITLE = {The {VC} Dimension of Metric Balls under {F}r\'{e}chet and {H}ausdorff Distances}, AUTHOR = {Driemel, Anne and Nusser, Andr{\'e} and Phillips, Jeff M. and Psarros, Ioannis}, LANGUAGE = {eng}, ISSN = {0179-5376}, DOI = {10.1007/s00454-021-00318-z}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Discrete \& Computational Geometry}, }
Endnote
%0 Journal Article %A Driemel, Anne %A Nusser, Andr&#233; %A Phillips, Jeff M. %A Psarros, Ioannis %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The VC Dimension of Metric Balls under Fr&#233;chet and Hausdorff Distances : %G eng %U http://hdl.handle.net/21.11116/0000-0009-414C-9 %R 10.1007/s00454-021-00318-z %7 2021 %D 2021 %J Discrete & Computational Geometry %I Springer %C New York, NY %@ false
[29]
A. M. Feit, M. Nancel, M. John, A. Karrenbauer, D. Weir, and A. Oulasvirta, “AZERTY Amélioré: Computational Design on a National Scale,” Communications of the ACM, vol. 64, no. 2, 2021.
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@article{FNJKWO2021, TITLE = {{AZERTY} Am\'{e}lior\'{e}: {C}omputational Design on a National Scale}, AUTHOR = {Feit, Anna Maria and Nancel, Mathieu and John, Maximilian and Karrenbauer, Andreas and Weir, Daryl and Oulasvirta, Antti}, LANGUAGE = {eng}, ISSN = {0001-0782}, DOI = {10.1145/3382035}, PUBLISHER = {Association for Computing Machinery, Inc.}, ADDRESS = {New York}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Communications of the ACM}, VOLUME = {64}, NUMBER = {2}, PAGES = {48--58}, }
Endnote
%0 Journal Article %A Feit, Anna Maria %A Nancel, Mathieu %A John, Maximilian %A Karrenbauer, Andreas %A Weir, Daryl %A Oulasvirta, Antti %+ 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 AZERTY Am&#233;lior&#233;: Computational Design on a National Scale : %G eng %U http://hdl.handle.net/21.11116/0000-0007-E78E-5 %R 10.1145/3382035 %7 2021 %D 2021 %K {F}r\'{e}chet %J Communications of the ACM %V 64 %N 2 %& 48 %P 48 - 58 %I Association for Computing Machinery, Inc. %C New York %@ false
[30]
M. Függer, A. Kinali, C. Lenzen, and B. Wiederhake, “Fast All-Digital Clock Frequency Adaptation Circuit for Voltage Droop Tolerance,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2021.
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@article{Fuegger2021, 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}, ISSN = {0278-0070}, DOI = {10.1109/TCAD.2021.3097599}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, }
Endnote
%0 Journal Article %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/21.11116/0000-0009-201C-4 %R 10.1109/TCAD.2021.3097599 %7 2021 %D 2021 %J IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems %I IEEE %C Piscataway, NJ %@ false
[31]
M. Grohe, D. Neuen, and D. Wiebking, “Isomorphism Testing for Graphs Excluding Small Minors,” in FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science, Durham, NC, USA (Virtual Conference), 2021.
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@inproceedings{Grohe_FOCS2020, TITLE = {Isomorphism Testing for Graphs Excluding Small Minors}, AUTHOR = {Grohe, Martin and Neuen, Daniel and Wiebking, Daniel}, LANGUAGE = {eng}, ISBN = {978-1-7281-9621-3}, DOI = {10.1109/FOCS46700.2020.00064}, PUBLISHER = {IEEE}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science}, PAGES = {625--636}, ADDRESS = {Durham, NC, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Grohe, Martin %A Neuen, Daniel %A Wiebking, Daniel %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Isomorphism Testing for Graphs Excluding Small Minors : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9947-D %R 10.1109/FOCS46700.2020.00064 %D 2021 %B 61st Annual IEEE Symposium on Foundations of Computer Science %Z date of event: 2020-11-16 - 2020-11-19 %C Durham, NC, USA (Virtual Conference) %B FOCS 2020 %P 625 - 636 %I IEEE %@ 978-1-7281-9621-3
[32]
P. Kleer, “Sampling from the Gibbs Distribution in Congestion Games,” 2021. [Online]. Available: https://arxiv.org/abs/2105.12982. (arXiv: 2105.12982)
Abstract
Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converges to the so-called Gibbs distribution over the set of all strategy profiles, when interpreted as a Markov chain. In general, logit dynamics might converge slowly to the Gibbs distribution, but beyond that, not much is known about their algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: i) Is there an efficient algorithm for sampling from the Gibbs distribution? ii) If yes, do there also exist natural randomized dynamics that converges quickly to the Gibbs distribution? We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics (in which we in addition are allowed to randomly interchange the strategies of two players) that converges quickly to the Gibbs distribution in such games. This answers both questions above affirmatively. We also address the first question for the class of so-called capacitated $k$-uniform congestion games. To prove our results, we rely on the recent breakthrough work of Anari, Liu, Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base of a matroid according to strongly log-concave probability distribution.
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@online{Kleer_2105.12982, TITLE = {Sampling from the {G}ibbs Distribution in Congestion Games}, AUTHOR = {Kleer, Pieter}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2105.12982}, EPRINT = {2105.12982}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converges to the so-called Gibbs distribution over the set of all strategy profiles, when interpreted as a Markov chain. In general, logit dynamics might converge slowly to the Gibbs distribution, but beyond that, not much is known about their algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: i) Is there an efficient algorithm for sampling from the Gibbs distribution? ii) If yes, do there also exist natural randomized dynamics that converges quickly to the Gibbs distribution? We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics (in which we in addition are allowed to randomly interchange the strategies of two players) that converges quickly to the Gibbs distribution in such games. This answers both questions above affirmatively. We also address the first question for the class of so-called capacitated $k$-uniform congestion games. To prove our results, we rely on the recent breakthrough work of Anari, Liu, Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base of a matroid according to strongly log-concave probability distribution.}, }
Endnote
%0 Report %A Kleer, Pieter %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sampling from the Gibbs Distribution in Congestion Games : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E54C-1 %U https://arxiv.org/abs/2105.12982 %D 2021 %X Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converges to the so-called Gibbs distribution over the set of all strategy profiles, when interpreted as a Markov chain. In general, logit dynamics might converge slowly to the Gibbs distribution, but beyond that, not much is known about their algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: i) Is there an efficient algorithm for sampling from the Gibbs distribution? ii) If yes, do there also exist natural randomized dynamics that converges quickly to the Gibbs distribution? We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics (in which we in addition are allowed to randomly interchange the strategies of two players) that converges quickly to the Gibbs distribution in such games. This answers both questions above affirmatively. We also address the first question for the class of so-called capacitated $k$-uniform congestion games. To prove our results, we rely on the recent breakthrough work of Anari, Liu, Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base of a matroid according to strongly log-concave probability distribution. %K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS
[33]
C. Lenzen and H. Vahidi, “Approximate Minimum Directed Spanning Trees Under Congestion,” in Structural Information and Communication Complexity (SIROCCO 2021), Wrocław, Poland (Online), 2021.
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@inproceedings{Lenzen_SIROCCO21, TITLE = {Approximate Minimum Directed Spanning Trees Under Congestion}, AUTHOR = {Lenzen, Christoph and Vahidi, Hossein}, LANGUAGE = {eng}, ISBN = {978-3-030-79526-9}, DOI = {10.1007/978-3-030-79527-6_20}, PUBLISHER = {Springer}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {Structural Information and Communication Complexity (SIROCCO 2021)}, EDITOR = {Jurdzi{\'n}ski, Tomasz and Schmid, Stefan}, PAGES = {352--369}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12810}, ADDRESS = {Wroc{\l}aw, Poland (Online)}, }
Endnote
%0 Conference Proceedings %A Lenzen, Christoph %A Vahidi, Hossein %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Approximate Minimum Directed Spanning Trees Under Congestion : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E553-8 %R 10.1007/978-3-030-79527-6_20 %D 2021 %B 28th International Colloquium on Structural Information and Communication Complexity %Z date of event: 2021-06-28 - 2021-07-01 %C Wroc&#322;aw, Poland (Online) %B Structural Information and Communication Complexity %E Jurdzi&#324;ski, Tomasz; Schmid, Stefan %P 352 - 369 %I Springer %@ 978-3-030-79526-9 %B Lecture Notes in Computer Science %N 12810
[34]
D. Lokshtanov, P. Misra, M. S. Ramanujan, S. Saurabh, and M. Zehavi, “FPT-approximation for FPT Problems,” in Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{FPTApprox21, TITLE = {{FPT}-approximation for {FPT} Problems}, AUTHOR = {Lokshtanov, Daniel and Misra, Pranabendu and Ramanujan, M. S. and Saurabh, Saket and Zehavi, Meirav}, LANGUAGE = {eng}, ISBN = {978-1-61197-646-5}, DOI = {10.1137/1.9781611976465.14}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021)}, EDITOR = {Marx, D{\'a}niel}, PAGES = {199--218}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Lokshtanov, Daniel %A Misra, Pranabendu %A Ramanujan, M. S. %A Saurabh, Saket %A Zehavi, Meirav %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T FPT-approximation for FPT Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D2AE-8 %R 10.1137/1.9781611976465.14 %D 2021 %B 32nd Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2021-01-10 - 2021-01-13 %C Alexandria, VA, USA (Virtual Conference) %B Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms %E Marx, D&#225;niel %P 199 - 218 %I SIAM %@ 978-1-61197-646-5
[35]
D. Lokshtanov, P. Misra, J. Mukherjee, F. Panolan, G. Philip, and S. Saurabh, “2-Approximating Feedback Vertex Set in Tournaments,” ACM Transactions on Algorithms, vol. 17, no. 2, 2021.
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@article{Lokshtanov2021, 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}, ISSN = {1549-6325}, DOI = {10.1145/3446969}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {17}, NUMBER = {2}, EID = {11}, }
Endnote
%0 Journal Article %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/21.11116/0000-0008-D8F8-D %R 10.1145/3446969 %7 2021 %D 2021 %J ACM Transactions on Algorithms %V 17 %N 2 %Z sequence number: 11 %I ACM %C New York, NY %@ false
[36]
J. Madathil, R. Sharma, and M. Zehavi, “A Sub-exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs,” Algorithmica, 2021.
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@article{Madathil2021, TITLE = {A Sub-exponential {FPT} Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs}, AUTHOR = {Madathil, Jayakrishnan and Sharma, Roohani and Zehavi, Meirav}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-021-00806-x}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, }
Endnote
%0 Journal Article %A Madathil, Jayakrishnan %A Sharma, Roohani %A Zehavi, Meirav %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Sub-exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs : %G eng %U http://hdl.handle.net/21.11116/0000-0008-2C54-9 %R 10.1007/s00453-021-00806-x %7 2021 %D 2021 %J Algorithmica %I Springer %C New York, NY %@ false
[37]
A. S. Nittala, A. Karrenbauer, A. Khan, T. Kraus, and J. Steimle, “Computational Design and Optimization of Electro-physiological Sensors,” Nature Communications, vol. 12, no. 1, 2021.
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@article{Nittala2021, TITLE = {Computational Design and Optimization of Electro-physiological Sensors}, AUTHOR = {Nittala, Aditya Shekhar and Karrenbauer, Andreas and Khan, Arshad and Kraus, Tobias and Steimle, J{\"u}rgen}, LANGUAGE = {eng}, ISSN = {2041-1723}, DOI = {10.1038/s41467-021-26442-1}, PUBLISHER = {Nature Publishing Group}, ADDRESS = {London}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, JOURNAL = {Nature Communications}, VOLUME = {12}, NUMBER = {1}, EID = {6351}, }
Endnote
%0 Journal Article %A Nittala, Aditya Shekhar %A Karrenbauer, Andreas %A Khan, Arshad %A Kraus, Tobias %A Steimle, J&#252;rgen %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Computational Design and Optimization of Electro-physiological Sensors : %G eng %U http://hdl.handle.net/21.11116/0000-0009-7E62-C %R 10.1038/s41467-021-26442-1 %7 2021 %D 2021 %J Nature Communications %O Nat. Commun. %V 12 %N 1 %Z sequence number: 6351 %I Nature Publishing Group %C London %@ false
[38]
A. Pandey, “Variety Membership Testing in Algebraic Complexity Theory,” Universität des Saarlandes, Saarbrücken, 2021.
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@phdthesis{Pandeyphd2021, TITLE = {Variety Membership Testing in Algebraic Complexity Theory}, AUTHOR = {Pandey, Anurag}, LANGUAGE = {eng}, DOI = {10.22028/D291-34244}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, }
Endnote
%0 Thesis %A Pandey, Anurag %Y Bl&#228;ser, Markus %A referee: Ikenmeyer, Christian %A referee: Mahajan, Meena %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society International Max Planck Research School, 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 Variety Membership Testing in Algebraic Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0008-E9F5-D %R 10.22028/D291-34244 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2021 %P 128 p. %V phd %9 phd %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/31479
[39]
B. Ray Chaudhury, J. Garg, P. McGlaughlin, and R. Mehta, “Competitive Allocation of a Mixed Manna,” in Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{Chaudhury_SODA21, TITLE = {Competitive Allocation of a Mixed Manna}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and McGlaughlin, Peter and Mehta, Ruta}, LANGUAGE = {eng}, ISBN = {978-1-61197-646-5}, DOI = {10.1137/1.9781611976465.85}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021)}, EDITOR = {Marx, D{\'a}niel}, PAGES = {1405--1424}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A McGlaughlin, Peter %A Mehta, Ruta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Competitive Allocation of a Mixed Manna : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9365-1 %R 10.1137/1.9781611976465.85 %D 2021 %B 32nd Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2021-01-10 - 2021-01-13 %C Alexandria, VA, USA (Virtual Conference) %B Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms %E Marx, D&#225;niel %P 1405 - 1424 %I SIAM %@ 978-1-61197-646-5
[40]
B. Ray Chaudhury, J. Garg, and R. Mehta, “Fair and Efficient Allocations under Subadditive Valuations,” in AAAI Technical Track on Game Theory and Economic Paradigms, Virtual Conference, 2021.
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@inproceedings{Chaudhury_AAAI21, TITLE = {Fair and Efficient Allocations under Subadditive Valuations}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehta, Ruta}, LANGUAGE = {eng}, ISBN = {978-1-57735-866-4}, URL = {https://ojs.aaai.org/index.php/AAAI/article/view/16665}, PUBLISHER = {AAAI}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {AAAI Technical Track on Game Theory and Economic Paradigms}, PAGES = {5269--5276}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A Mehta, Ruta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Fair and Efficient Allocations under Subadditive Valuations : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9370-4 %U https://ojs.aaai.org/index.php/AAAI/article/view/16665 %D 2021 %B Thirty-Fifth AAAI Conference on Artificial Intelligence %Z date of event: 2021-02-02 - 2021-02-09 %C Virtual Conference %B AAAI Technical Track on Game Theory and Economic Paradigms %P 5269 - 5276 %I AAAI %@ 978-1-57735-866-4 %U https://ojs.aaai.org/index.php/AAAI/article/view/16665
[41]
B. Ray Chaudhury, J. Garg, K. Mehlhorn, R. Mehta, and P. Misra, “Improving EFX Guarantees through Rainbow Cycle Number,” 2021. [Online]. Available: https://arxiv.org/abs/2103.01628. (arXiv: 2103.01628)
Abstract
We study the problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations. Envy-freeness up to any good (EFX) is arguably the most compelling fairness notion in this context. However, the existence of EFX allocations has not been settled and is one of the most important problems in fair division. Towards resolving this problem, many impressive results show the existence of its relaxations, e.g., the existence of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated goods. The latter result was recently improved for three agents, in which the two unallocated goods are allocated through an involved procedure. Reducing the number of unallocated goods for arbitrary number of agents is a systematic way to settle the big question. In this paper, we develop a new approach, and show that for every $\varepsilon \in (0,1/2]$, there always exists a $(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and high Nash welfare. For this, we reduce the EFX problem to a novel problem in extremal graph theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d \in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite digraph $G =(\cup_{i \in [k]} V_i, E)$, in which 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for all $i \in [k]$, 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming edge from some vertex in $V_j$ and vice-versa, and 3) there exists no cycle in $G$ that contains at most one vertex from each part. We show that any upper bound on $R(d)$ directly translates to a sublinear bound on the number of unallocated goods. We establish a polynomial upper bound on $R(d)$, yielding our main result. Furthermore, our approach is constructive, which also gives a polynomial-time algorithm for finding such an allocation.
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@online{RayChaudhury2103.01628, TITLE = {Improving {EFX} Guarantees through Rainbow Cycle Number}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta and Misra, Pranabendu}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2103.01628}, EPRINT = {2103.01628}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations. Envy-freeness up to any good (EFX) is arguably the most compelling fairness notion in this context. However, the existence of EFX allocations has not been settled and is one of the most important problems in fair division. Towards resolving this problem, many impressive results show the existence of its relaxations, e.g., the existence of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated goods. The latter result was recently improved for three agents, in which the two unallocated goods are allocated through an involved procedure. Reducing the number of unallocated goods for arbitrary number of agents is a systematic way to settle the big question. In this paper, we develop a new approach, and show that for every $\varepsilon \in (0,1/2]$, there always exists a $(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and high Nash welfare. For this, we reduce the EFX problem to a novel problem in extremal graph theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d \in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite digraph $G =(\cup_{i \in [k]} V_i, E)$, in which 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for all $i \in [k]$, 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming edge from some vertex in $V_j$ and vice-versa, and 3) there exists no cycle in $G$ that contains at most one vertex from each part. We show that any upper bound on $R(d)$ directly translates to a sublinear bound on the number of unallocated goods. We establish a polynomial upper bound on $R(d)$, yielding our main result. Furthermore, our approach is constructive, which also gives a polynomial-time algorithm for finding such an allocation.}, }
Endnote
%0 Report %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A Mehlhorn, Kurt %A Mehta, Ruta %A Misra, Pranabendu %+ 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 Improving EFX Guarantees through Rainbow Cycle Number : %G eng %U http://hdl.handle.net/21.11116/0000-0008-DB40-9 %U https://arxiv.org/abs/2103.01628 %D 2021 %X We study the problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations. Envy-freeness up to any good (EFX) is arguably the most compelling fairness notion in this context. However, the existence of EFX allocations has not been settled and is one of the most important problems in fair division. Towards resolving this problem, many impressive results show the existence of its relaxations, e.g., the existence of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated goods. The latter result was recently improved for three agents, in which the two unallocated goods are allocated through an involved procedure. Reducing the number of unallocated goods for arbitrary number of agents is a systematic way to settle the big question. In this paper, we develop a new approach, and show that for every $\varepsilon \in (0,1/2]$, there always exists a $(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and high Nash welfare. For this, we reduce the EFX problem to a novel problem in extremal graph theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d \in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite digraph $G =(\cup_{i \in [k]} V_i, E)$, in which 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for all $i \in [k]$, 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming edge from some vertex in $V_j$ and vice-versa, and 3) there exists no cycle in $G$ that contains at most one vertex from each part. We show that any upper bound on $R(d)$ directly translates to a sublinear bound on the number of unallocated goods. We establish a polynomial upper bound on $R(d)$, yielding our main result. Furthermore, our approach is constructive, which also gives a polynomial-time algorithm for finding such an allocation. %K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Data Structures and Algorithms, cs.DS
[42]
B. Ray Chaudhury, T. Kavitha, K. Mehlhorn, and A. Sgouritsa, “A Little Charity Guarantees Almost Envy-Freeness,” SIAM Journal on Computing, vol. 50, no. 4, 2021.
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@article{RayChaudhury21, TITLE = {A Little Charity Guarantees Almost Envy-Freeness}, AUTHOR = {Ray Chaudhury, Bhaskar and Kavitha, Telikepalli and Mehlhorn, Kurt and Sgouritsa, Alkmini}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/20M1359134}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {50}, NUMBER = {4}, PAGES = {1336--1358}, }
Endnote
%0 Journal Article %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/21.11116/0000-0009-2B38-9 %R 10.1137/20M1359134 %7 2021 %D 2021 %J SIAM Journal on Computing %V 50 %N 4 %& 1336 %P 1336 - 1358 %I SIAM %C Philadelphia, PA %@ false
[43]
M. Roth, J. Schmitt, and P. Wellnitz, “Counting Small Induced Subgraphs Satisfying Monotone Properties,” in FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science, Durham, NC, USA (Virtual Conference), 2021.
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@inproceedings{Roth_FOCS2020, TITLE = {Counting Small Induced Subgraphs Satisfying Monotone Properties}, AUTHOR = {Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-7281-9621-3}, DOI = {10.1109/FOCS46700.2020}, PUBLISHER = {IEEE}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {FOCS 2020, 61st Annual IEEE Symposium on Foundations of Computer Science}, PAGES = {1356--1367}, ADDRESS = {Durham, NC, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Roth, Marc %A Schmitt, Johannes %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Small Induced Subgraphs Satisfying Monotone Properties : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8C5E-3 %R 10.1109/FOCS46700.2020 %D 2021 %B 61st Annual IEEE Symposium on Foundations of Computer Science %Z date of event: 2020-11-16 - 2020-11-19 %C Durham, NC, USA (Virtual Conference) %B FOCS 2020 %P 1356 - 1367 %I IEEE %@ 978-1-7281-9621-3
[44]
K. Vitting Klinkby, P. Misra, and S. Saurabh, “Strong Connectivity Augmentation is FPT,” in Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021), Alexandria, VA, USA (Virtual Conference), 2021.
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@inproceedings{SCAug21, TITLE = {Strong Connectivity Augmentation is {FPT}}, AUTHOR = {Vitting Klinkby, Kristine and Misra, Pranabendu and Saurabh, Saket}, LANGUAGE = {eng}, ISBN = {978-1-61197-646-5}, DOI = {10.1137/1.9781611976465.15}, PUBLISHER = {SIAM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms (SODA 2021)}, EDITOR = {Marx, D{\'a}niel}, PAGES = {219--234}, ADDRESS = {Alexandria, VA, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Vitting Klinkby, Kristine %A Misra, Pranabendu %A Saurabh, Saket %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Strong Connectivity Augmentation is FPT : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D2A6-0 %R 10.1137/1.9781611976465.15 %D 2021 %B 32nd Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2021-01-10 - 2021-01-13 %C Alexandria, VA, USA (Virtual Conference) %B Proceedings of the Thirty-Second ACM-SIAM Symposium on Discrete Algorithms %E Marx, D&#225;niel %P 219 - 234 %I SIAM %@ 978-1-61197-646-5
2020
[45]
A. Abboud, K. Censor-Hillel, S. Khoury, and C. Lenzen, “Fooling Views: A New Lower Bound Technique for Distributed Computations under Congestion,” Distributed Computing, vol. 33, 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}, MARGINALMARK = {$\bullet$}, JOURNAL = {Distributed Computing}, VOLUME = {33}, PAGES = {545--559}, }
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 %V 33 %& 545 %P 545 - 559 %I Springer %C New York, NY %@ false
[46]
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}, MARGINALMARK = {$\bullet$}, 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
[47]
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}, MARGINALMARK = {$\bullet$}, 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
[48]
A. Abboud, A. Backurs, K. Bringmann, and M. Künnemann, “Impossibility Results for Grammar-Compressed Linear Algebra,” in Advances in Neural Information Processing Systems 33 (NeurIPS 2020), Virtual Event, 2020.
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@inproceedings{Abboud_NeurIPS20, TITLE = {Impossibility Results for Grammar-Compressed Linear Algebra}, AUTHOR = {Abboud, Amir and Backurs, Arturs and Bringmann, Karl and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, PUBLISHER = {Curran Associates, Inc.}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 33 (NeurIPS 2020)}, EDITOR = {Larochelle, H. and Ranzato, M. and Hadsell, R. and Balcan, M. F. and Lin, H.}, ADDRESS = {Virtual Event}, }
Endnote
%0 Conference Proceedings %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 Impossibility Results for Grammar-Compressed Linear Algebra : %G eng %U http://hdl.handle.net/21.11116/0000-0007-90DF-B %D 2020 %B 34th Conference on Neural Information Processing Systems %Z date of event: 2020-12-06 - 2020-12-12 %C Virtual Event %B Advances in Neural Information Processing Systems 33 %E Larochelle, H.; Ranzato, M.; Hadsell, R.; Balcan, M. F.; Lin, H. %I Curran Associates, Inc. %U https://proceedings.neurips.cc/paper/2020/hash/645e6bfdd05d1a69c5e47b20f0a91d46-Abstract.html
[49]
D. Achlioptas, T. Gouleakis, and F. Iliopoulos, “Simple Local Computation Algorithms for the General Lovász Local Lemma,” in SPAA ’20, 32nd ACM Symposium on Parallelism in Algorithms and Architectures, Virtual Event, USA, 2020.
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@inproceedings{Achlioptas_SPAA20, TITLE = {Simple Local Computation Algorithms for the General {Lov\'{a}sz} {Local Lemma}}, AUTHOR = {Achlioptas, Dimitris and Gouleakis, Themis and Iliopoulos, Fotis}, LANGUAGE = {eng}, ISBN = {9781450369350}, DOI = {10.1145/3350755.3400250}, PUBLISHER = {ACM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {SPAA '20, 32nd ACM Symposium on Parallelism in Algorithms and Architectures}, PAGES = {1--10}, ADDRESS = {Virtual Event, USA}, }
Endnote
%0 Conference Proceedings %A Achlioptas, Dimitris %A Gouleakis, Themis %A Iliopoulos, Fotis %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Simple Local Computation Algorithms for the General Lov&#225;sz Local Lemma : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8B6D-3 %R 10.1145/3350755.3400250 %D 2020 %B 32nd ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2020-07-15 - 2020-07-17 %C Virtual Event, USA %B SPAA '20 %P 1 - 10 %I ACM %@ 9781450369350
[50]
A. Agrawal, D. Lokshtanov, P. Misra, S. Saurabh, and M. Zehavi, “Polylogarithmic Approximation Algorithms for Weighted-F-deletion Problems,” ACM Transactions on Algorithms, vol. 16, no. 4, 2020.
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@article{Agrawal2020, TITLE = {Polylogarithmic Approximation Algorithms for Weighted-{$\mathcal{F}$}-deletion Problems}, 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}, MARGINALMARK = {$\bullet$}, 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 Problems : %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
[51]
A. Agrawal, M. Kundu, A. Sahu, S. Saurabh, and P. Tale, “Parameterized Complexity of MAXIMUM EDGE COLORABLE SUBGRAPH,” in Computing and Combinatorics (COCOON 2020), Atlanta, GA, USA, 2020.
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@inproceedings{DBLP:conf/cocoon/AgrawalKS0T20, TITLE = {{MAXIMUM EDGE COLORABLE SUBGRAPH}}, AUTHOR = {Agrawal, Akanksha and Kundu, Madhumita and Sahu, Abhishek and Saurabh, Saket and Tale, Prafullkumar}, LANGUAGE = {eng}, ISBN = {978-3-030-58149-7}, DOI = {10.1007/978-3-030-58150-3_50}, PUBLISHER = {Springer}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, BOOKTITLE = {Computing and Combinatorics (COCOON 2020)}, EDITOR = {Kim, Donghyun and Uma, R. N. and Cai, Zhipeng and Lee, Dong Hoon}, PAGES = {615--626}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12273}, ADDRESS = {Atlanta, GA, USA}, }
Endnote
%0 Conference Proceedings %A Agrawal, Akanksha %A Kundu, Madhumita %A Sahu, Abhishek %A Saurabh, Saket %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Parameterized Complexity of MAXIMUM EDGE COLORABLE SUBGRAPH : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D2A4-2 %R 10.1007/978-3-030-58150-3_50 %D 2020 %B 26th International Conference on Computing and Combinatorics %Z date of event: 2020-08-29 - 2020-08-31 %C Atlanta, GA, USA %B Computing and Combinatorics %E Kim, Donghyun; Uma, R. N.; Cai, Zhipeng; Lee, Dong Hoon %P 615 - 626 %I Springer %@ 978-3-030-58149-7 %B Lecture Notes in Computer Science %N 12273
[52]
H. Alkema, M. de Berg, and S. Kisfaludi-Bak, “Euclidean TSP in Narrow Strips,” in 36th International Symposium on Computational Geometry (SoCG 2020), Zürich, Switzerland (Virtual Conference), 2020.
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@inproceedings{AlkemaBK20, TITLE = {Euclidean {TSP} in Narrow Strips}, AUTHOR = {Alkema, Henk and de Berg, Mark and Kisfaludi-Bak, S{\'a}ndor}, LANGUAGE = {eng}, ISBN = {978-3-95977-143-6}, URL = {urn:nbn:de:0030-drops-121628}, DOI = {10.4230/LIPIcs.SoCG.2020.4}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {36th International Symposium on Computational Geometry (SoCG 2020)}, EDITOR = {Cabello, Sergio and Chen, Danny Z.}, PAGES = {1--16}, EID = {4}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {164}, ADDRESS = {Z{\"u}rich, Switzerland (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Alkema, Henk %A de Berg, Mark %A Kisfaludi-Bak, S&#225;ndor %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Euclidean TSP in Narrow Strips : %G eng %U http://hdl.handle.net/21.11116/0000-0007-76E5-2 %R 10.4230/LIPIcs.SoCG.2020.4 %U urn:nbn:de:0030-drops-121628 %D 2020 %B 36th International Symposium on Computational Geometry %Z date of event: 2020-06-23 - 2020-06-26 %C Z&#252;rich, Switzerland (Virtual Conference) %B 36th International Symposium on Computational Geometry %E Cabello, Sergio; Chen, Danny Z. %P 1 - 16 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-143-6 %B Leibniz International Proceedings in Informatics %N 164 %U https://drops.dagstuhl.de/opus/volltexte/2020/12162/https://creativecommons.org/licenses/by/3.0/legalcode
[53]
H. Alkema, M. de Berg, and S. Kisfaludi-Bak, “Euclidean TSP in Narrow Strips,” 2020. [Online]. Available: https://arxiv.org/abs/2003.09948. (arXiv: 2003.09948)
Abstract
We investigate how the complexity of Euclidean TSP for point sets $P$ inside the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width $\delta$. We obtain two main results. First, for the case where the points have distinct integer $x$-coordinates, we prove that a shortest bitonic tour (which can be computed in $O(n\log^2 n)$ time using an existing algorithm) is guaranteed to be a shortest tour overall when $\delta\leq 2\sqrt{2}$, a bound which is best possible. Second, we present an algorithm that is fixed-parameter tractable with respect to $\delta$. More precisely, our algorithm has running time $2^{O(\sqrt{\delta})} n^2$ for sparse point sets, where each $1\times\delta$ rectangle inside the strip contains $O(1)$ points. For random point sets, where the points are chosen uniformly at random from the rectangle~$[0,n]\times [0,\delta]$, it has an expected running time of $2^{O(\sqrt{\delta})} n^2 + O(n^3)$.
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@online{Alkema_arXiv2003.09948, TITLE = {Euclidean {TSP} in Narrow Strips}, AUTHOR = {Alkema, Henk and de Berg, Mark and Kisfaludi-Bak, S{\'a}ndor}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.09948}, EPRINT = {2003.09948}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We investigate how the complexity of Euclidean TSP for point sets $P$ inside the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width $\delta$. We obtain two main results. First, for the case where the points have distinct integer $x$-coordinates, we prove that a shortest bitonic tour (which can be computed in $O(n\log^2 n)$ time using an existing algorithm) is guaranteed to be a shortest tour overall when $\delta\leq 2\sqrt{2}$, a bound which is best possible. Second, we present an algorithm that is fixed-parameter tractable with respect to $\delta$. More precisely, our algorithm has running time $2^{O(\sqrt{\delta})} n^2$ for sparse point sets, where each $1\times\delta$ rectangle inside the strip contains $O(1)$ points. For random point sets, where the points are chosen uniformly at random from the rectangle~$[0,n]\times [0,\delta]$, it has an expected running time of $2^{O(\sqrt{\delta})} n^2 + O(n^3)$.}, }
Endnote
%0 Report %A Alkema, Henk %A de Berg, Mark %A Kisfaludi-Bak, S&#225;ndor %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Euclidean TSP in Narrow Strips : %G eng %U http://hdl.handle.net/21.11116/0000-0007-77A3-B %U https://arxiv.org/abs/2003.09948 %D 2020 %X We investigate how the complexity of Euclidean TSP for point sets $P$ inside the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width $\delta$. We obtain two main results. First, for the case where the points have distinct integer $x$-coordinates, we prove that a shortest bitonic tour (which can be computed in $O(n\log^2 n)$ time using an existing algorithm) is guaranteed to be a shortest tour overall when $\delta\leq 2\sqrt{2}$, a bound which is best possible. Second, we present an algorithm that is fixed-parameter tractable with respect to $\delta$. More precisely, our algorithm has running time $2^{O(\sqrt{\delta})} n^2$ for sparse point sets, where each $1\times\delta$ rectangle inside the strip contains $O(1)$ points. For random point sets, where the points are chosen uniformly at random from the rectangle~$[0,n]\times [0,\delta]$, it has an expected running time of $2^{O(\sqrt{\delta})} n^2 + O(n^3)$. %K Computer Science, Computational Geometry, cs.CG
[54]
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}, MARGINALMARK = {$\bullet$}, 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
[55]
S. A. Amiri and B. Wiederhake, “Distributed Distance-r Dominating Set on Sparse High-Girth Graphs,” 2020. [Online]. Available: https://arxiv.org/abs/1910.02794. (arXiv: 1910.02794)
Abstract
The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about distance-r domination. This is actually the case for other important closely-related covering problem, namely, the distance-$r$ independent set problem. By result of Kuhn et al. we know the distributed domination problem is hard on high girth graphs; we study the problem on a slightly restricted subclass of these graphs: graphs of bounded expansion with high girth, i.e. their girth should be at least $4r + 3$. We show that in such graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a constant-factor approximation of the minimum distance-$r$ dominating set problem, in a constant number of rounds. More precisely, our constants are dependent to $r$, not to the size of the graph. This is the first algorithm that shows there are non-trivial constant factor approximations in constant number of rounds for any distance $r$-covering problem in distributed settings. To show the dependency on r is inevitable, we provide an unconditional lower bound showing the same problem is hard already on rings. We also show that our analysis of the algorithm is relatively tight, that is any significant improvement to the approximation factor requires new algorithmic ideas.
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@online{Amiri_arXiv1910.02794, TITLE = {Distributed Distance-$r$ Dominating Set on Sparse High-Girth Graphs}, AUTHOR = {Amiri, Saeed Akhoondian and Wiederhake, Ben}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/1910.02794}, EPRINT = {1910.02794}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about distance-r domination. This is actually the case for other important closely-related covering problem, namely, the distance-$r$ independent set problem. By result of Kuhn et al. we know the distributed domination problem is hard on high girth graphs; we study the problem on a slightly restricted subclass of these graphs: graphs of bounded expansion with high girth, i.e. their girth should be at least $4r + 3$. We show that in such graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a constant-factor approximation of the minimum distance-$r$ dominating set problem, in a constant number of rounds. More precisely, our constants are dependent to $r$, not to the size of the graph. This is the first algorithm that shows there are non-trivial constant factor approximations in constant number of rounds for any distance $r$-covering problem in distributed settings. To show the dependency on r is inevitable, we provide an unconditional lower bound showing the same problem is hard already on rings. We also show that our analysis of the algorithm is relatively tight, that is any significant improvement to the approximation factor requires new algorithmic ideas.}, }
Endnote
%0 Report %A Amiri, Saeed Akhoondian %A Wiederhake, Ben %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Distributed Distance-r Dominating Set on Sparse High-Girth Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-905B-0 %U https://arxiv.org/abs/1910.02794 %D 2020 %X The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about distance-r domination. This is actually the case for other important closely-related covering problem, namely, the distance-$r$ independent set problem. By result of Kuhn et al. we know the distributed domination problem is hard on high girth graphs; we study the problem on a slightly restricted subclass of these graphs: graphs of bounded expansion with high girth, i.e. their girth should be at least $4r + 3$. We show that in such graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a constant-factor approximation of the minimum distance-$r$ dominating set problem, in a constant number of rounds. More precisely, our constants are dependent to $r$, not to the size of the graph. This is the first algorithm that shows there are non-trivial constant factor approximations in constant number of rounds for any distance $r$-covering problem in distributed settings. To show the dependency on r is inevitable, we provide an unconditional lower bound showing the same problem is hard already on rings. We also show that our analysis of the algorithm is relatively tight, that is any significant improvement to the approximation factor requires new algorithmic ideas. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Discrete Mathematics, cs.DM,Mathematics, Combinatorics, math.CO
[56]
S. A. Amiri, A. Popa, M. Roghani, G. Shahkarami, R. Soltani, and H. Vahidi, “Complexity of Computing the Anti-Ramsey Numbers for Paths,” in 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020), Prague, Czech Republic (Virtual Event), 2020.
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@inproceedings{Amiri_MFCS20, TITLE = {Complexity of Computing the Anti-{Ramsey} Numbers for Paths}, AUTHOR = {Amiri, Saeed Akhoondian and Popa, Alexandru and Roghani, Mohammad and Shahkarami, Golnoosh and Soltani, Reza and Vahidi, Hossein}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-159-7}, URL = {urn:nbn:de:0030-drops-126781}, DOI = {10.4230/LIPIcs.MFCS.2020.6}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)}, EDITOR = {Esparza, Javier and Kr{\a}l', Daniel}, EID = {6}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {170}, ADDRESS = {Prague, Czech Republic (Virtual Event)}, }
Endnote
%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Popa, Alexandru %A Roghani, Mohammad %A Shahkarami, Golnoosh %A Soltani, Reza %A Vahidi, Hossein %+ 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 Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Complexity of Computing the Anti-Ramsey Numbers for Paths : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9422-B %R 10.4230/LIPIcs.MFCS.2020.6 %U urn:nbn:de:0030-drops-126781 %D 2020 %B 45th International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2020-08-25 - 2020-08-26 %C Prague, Czech Republic (Virtual Event) %B 45th International Symposium on Mathematical Foundations of Computer Science %E Esparza, Javier; Kr&#224;l', Daniel %Z sequence number: 6 %I Schloss Dagstuhl %@ 978-3-95977-159-7 %B Leibniz International Proceedings in Informatics %N 170 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12678/https://creativecommons.org/licenses/by/3.0/legalcode
[57]
S. A. Amiri, K.-T. Foerster, and S. Schmid, “Walking Through Waypoints,” Algorithmica, vol. 82, no. 7, 2020.
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@article{Amiri_Walking20, TITLE = {Walking Through Waypoints}, AUTHOR = {Amiri, Saeed Akhoondian and Foerster, Klaus-Tycho and Schmid, Stefan}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-020-00672-z}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, JOURNAL = {Algorithmica}, VOLUME = {82}, NUMBER = {7}, PAGES = {1784--1812}, }
Endnote
%0 Journal Article %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/21.11116/0000-0007-EDEF-2 %R 10.1007/s00453-020-00672-z %7 2020 %D 2020 %J Algorithmica %V 82 %N 7 %& 1784 %P 1784 - 1812 %I Springer-Verlag %C New York %@ false
[58]
I. Anagnostides, T. Gouleakis, and A. Marashian, “Robust Learning under Strong Noise via SQs,” 2020. [Online]. Available: https://arxiv.org/abs/2010.09106. (arXiv: 2010.09106)
Abstract
This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise tolerance of distribution-independently evolvable concept classes under Massart noise. Specifically, we extend their characterization to more general noise models, including the Tsybakov model which considerably generalizes the Massart condition by allowing the flipping probability to be arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary, we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to obtain the first polynomial time algorithm with arbitrarily small excess error for learning linear threshold functions over any spherically symmetric distribution in the presence of spherically symmetric Tsybakov noise. Moreover, we posit access to a stronger oracle, in which for every labeled example we additionally obtain its flipping probability. In this model, we show that every SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$ misclassification error for a broad class of noise models. This setting substantially generalizes the widely-studied problem of classification under RCN with known noise rate, and corresponds to a non-convex optimization problem even when the noise function -- i.e. the flipping probabilities of all points -- is known in advance.
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@online{Anagnostides_arXiv2010.09106, TITLE = {Robust Learning under Strong Noise via {SQs}}, AUTHOR = {Anagnostides, Ioannis and Gouleakis, Themis and Marashian, Ali}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2010.09106}, EPRINT = {2010.09106}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise tolerance of distribution-independently evolvable concept classes under Massart noise. Specifically, we extend their characterization to more general noise models, including the Tsybakov model which considerably generalizes the Massart condition by allowing the flipping probability to be arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary, we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to obtain the first polynomial time algorithm with arbitrarily small excess error for learning linear threshold functions over any spherically symmetric distribution in the presence of spherically symmetric Tsybakov noise. Moreover, we posit access to a stronger oracle, in which for every labeled example we additionally obtain its flipping probability. In this model, we show that every SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$ misclassification error for a broad class of noise models. This setting substantially generalizes the widely-studied problem of classification under RCN with known noise rate, and corresponds to a non-convex optimization problem even when the noise function -- i.e. the flipping probabilities of all points -- is known in advance.}, }
Endnote
%0 Report %A Anagnostides, Ioannis %A Gouleakis, Themis %A Marashian, Ali %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Robust Learning under Strong Noise via SQs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8B5D-5 %U https://arxiv.org/abs/2010.09106 %D 2020 %X This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise tolerance of distribution-independently evolvable concept classes under Massart noise. Specifically, we extend their characterization to more general noise models, including the Tsybakov model which considerably generalizes the Massart condition by allowing the flipping probability to be arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary, we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to obtain the first polynomial time algorithm with arbitrarily small excess error for learning linear threshold functions over any spherically symmetric distribution in the presence of spherically symmetric Tsybakov noise. Moreover, we posit access to a stronger oracle, in which for every labeled example we additionally obtain its flipping probability. In this model, we show that every SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$ misclassification error for a broad class of noise models. This setting substantially generalizes the widely-studied problem of classification under RCN with known noise rate, and corresponds to a non-convex optimization problem even when the noise function -- i.e. the flipping probabilities of all points -- is known in advance. %K Statistics, Machine Learning, stat.ML,Computer Science, Learning, cs.LG
[59]
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}, MARGINALMARK = {$\bullet$}, 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
[60]
A. Antoniadis, S. Kisfaludi-Bak, B. Laekhanukit, and D. Vaz, “On the Approximability of the Traveling Salesman Problem with Line Neighborhoods,” 2020. [Online]. Available: https://arxiv.org/abs/2008.12075. (arXiv: 2008.12075)
Abstract
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are $\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is based on a reduction to the group Steiner tree problem. We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge 3$. More generally, this implies that TSP with $k$-dimensional flats does not admit a PTAS for any $1\le k \leq d-2$ unless $\mathrm{P}=\mathrm{NP}$, which gives a complete classification of the approximability of these problems, as there are known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to give a stronger inapproximability factor for $d=O(\log n)$ by showing that TSP with lines does not admit a $(2-\epsilon)$-approximation in $d$ dimensions under the unique games conjecture. On the positive side, we leverage recent results on restricted variants of the group Steiner tree problem in order to give an $O(\log^2 n)$-approximation algorithm for the problem, albeit with a running time of $n^{O(\log\log n)}$.
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@online{Antoniadis_arXiv2008.12075, TITLE = {On the Approximability of the Traveling Salesman Problem with Line Neighborhoods}, AUTHOR = {Antoniadis, Antonios and Kisfaludi-Bak, S{\'a}ndor and Laekhanukit, Bundit and Vaz, Daniel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2008.12075}, EPRINT = {2008.12075}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are $\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is based on a reduction to the group Steiner tree problem. We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge 3$. More generally, this implies that TSP with $k$-dimensional flats does not admit a PTAS for any $1\le k \leq d-2$ unless $\mathrm{P}=\mathrm{NP}$, which gives a complete classification of the approximability of these problems, as there are known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to give a stronger inapproximability factor for $d=O(\log n)$ by showing that TSP with lines does not admit a $(2-\epsilon)$-approximation in $d$ dimensions under the unique games conjecture. On the positive side, we leverage recent results on restricted variants of the group Steiner tree problem in order to give an $O(\log^2 n)$-approximation algorithm for the problem, albeit with a running time of $n^{O(\log\log n)}$.}, }
Endnote
%0 Report %A Antoniadis, Antonios %A Kisfaludi-Bak, S&#225;ndor %A Laekhanukit, Bundit %A Vaz, Daniel %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T On the Approximability of the Traveling Salesman Problem with Line Neighborhoods : %G eng %U http://hdl.handle.net/21.11116/0000-0007-77AD-1 %U https://arxiv.org/abs/2008.12075 %D 2020 %X We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are $\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is based on a reduction to the group Steiner tree problem. We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge 3$. More generally, this implies that TSP with $k$-dimensional flats does not admit a PTAS for any $1\le k \leq d-2$ unless $\mathrm{P}=\mathrm{NP}$, which gives a complete classification of the approximability of these problems, as there are known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to give a stronger inapproximability factor for $d=O(\log n)$ by showing that TSP with lines does not admit a $(2-\epsilon)$-approximation in $d$ dimensions under the unique games conjecture. On the positive side, we leverage recent results on restricted variants of the group Steiner tree problem in order to give an $O(\log^2 n)$-approximation algorithm for the problem, albeit with a running time of $n^{O(\log\log n)}$. %K Computer Science, Data Structures and Algorithms, cs.DS
[61]
A. Antoniadis, T. Gouleakis, P. Kleer, and P. Kolev, “Secretary and Online Matching Problems with Machine Learned Advice,” 2020. [Online]. Available: https://arxiv.org/abs/2006.01026. (arXiv: 2006.01026)
Abstract
The classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take them into account. In particular, we study the following online selection problems: (i) the classical secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classical online algorithm for each problem) when the predictions are sufficiently accurate. For each algorithm, we establish a trade-off between the competitive ratios obtained in the two respective cases.
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@online{Antoniadis_arXiv2006.01026, TITLE = {Secretary and Online Matching Problems with Machine Learned Advice}, AUTHOR = {Antoniadis, Antonios and Gouleakis, Themis and Kleer, Pieter and Kolev, Pavel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2006.01026}, EPRINT = {2006.01026}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take them into account. In particular, we study the following online selection problems: (i) the classical secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classical online algorithm for each problem) when the predictions are sufficiently accurate. For each algorithm, we establish a trade-off between the competitive ratios obtained in the two respective cases.}, }
Endnote
%0 Report %A Antoniadis, Antonios %A Gouleakis, Themis %A Kleer, Pieter %A Kolev, Pavel %+ 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 Secretary and Online Matching Problems with Machine Learned Advice : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8B7A-4 %U https://arxiv.org/abs/2006.01026 %D 2020 %X The classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take them into account. In particular, we study the following online selection problems: (i) the classical secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classical online algorithm for each problem) when the predictions are sufficiently accurate. For each algorithm, we establish a trade-off between the competitive ratios obtained in the two respective cases. %K Computer Science, Data Structures and Algorithms, cs.DS
[62]
A. Antoniadis, A. Cristi, T. Oosterwijk, and A. Sgouritsa, “A General Framework for Energy-Efficient Cloud Computing Mechanisms,” in AAMAS’20, 19th International Conference on Autonomous Agents and MultiAgent Systems, Auckland, New Zealand (Virtual), 2020.
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@inproceedings{Antoniadis_AAMAS20, TITLE = {A General Framework for Energy-Efficient Cloud Computing Mechanisms}, AUTHOR = {Antoniadis, Antonios and Cristi, Andr{\'e}s and Oosterwijk, Tim and Sgouritsa, Alkmini}, LANGUAGE = {eng}, ISBN = {978-1-4503-7518-4}, URL = {https://dl.acm.org/doi/10.5555/3398761.3398775}, PUBLISHER = {ACM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {AAMAS'20, 19th International Conference on Autonomous Agents and MultiAgent Systems}, EDITOR = {El Fallah Seghruchni, Amal and Sukthankr, Gita and An, Bo and Yorke-Smith, Neil}, PAGES = {70--78}, ADDRESS = {Auckland, New Zealand (Virtual)}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Cristi, Andr&#233;s %A Oosterwijk, Tim %A Sgouritsa, Alkmini %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T A General Framework for Energy-Efficient Cloud Computing Mechanisms : %G eng %U http://hdl.handle.net/21.11116/0000-0007-93A5-8 %U https://dl.acm.org/doi/10.5555/3398761.3398775 %D 2020 %B 19th International Conference on Autonomous Agents and MultiAgent Systems %Z date of event: 2020-05-09 - 2020-05-13 %C Auckland, New Zealand (Virtual) %B AAMAS'20 %E El Fallah Seghruchni, Amal; Sukthankr, Gita; An, Bo; Yorke-Smith, Neil %P 70 - 78 %I ACM %@ 978-1-4503-7518-4
[63]
A. Antoniadis, T. Gouleakis, P. Kleer, and P. Kolev, “Secretary and Online Matching Problems with Machine Learned Advice,” in Advances in Neural Information Processing Systems 33 (NeurIPS 2020), Virtual Event, 2020.
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@inproceedings{Antoniadis_NeurIPS20, TITLE = {Secretary and Online Matching Problems with Machine Learned Advice}, AUTHOR = {Antoniadis, Antonios and Gouleakis, Themis and Kleer, Pieter and Kolev, Pavel}, LANGUAGE = {eng}, PUBLISHER = {Curran Associates, Inc.}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 33 (NeurIPS 2020)}, EDITOR = {Larochelle, H. and Ranzato, M. and Hadsell, R. and Balcan, M. F. and Lin, H.}, ADDRESS = {Virtual Event}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Gouleakis, Themis %A Kleer, Pieter %A Kolev, Pavel %+ 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 Secretary and Online Matching Problems with Machine Learned Advice : %G eng %U http://hdl.handle.net/21.11116/0000-0007-93CA-F %D 2020 %B 34th Conference on Neural Information Processing Systems %Z date of event: 2020-12-06 - 2020-12-12 %C Virtual Event %B Advances in Neural Information Processing Systems 33 %E Larochelle, H.; Ranzato, M.; Hadsell, R.; Balcan, M. F.; Lin, H. %I Curran Associates, Inc.
[64]
A. Antoniadis, C. Coester, M. Elias, A. Polak, and B. Simon, “Online Metric Algorithms with Untrusted Predictions,” in Proceedings of the 37th International Conference on Machine Learning (ICML 2020), Virtual Conference, 2020.
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@inproceedings{Antoniadis_ICML2020, TITLE = {Online Metric Algorithms with Untrusted Predictions}, AUTHOR = {Antoniadis, Antonios and Coester, Christian and Elias, Marek and Polak, Adam and Simon, Bertrand}, LANGUAGE = {eng}, ISSN = {2640-3498}, PUBLISHER = {MLResearchPress}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 37th International Conference on Machine Learning (ICML 2020)}, EDITOR = {Daum{\'e}, Hal and Singh, Aarti}, PAGES = {345--355}, SERIES = {Proceedings of Machine Learning Research}, VOLUME = {119}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Coester, Christian %A Elias, Marek %A Polak, Adam %A Simon, Bertrand %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Online Metric Algorithms with Untrusted Predictions : %G eng %U http://hdl.handle.net/21.11116/0000-0007-93BF-C %D 2020 %B 37th International Conference on Machine Learning %Z date of event: 2020-07-13 - 2020-07-18 %C Virtual Conference %B Proceedings of the 37th International Conference on Machine Learning %E Daum&#233;, Hal; Singh, Aarti %P 345 - 355 %I MLResearchPress %B Proceedings of Machine Learning Research %N 119 %@ false %U http://proceedings.mlr.press/v119/antoniadis20a/antoniadis20a.pdf
[65]
A. Antoniadis, K. Fleszar, R. Hoeksma, and K. Schewior, “A PTAS for Euclidean TSP with Hyperplane Neighborhoods,” ACM Transactions on Algorithms, vol. 16, no. 3, 2020.
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@article{AntoniadisTOA2020, TITLE = {A {PTAS} for {Euclidean} {TSP} with Hyperplane Neighborhoods}, AUTHOR = {Antoniadis, Antonios and Fleszar, Krzysztof and Hoeksma, Ruben and Schewior, Kevin}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3383466}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {16}, NUMBER = {3}, EID = {38}, }
Endnote
%0 Journal Article %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 : %G eng %U http://hdl.handle.net/21.11116/0000-0008-0723-9 %R 10.1145/3383466 %7 2020 %D 2020 %J ACM Transactions on Algorithms %V 16 %N 3 %Z sequence number: 38 %I ACM %C New York, NY %@ false
[66]
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}, MARGINALMARK = {$\bullet$}, 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/
[67]
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}, MARGINALMARK = {$\bullet$}, 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
[68]
R. Becker, Y. Emek, and C. Lenzen, “Low Diameter Graph Decompositions by Approximate Distance Computation,” in 11th Innovations in Theoretical Computer Science Conference (ITCS 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}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {11th Innovations in Theoretical Computer Science Conference (ITCS 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
[69]
D. Bilò, L. Gualà, S. Leucci, and G. Proietti, “Tracking Routes in Communication Networks,” Theoretical Computer Science, vol. 844, 2020.
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@article{Bilo_2020, TITLE = {Tracking Routes in Communication Networks}, AUTHOR = {Bil{\o}, Davide and Gual{\a}, Luciano and Leucci, Stefano and Proietti, Guido}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2020.07.012}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, JOURNAL = {Theoretical Computer Science}, VOLUME = {844}, PAGES = {1--15}, }
Endnote
%0 Journal Article %A Bil&#242;, Davide %A Gual&#224;, Luciano %A Leucci, Stefano %A Proietti, Guido %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Tracking Routes in Communication Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0007-72EF-C %R 10.1016/j.tcs.2020.07.012 %7 2020 %D 2020 %J Theoretical Computer Science %V 844 %& 1 %P 1 - 15 %I Elsevier %C Amsterdam %@ false
[70]
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}, MARGINALMARK = {$\bullet$}, 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
[71]
M. Brankovic, K. Buchin, K. Klaren, A. Nusser, A. Popov, and S. Wong, “(k, l)-Medians Clustering of Trajectories Using Continuous Dynamic Time Warpin,” in 28th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2020), Seattle, WA, USA (Online), 2020.
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@inproceedings{Brankovic_._SIGSPATIAL2020, TITLE = {{(k, l)}-Medians Clustering of Trajectories Using Continuous Dynamic Time Warpin}, AUTHOR = {Brankovic, Milutin and Buchin, Kevin and Klaren, Koen and Nusser, Andr{\'e} and Popov, Aleksandr and Wong, Sampson}, LANGUAGE = {eng}, ISBN = {9781450380195}, DOI = {0.1145/3397536.3422245}, PUBLISHER = {ACM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {28th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS 2020)}, EDITOR = {Lu, Chang-Tien and Wag, Fusheng and Trajcevski, Goce and Huang, Yan and Newsam, Shawn and Xiong, Li}, PAGES = {99--110}, ADDRESS = {Seattle, WA, USA (Online)}, }
Endnote
%0 Conference Proceedings %A Brankovic, Milutin %A Buchin, Kevin %A Klaren, Koen %A Nusser, Andr&#233; %A Popov, Aleksandr %A Wong, Sampson %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T (k, l)-Medians Clustering of Trajectories Using Continuous Dynamic Time Warpin : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9068-1 %R 0.1145/3397536.3422245 %D 2020 %B 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems %Z date of event: 2020-11-03 - 2020-11-06 %C Seattle, WA, USA (Online) %B 28th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems %E Lu, Chang-Tien; Wag, Fusheng; Trajcevski, Goce; Huang, Yan; Newsam, Shawn; Xiong, Li %P 99 - 110 %I ACM %@ 9781450380195
[72]
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}, MARGINALMARK = {$\bullet$}, 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
[73]
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}, MARGINALMARK = {$\bullet$}, 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
[74]
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}, MARGINALMARK = {$\bullet$}, 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
[75]
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}, MARGINALMARK = {$\bullet$}, 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
[76]
K. Bringmann and V. Nakos, “Top-k-convolution and the Quest for Near-linear Output-sensitive Subset Sum,” in STOC ’20, 52nd Annual ACM SIGACT Symposium on Theory of Computing, 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}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '20, 52nd Annual ACM SIGACT Symposium on Theory of Computing}, 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
[77]
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}, MARGINALMARK = {$\bullet$}, 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
[78]
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}, MARGINALMARK = {$\bullet$}, 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
[79]
K. Bringmann and P. Wellnitz, “On Near-Linear-Time Algorithms for Dense Subset Sum,” 2020. [Online]. Available: https://arxiv.org/abs/2010.09096. (arXiv: 2010.09096)
Abstract
In the Subset Sum problem we are given a set of $n$ positive integers $X$ and a target $t$ and are asked whether some subset of $X$ sums to $t$. Natural parameters for this problem that have been studied in the literature are $n$ and $t$ as well as the maximum input number $\rm{mx}_X$ and the sum of all input numbers $\Sigma_X$. In this paper we study the dense case of Subset Sum, where all these parameters are polynomial in $n$. In this regime, standard pseudo-polynomial algorithms solve Subset Sum in polynomial time $n^{O(1)}$. Our main question is: When can dense Subset Sum be solved in near-linear time $\tilde{O}(n)$? We provide an essentially complete dichotomy by designing improved algorithms and proving conditional lower bounds, thereby determining essentially all settings of the parameters $n,t,\rm{mx}_X,\Sigma_X$ for which dense Subset Sum is in time $\tilde{O}(n)$. For notational convenience we assume without loss of generality that $t \ge \rm{mx}_X$ (as larger numbers can be ignored) and $t \le \Sigma_X/2$ (using symmetry). Then our dichotomy reads as follows: - By reviving and improving an additive-combinatorics-based approach by Galil and Margalit [SICOMP'91], we show that Subset Sum is in near-linear time $\tilde{O}(n)$ if $t \gg \rm{mx}_X \Sigma_X/n^2$. - We prove a matching conditional lower bound: If Subset Sum is in near-linear time for any setting with $t \ll \rm{mx}_X \Sigma_X/n^2$, then the Strong Exponential Time Hypothesis and the Strong k-Sum Hypothesis fail. We also generalize our algorithm from sets to multi-sets, albeit with non-matching upper and lower bounds.
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@online{Bringmann_arXiv2010.09096, TITLE = {On Near-Linear-Time Algorithms for Dense Subset Sum}, AUTHOR = {Bringmann, Karl and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2010.09096}, EPRINT = {2010.09096}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the Subset Sum problem we are given a set of $n$ positive integers $X$ and a target $t$ and are asked whether some subset of $X$ sums to $t$. Natural parameters for this problem that have been studied in the literature are $n$ and $t$ as well as the maximum input number $\rm{mx}_X$ and the sum of all input numbers $\Sigma_X$. In this paper we study the dense case of Subset Sum, where all these parameters are polynomial in $n$. In this regime, standard pseudo-polynomial algorithms solve Subset Sum in polynomial time $n^{O(1)}$. Our main question is: When can dense Subset Sum be solved in near-linear time $\tilde{O}(n)$? We provide an essentially complete dichotomy by designing improved algorithms and proving conditional lower bounds, thereby determining essentially all settings of the parameters $n,t,\rm{mx}_X,\Sigma_X$ for which dense Subset Sum is in time $\tilde{O}(n)$. For notational convenience we assume without loss of generality that $t \ge \rm{mx}_X$ (as larger numbers can be ignored) and $t \le \Sigma_X/2$ (using symmetry). Then our dichotomy reads as follows: -- By reviving and improving an additive-combinatorics-based approach by Galil and Margalit [SICOMP'91], we show that Subset Sum is in near-linear time $\tilde{O}(n)$ if $t \gg \rm{mx}_X \Sigma_X/n^2$. -- We prove a matching conditional lower bound: If Subset Sum is in near-linear time for any setting with $t \ll \rm{mx}_X \Sigma_X/n^2$, then the Strong Exponential Time Hypothesis and the Strong k-Sum Hypothesis fail. We also generalize our algorithm from sets to multi-sets, albeit with non-matching upper and lower bounds.}, }
Endnote
%0 Report %A Bringmann, Karl %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On Near-Linear-Time Algorithms for Dense Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8C97-1 %U https://arxiv.org/abs/2010.09096 %D 2020 %X In the Subset Sum problem we are given a set of $n$ positive integers $X$ and a target $t$ and are asked whether some subset of $X$ sums to $t$. Natural parameters for this problem that have been studied in the literature are $n$ and $t$ as well as the maximum input number $\rm{mx}_X$ and the sum of all input numbers $\Sigma_X$. In this paper we study the dense case of Subset Sum, where all these parameters are polynomial in $n$. In this regime, standard pseudo-polynomial algorithms solve Subset Sum in polynomial time $n^{O(1)}$. Our main question is: When can dense Subset Sum be solved in near-linear time $\tilde{O}(n)$? We provide an essentially complete dichotomy by designing improved algorithms and proving conditional lower bounds, thereby determining essentially all settings of the parameters $n,t,\rm{mx}_X,\Sigma_X$ for which dense Subset Sum is in time $\tilde{O}(n)$. For notational convenience we assume without loss of generality that $t \ge \rm{mx}_X$ (as larger numbers can be ignored) and $t \le \Sigma_X/2$ (using symmetry). Then our dichotomy reads as follows: - By reviving and improving an additive-combinatorics-based approach by Galil and Margalit [SICOMP'91], we show that Subset Sum is in near-linear time $\tilde{O}(n)$ if $t \gg \rm{mx}_X \Sigma_X/n^2$. - We prove a matching conditional lower bound: If Subset Sum is in near-linear time for any setting with $t \ll \rm{mx}_X \Sigma_X/n^2$, then the Strong Exponential Time Hypothesis and the Strong k-Sum Hypothesis fail. We also generalize our algorithm from sets to multi-sets, albeit with non-matching upper and lower bounds. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Discrete Mathematics, cs.DM
[80]
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}, MARGINALMARK = {$\bullet$}, 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
[81]
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}, MARGINALMARK = {$\bullet$}, 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
[82]
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}, MARGINALMARK = {$\bullet$}, 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
[83]
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}, MARGINALMARK = {$\bullet$}, 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
[84]
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}, MARGINALMARK = {$\bullet$}, 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
[85]
P. Charalampopoulos, T. Kociumaka, and P. Wellnitz, “Faster Approximate Pattern Matching: A Unified Approach,” 2020. [Online]. Available: https://arxiv.org/abs/2004.08350. (arXiv: 2004.08350)
Abstract
Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We consider the two most fundamental string metrics: the Hamming distance and the edit distance. Under the Hamming distance, we search for substrings of $T$ that have at most $k$ mismatches with $P$, while under the edit distance, we search for substrings of $T$ that can be transformed to $P$ with at most $k$ edits. Exact occurrences of $P$ in $T$ have a very simple structure: If we assume for simplicity that $|T| \le 3|P|/2$ and trim $T$ so that $P$ occurs both as a prefix and as a suffix of $T$, then both $P$ and $T$ are periodic with a common period. However, an analogous characterization for the structure of occurrences with up to $k$ mismatches was proved only recently by Bringmann et al. [SODA'19]: Either there are $O(k^2)$ $k$-mismatch occurrences of $P$ in $T$, or both $P$ and $T$ are at Hamming distance $O(k)$ from strings with a common period $O(m/k)$. We tighten this characterization by showing that there are $O(k)$ $k$-mismatch occurrences in the case when the pattern is not (approximately) periodic, and we lift it to the edit distance setting, where we tightly bound the number of $k$-edit occurrences by $O(k^2)$ in the non-periodic case. Our proofs are constructive and let us obtain a unified framework for approximate pattern matching for both considered distances. We showcase the generality of our framework with results for the fully-compressed setting (where $T$ and $P$ are given as a straight-line program) and for the dynamic setting (where we extend a data structure of Gawrychowski et al. [SODA'18]).
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@online{Charalampopoulos_arXiv2004.08350, TITLE = {Faster Approximate Pattern Matching: {A} Unified Approach}, AUTHOR = {Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2004.08350}, EPRINT = {2004.08350}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We consider the two most fundamental string metrics: the Hamming distance and the edit distance. Under the Hamming distance, we search for substrings of $T$ that have at most $k$ mismatches with $P$, while under the edit distance, we search for substrings of $T$ that can be transformed to $P$ with at most $k$ edits. Exact occurrences of $P$ in $T$ have a very simple structure: If we assume for simplicity that $|T| \le 3|P|/2$ and trim $T$ so that $P$ occurs both as a prefix and as a suffix of $T$, then both $P$ and $T$ are periodic with a common period. However, an analogous characterization for the structure of occurrences with up to $k$ mismatches was proved only recently by Bringmann et al. [SODA'19]: Either there are $O(k^2)$ $k$-mismatch occurrences of $P$ in $T$, or both $P$ and $T$ are at Hamming distance $O(k)$ from strings with a common period $O(m/k)$. We tighten this characterization by showing that there are $O(k)$ $k$-mismatch occurrences in the case when the pattern is not (approximately) periodic, and we lift it to the edit distance setting, where we tightly bound the number of $k$-edit occurrences by $O(k^2)$ in the non-periodic case. Our proofs are constructive and let us obtain a unified framework for approximate pattern matching for both considered distances. We showcase the generality of our framework with results for the fully-compressed setting (where $T$ and $P$ are given as a straight-line program) and for the dynamic setting (where we extend a data structure of Gawrychowski et al. [SODA'18]).}, }
Endnote
%0 Report %A Charalampopoulos, Panagiotis %A Kociumaka, Tomasz %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Approximate Pattern Matching: A Unified Approach : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8C63-C %U https://arxiv.org/abs/2004.08350 %D 2020 %X Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We consider the two most fundamental string metrics: the Hamming distance and the edit distance. Under the Hamming distance, we search for substrings of $T$ that have at most $k$ mismatches with $P$, while under the edit distance, we search for substrings of $T$ that can be transformed to $P$ with at most $k$ edits. Exact occurrences of $P$ in $T$ have a very simple structure: If we assume for simplicity that $|T| \le 3|P|/2$ and trim $T$ so that $P$ occurs both as a prefix and as a suffix of $T$, then both $P$ and $T$ are periodic with a common period. However, an analogous characterization for the structure of occurrences with up to $k$ mismatches was proved only recently by Bringmann et al. [SODA'19]: Either there are $O(k^2)$ $k$-mismatch occurrences of $P$ in $T$, or both $P$ and $T$ are at Hamming distance $O(k)$ from strings with a common period $O(m/k)$. We tighten this characterization by showing that there are $O(k)$ $k$-mismatch occurrences in the case when the pattern is not (approximately) periodic, and we lift it to the edit distance setting, where we tightly bound the number of $k$-edit occurrences by $O(k^2)$ in the non-periodic case. Our proofs are constructive and let us obtain a unified framework for approximate pattern matching for both considered distances. We showcase the generality of our framework with results for the fully-compressed setting (where $T$ and $P$ are given as a straight-line program) and for the dynamic setting (where we extend a data structure of Gawrychowski et al. [SODA'18]). %K Computer Science, Data Structures and Algorithms, cs.DS
[86]
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}, MARGINALMARK = {$\bullet$}, 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
[87]
G. Christodoulou, V. Gkatzelis, M. Latifian, and A. Sgouritsa, “Resource-Aware Protocols for Network Cost-Sharing Games,” in EC ’20, 21st ACM Conference on Economics and Computation, Virtual Event, Hungary, 2020.
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@inproceedings{Christodoulou_EC2020, TITLE = {Resource-Aware Protocols for Network Cost-Sharing Games}, AUTHOR = {Christodoulou, George and Gkatzelis, Vasilis and Latifian, Mohamad and Sgouritsa, Alkmini}, LANGUAGE = {eng}, ISBN = {9781450379755}, DOI = {10.1145/3391403.3399528}, PUBLISHER = {ACM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {EC '20, 21st ACM Conference on Economics and Computation}, EDITOR = {Bir{\'o}, P{\'e}ter and Hartline, Jason}, PAGES = {81--107}, ADDRESS = {Virtual Event, Hungary}, }
Endnote
%0 Conference Proceedings %A Christodoulou, George %A Gkatzelis, Vasilis %A Latifian, Mohamad %A Sgouritsa, Alkmini %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Resource-Aware Protocols for Network Cost-Sharing Games : %G eng %U http://hdl.handle.net/21.11116/0000-0007-938C-5 %R 10.1145/3391403.3399528 %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 81 - 107 %I ACM %@ 9781450379755
[88]
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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BibTeX
@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}, MARGINALMARK = {$\bullet$}, 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
[89]
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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BibTeX
@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}, MARGINALMARK = {$\bullet$}, 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 %+ Algorithms and Complexity, 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
[90]
N. R. Dayama, M. Shiripour, A. Oulasvirta, E. Ivanko, and A. Karrenbauer, “Foraging-based Optimization of Menu Systems,” 2020. . (arXiv: 2005.01292)
Abstract
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BibTeX
@online{Dayama_arXiv2005.01292, TITLE = {Foraging-based Optimization of Menu Systems}, AUTHOR = {Dayama, Niraj Ramesh and Shiripour, Morteza and Oulasvirta, Antti and Ivanko, Evgeny and Karrenbauer, Andreas}, LANGUAGE = {eng}, EPRINT = {2005.01292}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Computational design of menu systems has been solved in limited cases such as the linear menu (list) as an assignment task, where commands are assigned to menu positions while optimizing for for users selection performance and distance of associated items. We show that this approach falls short with larger, hierarchically organized menu systems, where one must also take into account how users navigate hierarchical structures. This paper presents a novel integer programming formulation that models hierarchical menus as a combination of the exact set covering problem and the assignment problem. It organizes commands into ordered groups of ordered groups via a novel objective function based on information foraging theory. It minimizes, on the one hand, the time required to select a command whose location is known from previous usage and, on the other, the time wasted in irrelevant parts of the menu while searching for commands whose location is not known. The convergence of these two factors yields usable, well-ordered command hierarchies from a single model. In generated menus, the lead (first) elements of a group or tab are good indicators of the remaining contents, thereby facilitating the search process. In a controlled usability evaluation, the performance of computationally designed menus was 25 faster than existing commercial designs with respect to selection time. The algorithm is efficient for large, representative instances of the problem. We further show applications in personalization and adaptation of menu systems.}, }
Endnote
[91]
M. de Berg and S. Kisfaludi-Bak, “Lower Bounds for Dominating Set in Ball Graphs and for Weighted Dominating Set in Unit-Ball Graphs,” in Treewidth, Kernels, and Algorithms, Berlin: Springer, 2020.
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@incollection{BergK20, TITLE = {Lower Bounds for Dominating Set in Ball Graphs and for Weighted Dominating Set in Unit-Ball Graphs}, AUTHOR = {de Berg, Mark and Kisfaludi-Bak, S{\'a}ndor}, LANGUAGE = {eng}, ISBN = {978-3-030-42070-3}, DOI = {10.1007/978-3-030-42071-0_5}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, BOOKTITLE = {Treewidth, Kernels, and Algorithms}, EDITOR = {Fomin, Fedor V. and Kratsch, Stefan and van Leeuwen, Erik Jan}, PAGES = {31--48}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12160}, }
Endnote
%0 Book Section %A de Berg, Mark %A Kisfaludi-Bak, S&#225;ndor %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Lower Bounds for Dominating Set in Ball Graphs and for Weighted Dominating Set in Unit-Ball Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-76CB-0 %R 10.1007/978-3-030-42071-0_5 %D 2020 %B Treewidth, Kernels, and Algorithms %E Fomin, Fedor V.; Kratsch, Stefan; van Leeuwen, Erik Jan %P 31 - 48 %I Springer %C Berlin %@ 978-3-030-42070-3 %S Lecture Notes in Computer Science %N 12160
[92]
M. de Berg, H. L. Bodlaender, S. Kisfaludi-Bak, D. Marx, and T. C. van der Zanden, “A Framework for Exponential-Time-Hypothesis-Tight Algorithms and Lower Bounds in Geometric Intersection Graphs,” SIAM Journal on Computing, vol. 49, no. 6, 2020.
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@article{BergBKMZ20, TITLE = {A Framework for Exponential-Time-Hypothesis-Tight Algorithms and Lower Bounds in Geometric Intersection Graphs}, AUTHOR = {de Berg, Mark and Bodlaender, Hans L. and Kisfaludi-Bak, S{\'a}ndor and Marx, D{\'a}niel and van der Zanden, Tom C.}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/20M1320870}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {49}, NUMBER = {6}, PAGES = {1291--1331}, }
Endnote
%0 Journal Article %A de Berg, Mark %A Bodlaender, Hans L. %A Kisfaludi-Bak, S&#225;ndor %A Marx, D&#225;niel %A van der Zanden, Tom C. %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Framework for Exponential-Time-Hypothesis-Tight Algorithms and Lower Bounds in Geometric Intersection Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-A582-B %R 10.1137/20M1320870 %7 2020 %D 2020 %J SIAM Journal on Computing %V 49 %N 6 %& 1291 %P 1291 - 1331 %I SIAM %C Philadelphia, PA %@ false
[93]
I. Diakonikolas, T. Gouleakis, D. M. Kane, J. Peebles, and E. Price, “Optimal Testing of Discrete Distributions with High Probability,” 2020. [Online]. Available: https://arxiv.org/abs/2009.06540. (arXiv: 2009.06540)
Abstract
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we want to distinguish {\em with probability at least $1-\delta$} whether these distributions satisfy $\mathcal{P}$ or are $\epsilon$-far from $\mathcal{P}$ in total variation distance. Most prior work in distribution testing studied the constant confidence case (corresponding to $\delta = \Omega(1)$), and provided sample-optimal testers for a range of properties. While one can always boost the confidence probability of any such tester by black-box amplification, this generic boosting method typically leads to sub-optimal sample bounds. Here we study the following broad question: For a given property $\mathcal{P}$, can we {\em characterize} the sample complexity of testing $\mathcal{P}$ as a function of all relevant problem parameters, including the error probability $\delta$? Prior to this work, uniformity testing was the only statistical task whose sample complexity had been characterized in this setting. As our main results, we provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors, as a function of all relevant parameters. We also show matching information-theoretic lower bounds on the sample complexity of these problems. Our techniques naturally extend to give optimal testers for related problems. To illustrate the generality of our methods, we give optimal algorithms for testing collections of distributions and testing closeness with unequal sized samples.
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@online{Diakonikolas_arXiv2009.06540, TITLE = {Optimal Testing of Discrete Distributions with High Probability}, AUTHOR = {Diakonikolas, Ilias and Gouleakis, Themis and Kane, Daniel M. and Peebles, John and Price, Eric}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2009.06540}, EPRINT = {2009.06540}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we want to distinguish {\em with probability at least $1-\delta$} whether these distributions satisfy $\mathcal{P}$ or are $\epsilon$-far from $\mathcal{P}$ in total variation distance. Most prior work in distribution testing studied the constant confidence case (corresponding to $\delta = \Omega(1)$), and provided sample-optimal testers for a range of properties. While one can always boost the confidence probability of any such tester by black-box amplification, this generic boosting method typically leads to sub-optimal sample bounds. Here we study the following broad question: For a given property $\mathcal{P}$, can we {\em characterize} the sample complexity of testing $\mathcal{P}$ as a function of all relevant problem parameters, including the error probability $\delta$? Prior to this work, uniformity testing was the only statistical task whose sample complexity had been characterized in this setting. As our main results, we provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors, as a function of all relevant parameters. We also show matching information-theoretic lower bounds on the sample complexity of these problems. Our techniques naturally extend to give optimal testers for related problems. To illustrate the generality of our methods, we give optimal algorithms for testing collections of distributions and testing closeness with unequal sized samples.}, }
Endnote
%0 Report %A Diakonikolas, Ilias %A Gouleakis, Themis %A Kane, Daniel M. %A Peebles, John %A Price, Eric %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Optimal Testing of Discrete Distributions with High Probability : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8B62-E %U https://arxiv.org/abs/2009.06540 %D 2020 %X We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we want to distinguish {\em with probability at least $1-\delta$} whether these distributions satisfy $\mathcal{P}$ or are $\epsilon$-far from $\mathcal{P}$ in total variation distance. Most prior work in distribution testing studied the constant confidence case (corresponding to $\delta = \Omega(1)$), and provided sample-optimal testers for a range of properties. While one can always boost the confidence probability of any such tester by black-box amplification, this generic boosting method typically leads to sub-optimal sample bounds. Here we study the following broad question: For a given property $\mathcal{P}$, can we {\em characterize} the sample complexity of testing $\mathcal{P}$ as a function of all relevant problem parameters, including the error probability $\delta$? Prior to this work, uniformity testing was the only statistical task whose sample complexity had been characterized in this setting. As our main results, we provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors, as a function of all relevant parameters. We also show matching information-theoretic lower bounds on the sample complexity of these problems. Our techniques naturally extend to give optimal testers for related problems. To illustrate the generality of our methods, we give optimal algorithms for testing collections of distributions and testing closeness with unequal sized samples. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Learning, cs.LG,Mathematics, Statistics, math.ST,Statistics, Machine Learning, stat.ML,Statistics, Statistics Theory, stat.TH
[94]
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}, MARGINALMARK = {$\bullet$}, 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
[95]
M. Dyer, C. Greenhill, P. Kleer, J. Ross, and L. Stougie, “Sampling Hypergraphs with Given Degrees,” 2020. [Online]. Available: https://arxiv.org/abs/2006.12021. (arXiv: 2006.12021)
Abstract
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm $\mathcal{A}$ for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm $\mathcal{A}$, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant.
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@online{Dyer_arXiv2006.12021, TITLE = {Sampling Hypergraphs with Given Degrees}, AUTHOR = {Dyer, Martin and Greenhill, Catherine and Kleer, Pieter and Ross, James and Stougie, Leen}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2006.12021}, EPRINT = {2006.12021}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm $\mathcal{A}$ for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm $\mathcal{A}$, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant.}, }
Endnote
%0 Report %A Dyer, Martin %A Greenhill, Catherine %A Kleer, Pieter %A Ross, James %A Stougie, Leen %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Sampling Hypergraphs with Given Degrees : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9152-8 %U https://arxiv.org/abs/2006.12021 %D 2020 %X There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm $\mathcal{A}$ for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm $\mathcal{A}$, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a constant. %K Computer Science, Discrete Mathematics, cs.DM
[96]
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}, MARGINALMARK = {$\bullet$}, 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
[97]
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}, MARGINALMARK = {$\bullet$}, 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
[98]
N. Fischer and C. Ikenmeyer, “The Computational Complexity of Plethysm Coefficients,” Computational Complexity, vol. 29, no. 2, 2020.
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@article{Fischer_2020, TITLE = {The Computational Complexity of Plethysm Coefficients}, AUTHOR = {Fischer, Nick and Ikenmeyer, Christian}, LANGUAGE = {eng}, DOI = {10.1007/s00037-020-00198-4}, PUBLISHER = {Springer}, ADDRESS = {New York,NY}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, JOURNAL = {Computational Complexity}, VOLUME = {29}, NUMBER = {2}, EID = {8}, }
Endnote
%0 Journal Article %A Fischer, Nick %A Ikenmeyer, Christian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T The Computational Complexity of Plethysm Coefficients : %G eng %U http://hdl.handle.net/21.11116/0000-0007-72D0-D %R 10.1007/s00037-020-00198-4 %7 2020 %D 2020 %J Computational Complexity %V 29 %N 2 %Z sequence number: 8 %I Springer %C New York,NY
[99]
F. V. Fomin, P. A. Golovach, W. Lochet, P. Misra, S. Saket, and R. Sharma, “Parameterized Complexity of Directed Spanner Problems,” in 15th International Symposium on Parameterized and Exact Computation (IPEC 2020), Hong Kong, China (Virtual Conference), 2020.
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@inproceedings{Fomin_IPEC20, TITLE = {Parameterized Complexity of Directed Spanner Problems}, AUTHOR = {Fomin, Fedor V. and Golovach, Petr A. and Lochet, William and Misra, Pranabendu and Saket, Saurabh and Sharma, Roohani}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-172-6}, URL = {urn:nbn:de:0030-drops-133156}, DOI = {10.4230/LIPIcs.IPEC.2020.12}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {15th International Symposium on Parameterized and Exact Computation (IPEC 2020)}, EDITOR = {Cao, Yixin and Pilipczuk, Marcin}, EID = {12}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {180}, ADDRESS = {Hong Kong, China (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Fomin, Fedor V. %A Golovach, Petr A. %A Lochet, William %A Misra, Pranabendu %A Saket, Saurabh %A Sharma, Roohani %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Parameterized Complexity of Directed Spanner Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9373-1 %R 10.4230/LIPIcs.IPEC.2020.12 %U urn:nbn:de:0030-drops-133156 %D 2020 %B 15th International Symposium on Parameterized and Exact Computation %Z date of event: 2020-12-14 - 2020-12-18 %C Hong Kong, China (Virtual Conference) %B 15th International Symposium on Parameterized and Exact Computation %E Cao, Yixin; Pilipczuk, Marcin %Z sequence number: 12 %I Schloss Dagstuhl %@ 978-3-95977-172-6 %B Leibniz International Proceedings in Informatics %N 180 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/13315/https://creativecommons.org/licenses/by/3.0/legalcode
[100]
F. V. Fomin, P. Golovach, P. Misra, and M. S. Ramanujan, “On the Complexity of Recovering Incidence Matrices,” in 28th Annual European Symposium on Algorithms (ESA 2020), Pisa, Italy (Virtual Conference), 2020.
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@inproceedings{DBLP:conf/esa/FominGMR20, TITLE = {On the Complexity of Recovering Incidence Matrices}, AUTHOR = {Fomin, Fedor V. and Golovach, Petr and Misra, Pranabendu and Ramanujan, M. S.}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-162-7}, URL = {urn:nbn:de:0030-drops-129164}, DOI = {10.4230/LIPIcs.ESA.2020.50}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {28th Annual European Symposium on Algorithms (ESA 2020)}, EDITOR = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, EID = {50}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {173}, ADDRESS = {Pisa, Italy (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Fomin, Fedor V. %A Golovach, Petr %A Misra, Pranabendu %A Ramanujan, M. S. %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Complexity of Recovering Incidence Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D2B0-4 %R 10.4230/LIPIcs.ESA.2020.50 %U urn:nbn:de:0030-drops-129164 %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: 50 %I Schloss Dagstuhl %@ 978-3-95977-162-7 %B Leibniz International Proceedings in Informatics %N 173 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12916/https://creativecommons.org/licenses/by/3.0/legalcode
[101]
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}, MARGINALMARK = {$\bullet$}, 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
[102]
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}, MARGINALMARK = {$\bullet$}, 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
[103]
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}, MARGINALMARK = {$\bullet$}, 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
[104]
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}, MARGINALMARK = {$\bullet$}, 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
[105]
M. Grohe, D. Neuen, and D. Wiebking, “Isomorphism Testing for Graphs Excluding Small Minors,” 2020. [Online]. Available: https://arxiv.org/abs/2004.07671. (arXiv: 2004.07671)
Abstract
We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.
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@online{Grohe_arXiv2004.07671, TITLE = {Isomorphism Testing for Graphs Excluding Small Minors}, AUTHOR = {Grohe, Martin and Neuen, Daniel and Wiebking, Daniel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2004.07671}, EPRINT = {2004.07671}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments.}, }
Endnote
%0 Report %A Grohe, Martin %A Neuen, Daniel %A Wiebking, Daniel %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Isomorphism Testing for Graphs Excluding Small Minors : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9943-1 %U https://arxiv.org/abs/2004.07671 %D 2020 %X We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988) and $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016). For the algorithm we combine recent advances in the group-theoretic graph isomorphism machinery with new graph-theoretic arguments. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Discrete Mathematics, cs.DM,Mathematics, Combinatorics, math.CO
[106]
S. Gunda, P. Jain, D. Lokshtanov, S. Saurabh, and P. Tale, “On the Parameterized Approximability of Contraction to Classes of Chordal Graphs,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020), Virtual Conference, 2020.
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@inproceedings{Gunda_APPROXRANDOM20, TITLE = {On the Parameterized Approximability of Contraction to Classes of Chordal Graphs}, AUTHOR = {Gunda, Spoorthy and Jain, Pallavi and Lokshtanov, Daniel and Saurabh, Saket and Tale, Prafullkumar}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-164-1}, URL = {urn:nbn:de:0030-drops-126545}, DOI = {10.4230/LIPIcs.APPROX/RANDOM.2020.51}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, EDITOR = {Byrka, Jaros{\l}av and Meka, Raghu}, PAGES = {1--19}, EID = {51}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {176}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Gunda, Spoorthy %A Jain, Pallavi %A Lokshtanov, Daniel %A Saurabh, Saket %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Parameterized Approximability of Contraction to Classes of Chordal Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-874F-9 %R 10.4230/LIPIcs.APPROX/RANDOM.2020.51 %U urn:nbn:de:0030-drops-126545 %D 2020 %B 23rd International Conference on Approximation Algorithms for Combinatorial Optimization Problems / 24th International Conference on Randomization and Computation %Z date of event: 2020-08-17 - 2020-08-19 %C Virtual Conference %B Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques %E Byrka, Jaros&#322;av; Meka, Raghu %P 1 - 19 %Z sequence number: 51 %I Schloss Dagstuhl %@ 978-3-95977-164-1 %B Leibniz International Proceedings in Informatics %N 176 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12654/
[107]
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}, MARGINALMARK = {$\bullet$}, 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
[108]
P. Jain, L. Kanesh, and P. Misra, “Conflict Free Version of Covering Problems on Graphs: Classical and Parameterized,” Theory of Computing Systems, vol. 64, 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}, MARGINALMARK = {$\bullet$}, JOURNAL = {Theory of Computing Systems}, VOLUME = {64}, PAGES = {1067--1093}, }
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 %V 64 %& 1067 %P 1067 - 1093 %I Springer %C New York, NY %@ false
[109]
M. John, “Of Keyboards and Beyond,” Universität des Saarlandes, Saarbrücken, 2020.
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@phdthesis{John_2019, TITLE = {Of Keyboards and Beyond}, AUTHOR = {John, Maximilian}, DOI = {10.22028/D291-30635}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, }
Endnote
%0 Thesis %A John, Maximilian %Y Karrenbauer, Andreas %A referee: Mehlhorn, Kurt %+ 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 %T Of Keyboards and Beyond : Optimization in Human-Computer Interaction %U http://hdl.handle.net/21.11116/0000-0007-7152-D %R 10.22028/D291-30635 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2020 %P 91 p. %V phd %9 phd %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/28954
[110]
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}, MARGINALMARK = {$\bullet$}, 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
[111]
A. Karrenbauer and E. Kovalevskaya, “Reading Articles Online,” in Combinatorial Optimization and Applications (COCOA 2020), Dallas, TX, USA (Virtual Conference), 2020.
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@inproceedings{KK2020, TITLE = {Reading Articles Online}, AUTHOR = {Karrenbauer, Andreas and Kovalevskaya, Elizaveta}, LANGUAGE = {eng}, ISBN = {978-3-030-64842-8}, DOI = {10.1007/978-3-030-64843-5_43}, PUBLISHER = {Springer}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, BOOKTITLE = {Combinatorial Optimization and Applications (COCOA 2020)}, EDITOR = {Wu, Weili and Zhang, Zhongnan}, PAGES = {639--654}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12577}, ADDRESS = {Dallas, TX, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Karrenbauer, Andreas %A Kovalevskaya, Elizaveta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Reading Articles Online : %G eng %U http://hdl.handle.net/21.11116/0000-0007-E787-C %R 10.1007/978-3-030-64843-5_43 %D 2020 %B 14th Annual International Conference on Combinatorial Optimization and Application %Z date of event: 2020-12-11 - 2020-12-13 %C Dallas, TX, USA (Virtual Conference) %B Combinatorial Optimization and Applications %E Wu, Weili; Zhang, Zhongnan %P 639 - 654 %I Springer %@ 978-3-030-64842-8 %B Lecture Notes in Computer Science %N 12577
[112]
D. M. Katz, C. Coupette, J. Beckedorf, and D. Hartung, “Complex Societies and the Growth of the Law,” Scientific Reports, vol. 10, 2020.
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@article{Katz2020, TITLE = {Complex Societies and the Growth of the Law}, AUTHOR = {Katz, Daniel Martin and Coupette, Corinna and Beckedorf, Janis and Hartung, Dirk}, LANGUAGE = {eng}, ISSN = {2045-2322}, DOI = {10.1038/s41598-020-73623-x}, PUBLISHER = {Nature Publishing Group}, ADDRESS = {London, UK}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, JOURNAL = {Scientific Reports}, VOLUME = {10}, EID = {18737}, }
Endnote
%0 Journal Article %A Katz, Daniel Martin %A Coupette, Corinna %A Beckedorf, Janis %A Hartung, Dirk %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Complex Societies and the Growth of the Law : %G eng %U http://hdl.handle.net/21.11116/0000-0007-5C0B-7 %R 10.1038/s41598-020-73623-x %7 2020 %D 2020 %J Scientific Reports %O Sci. Rep. %V 10 %Z sequence number: 18737 %I Nature Publishing Group %C London, UK %@ false
[113]
S. Kisfaludi-Bak, “A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic TSP,” in 36th International Symposium on Computational Geometry (SoCG 2020), Zürich, Switzerland (Virtual Conference), 2020.
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@inproceedings{SoCG/Kisfaludi-Bak20, TITLE = {A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic {TSP}}, AUTHOR = {Kisfaludi-Bak, S{\'a}ndor}, LANGUAGE = {eng}, ISBN = {978-3-95977-143-6}, URL = {urn:nbn:de:0030-drops-122135}, DOI = {10.4230/LIPIcs.SoCG.2020.55}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {36th International Symposium on Computational Geometry (SoCG 2020)}, EDITOR = {Cabello, Sergio and Chen, Danny Z.}, PAGES = {1--15}, EID = {55}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {164}, ADDRESS = {Z{\"u}rich, Switzerland (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Kisfaludi-Bak, S&#225;ndor %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic TSP : %G eng %U http://hdl.handle.net/21.11116/0000-0007-76E8-F %R 10.4230/LIPIcs.SoCG.2020.55 %U urn:nbn:de:0030-drops-122135 %D 2020 %B 36th International Symposium on Computational Geometry %Z date of event: 2020-06-23 - 2020-06-26 %C Z&#252;rich, Switzerland (Virtual Conference) %B 36th International Symposium on Computational Geometry %E Cabello, Sergio; Chen, Danny Z. %P 1 - 15 %Z sequence number: 55 %I Schloss Dagstuhl %@ 978-3-95977-143-6 %B Leibniz International Proceedings in Informatics %N 164 %U https://drops.dagstuhl.de/opus/volltexte/2020/12213/https://creativecommons.org/licenses/by/3.0/legalcode
[114]
S. Kisfaludi-Bak, “Hyperbolic Intersection Graphs and (Quasi)-Polynomial Time,” 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{SODA/Kisfaludi-Bak20, TITLE = {Hyperbolic Intersection Graphs and (Quasi)-Polynomial Time}, AUTHOR = {Kisfaludi-Bak, S{\'a}ndor}, LANGUAGE = {eng}, ISBN = {978-1-61197-599-4}, DOI = {10.1137/1.9781611975994.100}, PUBLISHER = {SIAM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)}, EDITOR = {Chawla, Shuchi}, PAGES = {1621--1638}, ADDRESS = {Salt Lake City, UT, USA}, }
Endnote
%0 Conference Proceedings %A Kisfaludi-Bak, S&#225;ndor %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Hyperbolic Intersection Graphs and (Quasi)-Polynomial Time : %G eng %U http://hdl.handle.net/21.11116/0000-0007-76EB-C %R 10.1137/1.9781611975994.100 %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 1621 - 1638 %I SIAM %@ 978-1-61197-599-4
[115]
S. Kisfaludi-Bak, J. Nederlof, and K. Węgrzycki, “A Gap-ETH-Tight Approximation Scheme for Euclidean TSP,” 2020. [Online]. Available: https://arxiv.org/abs/2011.03778. (arXiv: 2011.03778)
Abstract
We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})} n\log n$ time. This improves the previously smallest dependence on $\varepsilon$ in the running time $(1/\varepsilon)^{\mathcal{O}(1/\varepsilon^{d-1})}n \log n$ of the algorithm by Rao and Smith (STOC 1998). We also show that a $2^{o(1/\varepsilon^{d-1})}\text{poly}(n)$ algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH). Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call \emph{sparsity-sensitive patching}. On a high level this lets the granularity with which we simplify the tour depend on how sparse it is locally. Our approach is (arguably) simpler than the one by Rao and Smith since it can work without geometric spanners. We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree.
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@online{Kisfaludi-BakNW20, TITLE = {A Gap-{ETH}-Tight Approximation Scheme for Euclidean {TSP}}, AUTHOR = {Kisfaludi-Bak, S{\'a}ndor and Nederlof, Jesper and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2011.03778}, EPRINT = {2011.03778}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})} n\log n$ time. This improves the previously smallest dependence on $\varepsilon$ in the running time $(1/\varepsilon)^{\mathcal{O}(1/\varepsilon^{d-1})}n \log n$ of the algorithm by Rao and Smith (STOC 1998). We also show that a $2^{o(1/\varepsilon^{d-1})}\text{poly}(n)$ algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH). Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call \emph{sparsity-sensitive patching}. On a high level this lets the granularity with which we simplify the tour depend on how sparse it is locally. Our approach is (arguably) simpler than the one by Rao and Smith since it can work without geometric spanners. We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree.}, }
Endnote
%0 Report %A Kisfaludi-Bak, S&#225;ndor %A Nederlof, Jesper %A W&#281;grzycki, Karol %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Gap-ETH-Tight Approximation Scheme for Euclidean TSP : %G eng %U http://hdl.handle.net/21.11116/0000-0007-7774-1 %U https://arxiv.org/abs/2011.03778 %D 2020 %X We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})} n\log n$ time. This improves the previously smallest dependence on $\varepsilon$ in the running time $(1/\varepsilon)^{\mathcal{O}(1/\varepsilon^{d-1})}n \log n$ of the algorithm by Rao and Smith (STOC 1998). We also show that a $2^{o(1/\varepsilon^{d-1})}\text{poly}(n)$ algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH). Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call \emph{sparsity-sensitive patching}. On a high level this lets the granularity with which we simplify the tour depend on how sparse it is locally. Our approach is (arguably) simpler than the one by Rao and Smith since it can work without geometric spanners. We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree. %K Computer Science, Computational Geometry, cs.CG,Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[116]
S. Kisfaludi-Bak, J. Nederlof, and E. J. van Leeuwen, “Nearly ETH-tight Algorithms for Planar Steiner Tree with Terminals on Few Faces,” ACM Transactions on Algorithms, vol. 16, no. 3, 2020.
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@article{Kisfaludi-BakNL20b, TITLE = {Nearly {ETH}-tight Algorithms for Planar {Steiner} Tree with Terminals on Few Faces}, AUTHOR = {Kisfaludi-Bak, S{\'a}ndor and Nederlof, Jesper and van Leeuwen, Erik Jan}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3371389}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {16}, NUMBER = {3}, EID = {28}, }
Endnote
%0 Journal Article %A Kisfaludi-Bak, S&#225;ndor %A Nederlof, Jesper %A van Leeuwen, Erik Jan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Nearly ETH-tight Algorithms for Planar Steiner Tree with Terminals on Few Faces : %G eng %U http://hdl.handle.net/21.11116/0000-0007-7796-A %R 10.1145/3371389 %7 2020 %D 2020 %J ACM Transactions on Algorithms %V 16 %N 3 %Z sequence number: 28 %I ACM %C New York, NY %@ false
[117]
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}, MARGINALMARK = {$\bullet$}, 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
[118]
P. Kleer, V. Patel, and F. Stroh, “Switch-Based Markov Chains for Sampling Hamiltonian Cycles in Dense Graphs,” The Electronic Journal of Combinatorics, vol. 27, no. 4, 2020.
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@article{Kleer_Patel2020, TITLE = {Switch-Based {Markov} Chains for Sampling {Hamiltonian} Cycles in Dense Graphs}, AUTHOR = {Kleer, Pieter and Patel, Viresh and Stroh, Fabian}, LANGUAGE = {eng}, ISSN = {1077-8926}, DOI = {10.37236/9503}, PUBLISHER = {N.J. Calkin and H.S. Wilf}, ADDRESS = {Atlanta, Ga.}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, JOURNAL = {The Electronic Journal of Combinatorics}, VOLUME = {27}, NUMBER = {4}, EID = {P4.29}, }
Endnote
%0 Journal Article %A Kleer, Pieter %A Patel, Viresh %A Stroh, Fabian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Switch-Based Markov Chains for Sampling Hamiltonian Cycles in Dense Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-914C-0 %R 10.37236/9503 %7 2020 %D 2020 %J The Electronic Journal of Combinatorics %V 27 %N 4 %Z sequence number: P4.29 %I N.J. Calkin and H.S. Wilf %C Atlanta, Ga. %@ false %U https://doi.org/10.37236/9503
[119]
P. Kleer and G. Schäfer, “Topological Price of Anarchy Bounds for Clustering Games on Networks,” 2020. [Online]. Available: https://arxiv.org/abs/2011.09717. (arXiv: 2011.09717)
Abstract
We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total utility generated in centralized outcomes and equilibrium outcomes in which players selfishly try to maximize their utility. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erd\H{o}s-R\'enyi random graphs (where every possible edge in the network is present with a fixed probability), which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds.
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@online{Kleer_arXiv2011.09717, TITLE = {Topological Price of Anarchy Bounds for Clustering Games on Networks}, AUTHOR = {Kleer, Pieter and Sch{\"a}fer, Guido}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2011.09717}, DOI = {10.1007/978-3-030-35389-6_18}, EPRINT = {2011.09717}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total utility generated in centralized outcomes and equilibrium outcomes in which players selfishly try to maximize their utility. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erd\H{o}s-R\'enyi random graphs (where every possible edge in the network is present with a fixed probability), which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds.}, }
Endnote
%0 Report %A Kleer, Pieter %A Sch&#228;fer, Guido %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Topological Price of Anarchy Bounds for Clustering Games on Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0007-915F-B %R 10.1007/978-3-030-35389-6_18 %U https://arxiv.org/abs/2011.09717 %D 2020 %X We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total utility generated in centralized outcomes and equilibrium outcomes in which players selfishly try to maximize their utility. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erd\H{o}s-R\'enyi random graphs (where every possible edge in the network is present with a fixed probability), which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds. %K Computer Science, Computer Science and Game Theory, cs.GT
[120]
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}, MARGINALMARK = {$\bullet$}, 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
[121]
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}, MARGINALMARK = {$\bullet$}, 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
[122]
C. Lenzen and B. Wiederhake, “Brief Announcement: TRIX: Low-Skew Pulse Propagation for Fault-Tolerant Hardware,” in Stabilization, Safety, and Security of Distributed Systems (SSS 2020), Austin, TX, USA (Virtual Event), 2020.
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@inproceedings{Lenzen_SSS2020, TITLE = {Brief Announcement: {TRIX}: {L}ow-Skew Pulse Propagation for Fault-Tolerant Hardware}, AUTHOR = {Lenzen, Christoph and Wiederhake, Ben}, LANGUAGE = {eng}, ISBN = {978-3-030-64347-8}, DOI = {10.1007/978-3-030-64348-5_23}, PUBLISHER = {Springer}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, BOOKTITLE = {Stabilization, Safety, and Security of Distributed Systems (SSS 2020)}, EDITOR = {Devismes, St{\'e}phane and Mittal, Neeraj}, PAGES = {295--300}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12514}, ADDRESS = {Austin, TX, USA (Virtual Event)}, }
Endnote
%0 Conference Proceedings %A Lenzen, Christoph %A Wiederhake, Ben %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Brief Announcement: TRIX: Low-Skew Pulse Propagation for Fault-Tolerant Hardware : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9058-3 %R 10.1007/978-3-030-64348-5_23 %D 2020 %B 22nd International Symposium on Stabilization, Safety, and Security of Distributed Systems %Z date of event: 2020-11-18 - 2020-11-21 %C Austin, TX, USA (Virtual Event) %B Stabilization, Safety, and Security of Distributed Systems %E Devismes, St&#233;phane; Mittal, Neeraj %P 295 - 300 %I Springer %@ 978-3-030-64347-8 %B Lecture Notes in Computer Science %N 12514
[123]
C. Lenzen and B. Wiederhake, “TRIX: Low-Skew Pulse Propagation for Fault-Tolerant Hardware,” 2020. [Online]. Available: https://arxiv.org/abs/2010.01415. (arXiv: 2010.01415)
Abstract
The vast majority of hardware architectures use a carefully timed reference signal to clock their computational logic. However, standard distribution solutions are not fault-tolerant. In this work, we present a simple grid structure as a more reliable clock propagation method and study it by means of simulation experiments. Fault-tolerance is achieved by forwarding clock pulses on arrival of the second of three incoming signals from the previous layer. A key question is how well neighboring grid nodes are synchronized, even without faults. Analyzing the clock skew under typical-case conditions is highly challenging. Because the forwarding mechanism involves taking the median, standard probabilistic tools fail, even when modeling link delays just by unbiased coin flips. Our statistical approach provides substantial evidence that this system performs surprisingly well. Specifically, in an "infinitely wide" grid of height~$H$, the delay at a pre-selected node exhibits a standard deviation of $O(H^{1/4})$ ($\approx 2.7$ link delay uncertainties for $H=2000$) and skew between adjacent nodes of $o(\log \log H)$ ($\approx 0.77$ link delay uncertainties for $H=2000$). We conclude that the proposed system is a very promising clock distribution method. This leads to the open problem of a stochastic explanation of the tight concentration of delays and skews. More generally, we believe that understanding our very simple abstraction of the system is of mathematical interest in its own right.
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@online{Lenzen_arXiv2010.01415, TITLE = {{TRIX}: {L}ow-Skew Pulse Propagation for Fault-Tolerant Hardware}, AUTHOR = {Lenzen, Christoph and Wiederhake, Ben}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2010.01415}, EPRINT = {2010.01415}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The vast majority of hardware architectures use a carefully timed reference signal to clock their computational logic. However, standard distribution solutions are not fault-tolerant. In this work, we present a simple grid structure as a more reliable clock propagation method and study it by means of simulation experiments. Fault-tolerance is achieved by forwarding clock pulses on arrival of the second of three incoming signals from the previous layer. A key question is how well neighboring grid nodes are synchronized, even without faults. Analyzing the clock skew under typical-case conditions is highly challenging. Because the forwarding mechanism involves taking the median, standard probabilistic tools fail, even when modeling link delays just by unbiased coin flips. Our statistical approach provides substantial evidence that this system performs surprisingly well. Specifically, in an "infinitely wide" grid of height~$H$, the delay at a pre-selected node exhibits a standard deviation of $O(H^{1/4})$ ($\approx 2.7$ link delay uncertainties for $H=2000$) and skew between adjacent nodes of $o(\log \log H)$ ($\approx 0.77$ link delay uncertainties for $H=2000$). We conclude that the proposed system is a very promising clock distribution method. This leads to the open problem of a stochastic explanation of the tight concentration of delays and skews. More generally, we believe that understanding our very simple abstraction of the system is of mathematical interest in its own right.}, }
Endnote
%0 Report %A Lenzen, Christoph %A Wiederhake, Ben %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T TRIX: Low-Skew Pulse Propagation for Fault-Tolerant Hardware : %G eng %U http://hdl.handle.net/21.11116/0000-0007-904F-E %U https://arxiv.org/abs/2010.01415 %D 2020 %X The vast majority of hardware architectures use a carefully timed reference signal to clock their computational logic. However, standard distribution solutions are not fault-tolerant. In this work, we present a simple grid structure as a more reliable clock propagation method and study it by means of simulation experiments. Fault-tolerance is achieved by forwarding clock pulses on arrival of the second of three incoming signals from the previous layer. A key question is how well neighboring grid nodes are synchronized, even without faults. Analyzing the clock skew under typical-case conditions is highly challenging. Because the forwarding mechanism involves taking the median, standard probabilistic tools fail, even when modeling link delays just by unbiased coin flips. Our statistical approach provides substantial evidence that this system performs surprisingly well. Specifically, in an "infinitely wide" grid of height~$H$, the delay at a pre-selected node exhibits a standard deviation of $O(H^{1/4})$ ($\approx 2.7$ link delay uncertainties for $H=2000$) and skew between adjacent nodes of $o(\log \log H)$ ($\approx 0.77$ link delay uncertainties for $H=2000$). We conclude that the proposed system is a very promising clock distribution method. This leads to the open problem of a stochastic explanation of the tight concentration of delays and skews. More generally, we believe that understanding our very simple abstraction of the system is of mathematical interest in its own right. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[124]
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}, MARGINALMARK = {$\bullet$}, 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
[125]
Y. Li and V. Nakos, “Sublinear-Time Algorithms for Compressive Phase Retrieval,” IEEE Transactions on Information Theory, vol. 66, no. 11, 2020.
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@article{Li_10.1109/TIT.2020.3020701, TITLE = {Sublinear-Time Algorithms for Compressive Phase Retrieval}, AUTHOR = {Li, Yi and Nakos, Vasileios}, LANGUAGE = {eng}, ISSN = {0018-9448}, DOI = {10.1109/TIT.2020.3020701}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, JOURNAL = {IEEE Transactions on Information Theory}, VOLUME = {66}, NUMBER = {11}, PAGES = {7302--7310}, }
Endnote
%0 Journal Article %A Li, Yi %A Nakos, Vasileios %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sublinear-Time Algorithms for Compressive Phase Retrieval : %G eng %U http://hdl.handle.net/21.11116/0000-0007-567C-E %R 10.1109/TIT.2020.3020701 %7 2020 %D 2020 %J IEEE Transactions on Information Theory %V 66 %N 11 %& 7302 %P 7302 - 7310 %I IEEE %C Piscataway, NJ %@ false
[126]
Y. Li and V. Nakos, “Deterministic Sparse Fourier Transform with an ℓ_{∞} Guarantee,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Li_ICALP2020, TITLE = {Deterministic Sparse {F}ourier Transform with an $\ell_{\infty}$ Guarantee}, AUTHOR = {Li, Yi and Nakos, Vasileios}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124844}, DOI = {10.4230/LIPIcs.ICALP.2020.77}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {77}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Li, Yi %A Nakos, Vasileios %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Deterministic Sparse Fourier Transform with an &#8467;_{&#8734;} Guarantee : %G eng %U http://hdl.handle.net/21.11116/0000-0007-56A6-D %R 10.4230/LIPIcs.ICALP.2020.77 %U urn:nbn:de:0030-drops-124844 %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: 77 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12484/
[127]
W. Lochet, D. Lokshtanov, P. Misra, S. Saurabh, R. Sharma, and M. Zehavi, “Fault Tolerant Subgraphs with Applications in Kernelization,” in 11th Innovations in Theoretical Computer Science Conference (ITCS 2020), Seattle, WA, USA, 2020.
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@inproceedings{DBLP:conf/innovations/LochetLM0SZ20, TITLE = {Fault Tolerant Subgraphs with Applications in Kernelization}, AUTHOR = {Lochet, William and Lokshtanov, Daniel and Misra, Pranabendu and Saurabh, Saket and Sharma, Roohani and Zehavi, Meirav}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-134-4}, URL = {urn:nbn:de:0030-drops-117326}, DOI = {10.4230/LIPIcs.ITCS.2020.47}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, EDITOR = {Vidick, Thomas}, EID = {47}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {151}, ADDRESS = {Seattle, WA, USA}, }
Endnote
%0 Conference Proceedings %A Lochet, William %A Lokshtanov, Daniel %A Misra, Pranabendu %A Saurabh, Saket %A Sharma, Roohani %A Zehavi, Meirav %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Fault Tolerant Subgraphs with Applications in Kernelization : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D2A8-E %R 10.4230/LIPIcs.ITCS.2020.47 %U urn:nbn:de:0030-drops-117326 %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: 47 %I Schloss Dagstuhl %@ 978-3-95977-134-4 %B Leibniz International Proceedings in Informatics %N 151 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/11732https://creativecommons.org/licenses/by/3.0/legalcode
[128]
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}, MARGINALMARK = {$\bullet$}, 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
[129]
D. Lokshtanov, P. Misra, F. Panolan, G. Philip, and S. Saurabh, “A (2 + ε)-Factor Approximation Algorithm for Split Vertex Deletion,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Lokshtanov_ICALP2020, TITLE = {A (2 + $\epsilon$)-Factor Approximation Algorithm for Split Vertex Deletion}, AUTHOR = {Lokshtanov, Daniel and Misra, Pranabendu and Panolan, Fahad and Philip, Geevarghese and Saurabh, Saket}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124879}, DOI = {10.4230/LIPIcs.ICALP.2020.80}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {80}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Lokshtanov, Daniel %A Misra, Pranabendu %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 %T A (2 + &#949;)-Factor Approximation Algorithm for Split Vertex Deletion : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8EF5-5 %R 10.4230/LIPIcs.ICALP.2020.80 %U urn:nbn:de:0030-drops-124879 %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: 80 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12487/https://creativecommons.org/licenses/by/3.0/legalcode
[130]
D. Lokshtanov, P. Misra, M. Pilipczuk, S. Saurabh, and M. Zehavi, “An Exponential Time Parameterized Algorithm for Planar Disjoint Paths,” in STOC ’20, 52nd Annual ACM SIGACT Symposium on Theory of Computing, Chicago, IL, USA, 2020.
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@inproceedings{DBLP:conf/stoc/LokshtanovMP0Z20, TITLE = {An Exponential Time Parameterized Algorithm for Planar Disjoint Paths}, AUTHOR = {Lokshtanov, Daniel and Misra, Pranabendu and Pilipczuk, Micha{\l} and Saurabh, Saket and Zehavi, Meirav}, LANGUAGE = {eng}, ISBN = {978-1-4503-6979-4}, DOI = {10.1145/3357713.3384250}, PUBLISHER = {ACM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '20, 52nd Annual ACM SIGACT Symposium on Theory of Computing}, EDITOR = {Makarychev, Konstantin and Makarychev, Yury and Tulsiani, Madhur and Kamath, Gautam and Chuzhoy, Julia}, PAGES = {1307--1316}, ADDRESS = {Chicago, IL, USA}, }
Endnote
%0 Conference Proceedings %A Lokshtanov, Daniel %A Misra, Pranabendu %A Pilipczuk, Micha&#322; %A Saurabh, Saket %A Zehavi, Meirav %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T An Exponential Time Parameterized Algorithm for Planar Disjoint Paths : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D2AA-C %R 10.1145/3357713.3384250 %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 1307 - 1316 %I ACM %@ 978-1-4503-6979-4
[131]
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}, MARGINALMARK = {$\bullet$}, 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
[132]
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{Marx_arXiv2004.11761, 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}, MARGINALMARK = {$\bullet$}, 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
[133]
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}, MARGINALMARK = {$\bullet$}, 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
[134]
P. Misra, F. Panolan, A. Rai, S. Saket, and R. Sharma, “Quick Separation in Chordal and Split Graphs,” in 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020), Prague, Czech Republic (Virtual Event), 2020.
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@inproceedings{Misra_MFCS20, TITLE = {Quick Separation in Chordal and Split Graphs}, AUTHOR = {Misra, Pranabendu and Panolan, Fahad and Rai, Ashutosh and Saket, Saurabh and Sharma, Roohani}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-159-7}, URL = {urn:nbn:de:0030-drops-127391}, DOI = {10.4230/LIPIcs.MFCS.2020.70}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)}, EDITOR = {Esparza, Javier and Kr{\a}l', Daniel}, EID = {70}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {170}, ADDRESS = {Prague, Czech Republic (Virtual Event)}, }
Endnote
%0 Conference Proceedings %A Misra, Pranabendu %A Panolan, Fahad %A Rai, Ashutosh %A Saket, Saurabh %A Sharma, Roohani %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Quick Separation in Chordal and Split Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9380-1 %R 10.4230/LIPIcs.MFCS.2020.70 %U urn:nbn:de:0030-drops-127391 %D 2020 %B 45th International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2020-08-25 - 2020-08-26 %C Prague, Czech Republic (Virtual Event) %B 45th International Symposium on Mathematical Foundations of Computer Science %E Esparza, Javier; Kr&#224;l', Daniel %Z sequence number: 70 %I Schloss Dagstuhl %@ 978-3-95977-159-7 %B Leibniz International Proceedings in Informatics %N 170 %@ false %U https://drops.dagstuhl.de/opus/frontdoor.php?source_opus=12739https://creativecommons.org/licenses/by/3.0/legalcode
[135]
V. Nakos, “Nearly Optimal Sparse Polynomial Multiplication,” IEEE Transactions on Information Theory, vol. 66, no. 11, 2020.
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@article{Nakos_10.1109/TIT.2020.2989385, TITLE = {Nearly Optimal Sparse Polynomial Multiplication}, AUTHOR = {Nakos, Vasileios}, LANGUAGE = {eng}, ISSN = {0018-9448}, DOI = {10.1109/TIT.2020.2989385}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, JOURNAL = {IEEE Transactions on Information Theory}, VOLUME = {66}, NUMBER = {11}, PAGES = {7231--7236}, }
Endnote
%0 Journal Article %A Nakos, Vasileios %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Nearly Optimal Sparse Polynomial Multiplication : %G eng %U http://hdl.handle.net/21.11116/0000-0007-567A-0 %R 10.1109/TIT.2020.2989385 %7 2020 %D 2020 %J IEEE Transactions on Information Theory %V 66 %N 11 %& 7231 %P 7231 - 7236 %I IEEE %C Piscataway, NJ %@ false
[136]
D. Neuen, “Hypergraph Isomorphism for Groups with Restricted Composition Factors,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Neuen_ICALP2020, TITLE = {Hypergraph Isomorphism for Groups with Restricted Composition Factors}, AUTHOR = {Neuen, Daniel}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124959}, DOI = {10.4230/LIPIcs.ICALP.2020.88}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {88}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Neuen, Daniel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Hypergraph Isomorphism for Groups with Restricted Composition Factors : %G eng %U http://hdl.handle.net/21.11116/0000-0007-6DCA-C %R 10.4230/LIPIcs.ICALP.2020.88 %U urn:nbn:de:0030-drops-124959 %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: 88 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12495/https://creativecommons.org/licenses/by/3.0/legalcode
[137]
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}, MARGINALMARK = {$\bullet$}, 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
[138]
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}, MARGINALMARK = {$\bullet$}, 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
[139]
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}, MARGINALMARK = {$\bullet$}, 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
[140]
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}, MARGINALMARK = {$\bullet$}, 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,
[141]
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}, MARGINALMARK = {$\bullet$}, 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
[142]
B. Ray Chaudhury, J. Garg, P. McGlaughlin, and R. Mehta, “Competitive Allocation of a Mixed Manna,” 2020. [Online]. Available: https://arxiv.org/abs/2008.02753. (arXiv: 2008.02753)
Abstract
We study the fair division problem of allocating a mixed manna under additively separable piecewise linear concave (SPLC) utilities. A mixed manna contains goods that everyone likes and bads that everyone dislikes, as well as items that some like and others dislike. The seminal work of Bogomolnaia et al. [Econometrica'17] argue why allocating a mixed manna is genuinely more complicated than a good or a bad manna, and why competitive equilibrium is the best mechanism. They also provide the existence of equilibrium and establish its peculiar properties (e.g., non-convex and disconnected set of equilibria even under linear utilities), but leave the problem of computing an equilibrium open. This problem remained unresolved even for only bad manna under linear utilities. Our main result is a simplex-like algorithm based on Lemke's scheme for computing a competitive allocation of a mixed manna under SPLC utilities, a strict generalization of linear. Experimental results on randomly generated instances suggest that our algorithm will be fast in practice. The problem is known to be PPAD-hard for the case of good manna, and we also show a similar result for the case of bad manna. Given these PPAD-hardness results, designing such an algorithm is the only non-brute-force (non-enumerative) option known, e.g., the classic Lemke-Howson algorithm (1964) for computing a Nash equilibrium in a 2-player game is still one of the most widely used algorithms in practice. Our algorithm also yields several new structural properties as simple corollaries. We obtain a (constructive) proof of existence for a far more general setting, membership of the problem in PPAD, rational-valued solution, and odd number of solutions property. The last property also settles the conjecture of Bogomolnaia et al. in the affirmative.
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@online{Chaudhury_arXiv2008.02753, TITLE = {Competitive Allocation of a Mixed Manna}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and McGlaughlin, Peter and Mehta, Ruta}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2008.02753}, EPRINT = {2008.02753}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the fair division problem of allocating a mixed manna under additively separable piecewise linear concave (SPLC) utilities. A mixed manna contains goods that everyone likes and bads that everyone dislikes, as well as items that some like and others dislike. The seminal work of Bogomolnaia et al. [Econometrica'17] argue why allocating a mixed manna is genuinely more complicated than a good or a bad manna, and why competitive equilibrium is the best mechanism. They also provide the existence of equilibrium and establish its peculiar properties (e.g., non-convex and disconnected set of equilibria even under linear utilities), but leave the problem of computing an equilibrium open. This problem remained unresolved even for only bad manna under linear utilities. Our main result is a simplex-like algorithm based on Lemke's scheme for computing a competitive allocation of a mixed manna under SPLC utilities, a strict generalization of linear. Experimental results on randomly generated instances suggest that our algorithm will be fast in practice. The problem is known to be PPAD-hard for the case of good manna, and we also show a similar result for the case of bad manna. Given these PPAD-hardness results, designing such an algorithm is the only non-brute-force (non-enumerative) option known, e.g., the classic Lemke-Howson algorithm (1964) for computing a Nash equilibrium in a 2-player game is still one of the most widely used algorithms in practice. Our algorithm also yields several new structural properties as simple corollaries. We obtain a (constructive) proof of existence for a far more general setting, membership of the problem in PPAD, rational-valued solution, and odd number of solutions property. The last property also settles the conjecture of Bogomolnaia et al. in the affirmative.}, }
Endnote
%0 Report %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A McGlaughlin, Peter %A Mehta, Ruta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Competitive Allocation of a Mixed Manna : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9361-5 %U https://arxiv.org/abs/2008.02753 %D 2020 %X We study the fair division problem of allocating a mixed manna under additively separable piecewise linear concave (SPLC) utilities. A mixed manna contains goods that everyone likes and bads that everyone dislikes, as well as items that some like and others dislike. The seminal work of Bogomolnaia et al. [Econometrica'17] argue why allocating a mixed manna is genuinely more complicated than a good or a bad manna, and why competitive equilibrium is the best mechanism. They also provide the existence of equilibrium and establish its peculiar properties (e.g., non-convex and disconnected set of equilibria even under linear utilities), but leave the problem of computing an equilibrium open. This problem remained unresolved even for only bad manna under linear utilities. Our main result is a simplex-like algorithm based on Lemke's scheme for computing a competitive allocation of a mixed manna under SPLC utilities, a strict generalization of linear. Experimental results on randomly generated instances suggest that our algorithm will be fast in practice. The problem is known to be PPAD-hard for the case of good manna, and we also show a similar result for the case of bad manna. Given these PPAD-hardness results, designing such an algorithm is the only non-brute-force (non-enumerative) option known, e.g., the classic Lemke-Howson algorithm (1964) for computing a Nash equilibrium in a 2-player game is still one of the most widely used algorithms in practice. Our algorithm also yields several new structural properties as simple corollaries. We obtain a (constructive) proof of existence for a far more general setting, membership of the problem in PPAD, rational-valued solution, and odd number of solutions property. The last property also settles the conjecture of Bogomolnaia et al. in the affirmative. %K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Computational Complexity, cs.CC,Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Multiagent Systems, cs.MA
[143]
B. Ray Chaudhury, J. Garg, and R. Mehta, “Fair and Efficient Allocations under Subadditive Valuations,” 2020. [Online]. Available: https://arxiv.org/abs/2005.06511. (arXiv: 2005.06511)
Abstract
We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of indivisible goods. Although the existence of EFX is not known beyond the simple case of two agents with subadditive valuations, some good approximations of EFX are known to exist, namely $\tfrac{1}{2}$-EFX allocation and EFX allocations with bounded charity. Nash welfare (the geometric mean of agents' valuations) is one of the most commonly used measures of efficiency. In case of additive valuations, an allocation that maximizes Nash welfare also satisfies fairness properties like Envy-Free up to one good (EF1). Although there is substantial work on approximating Nash welfare when agents have additive valuations, very little is known when agents have subadditive valuations. In this paper, we design a polynomial-time algorithm that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an $\mathcal{O}(n)$ approximation to the Nash welfare. Our result also improves the current best-known approximation of $\mathcal{O}(n \log n)$ and $\mathcal{O}(m)$ to Nash welfare when agents have submodular and subadditive valuations, respectively. Furthermore, our technique also gives an $\mathcal{O}(n)$ approximation to a family of welfare measures, $p$-mean of valuations for $p\in (-\infty, 1]$, thereby also matching asymptotically the current best known approximation ratio for special cases like $p =-\infty$ while also retaining the fairness properties.
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@online{Chaudhury_arXiv2005.06511, TITLE = {Fair and Efficient Allocations under Subadditive Valuations}, AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehta, Ruta}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2005.06511}, EPRINT = {2005.06511}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of indivisible goods. Although the existence of EFX is not known beyond the simple case of two agents with subadditive valuations, some good approximations of EFX are known to exist, namely $\tfrac{1}{2}$-EFX allocation and EFX allocations with bounded charity. Nash welfare (the geometric mean of agents' valuations) is one of the most commonly used measures of efficiency. In case of additive valuations, an allocation that maximizes Nash welfare also satisfies fairness properties like Envy-Free up to one good (EF1). Although there is substantial work on approximating Nash welfare when agents have additive valuations, very little is known when agents have subadditive valuations. In this paper, we design a polynomial-time algorithm that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an $\mathcal{O}(n)$ approximation to the Nash welfare. Our result also improves the current best-known approximation of $\mathcal{O}(n \log n)$ and $\mathcal{O}(m)$ to Nash welfare when agents have submodular and subadditive valuations, respectively. Furthermore, our technique also gives an $\mathcal{O}(n)$ approximation to a family of welfare measures, $p$-mean of valuations for $p\in (-\infty, 1]$, thereby also matching asymptotically the current best known approximation ratio for special cases like $p =-\infty$ while also retaining the fairness properties.}, }
Endnote
%0 Report %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A Mehta, Ruta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Fair and Efficient Allocations under Subadditive Valuations : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9369-D %U https://arxiv.org/abs/2005.06511 %D 2020 %X We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of indivisible goods. Although the existence of EFX is not known beyond the simple case of two agents with subadditive valuations, some good approximations of EFX are known to exist, namely $\tfrac{1}{2}$-EFX allocation and EFX allocations with bounded charity. Nash welfare (the geometric mean of agents' valuations) is one of the most commonly used measures of efficiency. In case of additive valuations, an allocation that maximizes Nash welfare also satisfies fairness properties like Envy-Free up to one good (EF1). Although there is substantial work on approximating Nash welfare when agents have additive valuations, very little is known when agents have subadditive valuations. In this paper, we design a polynomial-time algorithm that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an $\mathcal{O}(n)$ approximation to the Nash welfare. Our result also improves the current best-known approximation of $\mathcal{O}(n \log n)$ and $\mathcal{O}(m)$ to Nash welfare when agents have submodular and subadditive valuations, respectively. Furthermore, our technique also gives an $\mathcal{O}(n)$ approximation to a family of welfare measures, $p$-mean of valuations for $p\in (-\infty, 1]$, thereby also matching asymptotically the current best known approximation ratio for special cases like $p =-\infty$ while also retaining the fairness properties. %K Computer Science, Computer Science and Game Theory, cs.GT,
[144]
W. Rosenbaum and J. Suomela, “Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems,” 2020. [Online]. Available: https://arxiv.org/abs/1907.08160. (arXiv: 1907.08160)
Abstract
Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph at least up to distance $\Omega(\log n)$ in order to produce its output. We consider the complexity of such problems from the perspective of volume: how large a subgraph does a node need to see in order to produce its output. We study locally checkable graph problems on bounded-degree graphs. We give a number of constructions that exhibit tradeoffs between deterministic distance, randomized distance, deterministic volume, and randomized volume: - If the deterministic distance is linear, it is also known that randomized distance is near-linear. In contrast, we show that there are problems with linear deterministic volume but only logarithmic randomized volume. - We prove a volume hierarchy theorem for randomized complexity: among problems with linear deterministic volume complexity, there are infinitely many distinct randomized volume complexity classes between $\Omega(\log n)$ and $O(n)$. This hierarchy persists even when restricting to problems whose randomized and deterministic distance complexities are $\Theta(\log n)$. - Similar hierarchies exist for polynomial distance complexities: for any $k, \ell \in N$ with $k \leq \ell$, there are problems whose randomized and deterministic distance complexities are $\Theta(n^{1/\ell})$, randomized volume complexities are $\Theta(n^{1/k})$, and whose deterministic volume complexities are $\Theta(n)$. Additionally, we consider connections between our volume model and massively parallel computation (MPC). We give a general simulation argument that any volume-efficient algorithm can be transformed into a space-efficient MPC algorithm.
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@online{Rosenbaum_arXiv1907.08160, TITLE = {Seeing Far vs. Seeing Wide: {V}olume Complexity of Local Graph Problems}, AUTHOR = {Rosenbaum, Will and Suomela, Jukka}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/1907.08160}, EPRINT = {1907.08160}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph at least up to distance $\Omega(\log n)$ in order to produce its output. We consider the complexity of such problems from the perspective of volume: how large a subgraph does a node need to see in order to produce its output. We study locally checkable graph problems on bounded-degree graphs. We give a number of constructions that exhibit tradeoffs between deterministic distance, randomized distance, deterministic volume, and randomized volume: -- If the deterministic distance is linear, it is also known that randomized distance is near-linear. In contrast, we show that there are problems with linear deterministic volume but only logarithmic randomized volume. -- We prove a volume hierarchy theorem for randomized complexity: among problems with linear deterministic volume complexity, there are infinitely many distinct randomized volume complexity classes between $\Omega(\log n)$ and $O(n)$. This hierarchy persists even when restricting to problems whose randomized and deterministic distance complexities are $\Theta(\log n)$. -- Similar hierarchies exist for polynomial distance complexities: for any $k, \ell \in N$ with $k \leq \ell$, there are problems whose randomized and deterministic distance complexities are $\Theta(n^{1/\ell})$, randomized volume complexities are $\Theta(n^{1/k})$, and whose deterministic volume complexities are $\Theta(n)$. Additionally, we consider connections between our volume model and massively parallel computation (MPC). We give a general simulation argument that any volume-efficient algorithm can be transformed into a space-efficient MPC algorithm.}, }
Endnote
%0 Report %A Rosenbaum, Will %A Suomela, Jukka %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0007-98C0-4 %U https://arxiv.org/abs/1907.08160 %D 2020 %X Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph at least up to distance $\Omega(\log n)$ in order to produce its output. We consider the complexity of such problems from the perspective of volume: how large a subgraph does a node need to see in order to produce its output. We study locally checkable graph problems on bounded-degree graphs. We give a number of constructions that exhibit tradeoffs between deterministic distance, randomized distance, deterministic volume, and randomized volume: - If the deterministic distance is linear, it is also known that randomized distance is near-linear. In contrast, we show that there are problems with linear deterministic volume but only logarithmic randomized volume. - We prove a volume hierarchy theorem for randomized complexity: among problems with linear deterministic volume complexity, there are infinitely many distinct randomized volume complexity classes between $\Omega(\log n)$ and $O(n)$. This hierarchy persists even when restricting to problems whose randomized and deterministic distance complexities are $\Theta(\log n)$. - Similar hierarchies exist for polynomial distance complexities: for any $k, \ell \in N$ with $k \leq \ell$, there are problems whose randomized and deterministic distance complexities are $\Theta(n^{1/\ell})$, randomized volume complexities are $\Theta(n^{1/k})$, and whose deterministic volume complexities are $\Theta(n)$. Additionally, we consider connections between our volume model and massively parallel computation (MPC). We give a general simulation argument that any volume-efficient algorithm can be transformed into a space-efficient MPC algorithm. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[145]
W. Rosenbaum and J. Suomela, “Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems Share on,” in PODC ’20, 39th Symposium on Principles of Distributed Computing, Virtual Event, Italy, 2020.
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@inproceedings{Rosenbaum_PODC2020, TITLE = {Seeing Far vs. Seeing Wide: {V}olume Complexity of Local Graph Problems Share on}, AUTHOR = {Rosenbaum, Will and Suomela, Jukka}, LANGUAGE = {eng}, ISBN = {9781450375825{\textbraceright}}, DOI = {10.1145/3382734.3405721}, PUBLISHER = {ACM}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {PODC '20, 39th Symposium on Principles of Distributed Computing}, PAGES = {89--98}, ADDRESS = {Virtual Event, Italy}, }
Endnote
%0 Conference Proceedings %A Rosenbaum, Will %A Suomela, Jukka %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems Share on : %G eng %U http://hdl.handle.net/21.11116/0000-0007-9A54-D %R 10.1145/3382734.3405721 %D 2020 %B 39th Symposium on Principles of Distributed Computing %Z date of event: 2020-08-03 - 2020-08-07 %C Virtual Event, Italy %B PODC '20 %P 89 - 98 %I ACM %@ 9781450375825}
[146]
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}, MARGINALMARK = {$\bullet$}, 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
[147]
M. Roth, J. Schmitt, and P. Wellnitz, “Counting Small Induced Subgraphs Satisfying Monotone Properties,” 2020. [Online]. Available: https://arxiv.org/abs/2004.06595. (arXiv: 2004.06595)
Abstract
Given a graph property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ asks, on input a graph $G$ and a positive integer $k$, to compute the number of induced subgraphs of size $k$ in $G$ that satisfy $\Phi$. The search for explicit criteria on $\Phi$ ensuring that $\#\mathsf{IndSub}(\Phi)$ is hard was initiated by Jerrum and Meeks [J. Comput. Syst. Sci. 15] and is part of the major line of research on counting small patterns in graphs. However, apart from an implicit result due to Curticapean, Dell and Marx [STOC 17] proving that a full classification into "easy" and "hard" properties is possible and some partial results on edge-monotone properties due to Meeks [Discret. Appl. Math. 16] and D\"orfler et al. [MFCS 19], not much is known. In this work, we fully answer and explicitly classify the case of monotone, that is subgraph-closed, properties: We show that for any non-trivial monotone property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ cannot be solved in time $f(k)\cdot |V(G)|^{o(k/ {\log^{1/2}(k)})}$ for any function $f$, unless the Exponential Time Hypothesis fails. By this, we establish that any significant improvement over the brute-force approach is unlikely; in the language of parameterized complexity, we also obtain a $\#\mathsf{W}[1]$-completeness result.
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@online{Roth_arXiv2004.06595, TITLE = {Counting Small Induced Subgraphs Satisfying Monotone Properties}, AUTHOR = {Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2004.06595}, EPRINT = {2004.06595}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Given a graph property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ asks, on input a graph $G$ and a positive integer $k$, to compute the number of induced subgraphs of size $k$ in $G$ that satisfy $\Phi$. The search for explicit criteria on $\Phi$ ensuring that $\#\mathsf{IndSub}(\Phi)$ is hard was initiated by Jerrum and Meeks [J. Comput. Syst. Sci. 15] and is part of the major line of research on counting small patterns in graphs. However, apart from an implicit result due to Curticapean, Dell and Marx [STOC 17] proving that a full classification into "easy" and "hard" properties is possible and some partial results on edge-monotone properties due to Meeks [Discret. Appl. Math. 16] and D\"orfler et al. [MFCS 19], not much is known. In this work, we fully answer and explicitly classify the case of monotone, that is subgraph-closed, properties: We show that for any non-trivial monotone property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ cannot be solved in time $f(k)\cdot |V(G)|^{o(k/ {\log^{1/2}(k)})}$ for any function $f$, unless the Exponential Time Hypothesis fails. By this, we establish that any significant improvement over the brute-force approach is unlikely; in the language of parameterized complexity, we also obtain a $\#\mathsf{W}[1]$-completeness result.}, }
Endnote
%0 Report %A Roth, Marc %A Schmitt, Johannes %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Small Induced Subgraphs Satisfying Monotone Properties : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8C60-F %U https://arxiv.org/abs/2004.06595 %D 2020 %X Given a graph property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ asks, on input a graph $G$ and a positive integer $k$, to compute the number of induced subgraphs of size $k$ in $G$ that satisfy $\Phi$. The search for explicit criteria on $\Phi$ ensuring that $\#\mathsf{IndSub}(\Phi)$ is hard was initiated by Jerrum and Meeks [J. Comput. Syst. Sci. 15] and is part of the major line of research on counting small patterns in graphs. However, apart from an implicit result due to Curticapean, Dell and Marx [STOC 17] proving that a full classification into "easy" and "hard" properties is possible and some partial results on edge-monotone properties due to Meeks [Discret. Appl. Math. 16] and D\"orfler et al. [MFCS 19], not much is known. In this work, we fully answer and explicitly classify the case of monotone, that is subgraph-closed, properties: We show that for any non-trivial monotone property $\Phi$, the problem $\#\mathsf{IndSub}(\Phi)$ cannot be solved in time $f(k)\cdot |V(G)|^{o(k/ {\log^{1/2}(k)})}$ for any function $f$, unless the Exponential Time Hypothesis fails. By this, we establish that any significant improvement over the brute-force approach is unlikely; in the language of parameterized complexity, we also obtain a $\#\mathsf{W}[1]$-completeness result. %K Computer Science, Computational Complexity, cs.CC
[148]
M. Roth, J. Schmitt, and P. Wellnitz, “Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders,” 2020. [Online]. Available: https://arxiv.org/abs/2011.03433. (arXiv: 2011.03433)
Abstract
Given a graph property $\Phi$, we consider the problem $\mathtt{EdgeSub}(\Phi)$, where the input is a pair of a graph $G$ and a positive integer $k$, and the task is to decide whether $G$ contains a $k$-edge subgraph that satisfies $\Phi$. Specifically, we study the parameterized complexity of $\mathtt{EdgeSub}(\Phi)$ and of its counting problem $\#\mathtt{EdgeSub}(\Phi)$ with respect to both approximate and exact counting. We obtain a complete picture for minor-closed properties $\Phi$: the decision problem $\mathtt{EdgeSub}(\Phi)$ always admits an FPT algorithm and the counting problem $\#\mathtt{EdgeSub}(\Phi)$ always admits an FPTRAS. For exact counting, we present an exhaustive and explicit criterion on the property $\Phi$ which, if satisfied, yields fixed-parameter tractability and otherwise $\#\mathsf{W[1]}$-hardness. Additionally, most of our hardness results come with an almost tight conditional lower bound under the so-called Exponential Time Hypothesis, ruling out algorithms for $\#\mathtt{EdgeSub}(\Phi)$ that run in time $f(k)\cdot|G|^{o(k/\log k)}$ for any computable function $f$. As a main technical result, we gain a complete understanding of the coefficients of toroidal grids and selected Cayley graph expanders in the homomorphism basis of $\#\mathtt{EdgeSub}(\Phi)$. This allows us to establish hardness of exact counting using the Complexity Monotonicity framework due to Curticapean, Dell and Marx (STOC'17). Our methods can also be applied to a parameterized variant of the Tutte Polynomial $T^k_G$ of a graph $G$, to which many known combinatorial interpretations of values of the (classical) Tutte Polynomial can be extended. As an example, $T^k_G(2,1)$ corresponds to the number of $k$-forests in the graph $G$. Our techniques allow us to completely understand the parametrized complexity of computing the evaluation of $T^k_G$ at every pair of rational coordinates $(x,y)$.
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@online{Roth_arXiv2011.03433, TITLE = {Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders}, AUTHOR = {Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2011.03433}, EPRINT = {2011.03433}, EPRINTTYPE = {arXiv}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Given a graph property $\Phi$, we consider the problem $\mathtt{EdgeSub}(\Phi)$, where the input is a pair of a graph $G$ and a positive integer $k$, and the task is to decide whether $G$ contains a $k$-edge subgraph that satisfies $\Phi$. Specifically, we study the parameterized complexity of $\mathtt{EdgeSub}(\Phi)$ and of its counting problem $\#\mathtt{EdgeSub}(\Phi)$ with respect to both approximate and exact counting. We obtain a complete picture for minor-closed properties $\Phi$: the decision problem $\mathtt{EdgeSub}(\Phi)$ always admits an FPT algorithm and the counting problem $\#\mathtt{EdgeSub}(\Phi)$ always admits an FPTRAS. For exact counting, we present an exhaustive and explicit criterion on the property $\Phi$ which, if satisfied, yields fixed-parameter tractability and otherwise $\#\mathsf{W[1]}$-hardness. Additionally, most of our hardness results come with an almost tight conditional lower bound under the so-called Exponential Time Hypothesis, ruling out algorithms for $\#\mathtt{EdgeSub}(\Phi)$ that run in time $f(k)\cdot|G|^{o(k/\log k)}$ for any computable function $f$. As a main technical result, we gain a complete understanding of the coefficients of toroidal grids and selected Cayley graph expanders in the homomorphism basis of $\#\mathtt{EdgeSub}(\Phi)$. This allows us to establish hardness of exact counting using the Complexity Monotonicity framework due to Curticapean, Dell and Marx (STOC'17). Our methods can also be applied to a parameterized variant of the Tutte Polynomial $T^k_G$ of a graph $G$, to which many known combinatorial interpretations of values of the (classical) Tutte Polynomial can be extended. As an example, $T^k_G(2,1)$ corresponds to the number of $k$-forests in the graph $G$. Our techniques allow us to completely understand the parametrized complexity of computing the evaluation of $T^k_G$ at every pair of rational coordinates $(x,y)$.}, }
Endnote
%0 Report %A Roth, Marc %A Schmitt, Johannes %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8CA1-5 %U https://arxiv.org/abs/2011.03433 %D 2020 %X Given a graph property $\Phi$, we consider the problem $\mathtt{EdgeSub}(\Phi)$, where the input is a pair of a graph $G$ and a positive integer $k$, and the task is to decide whether $G$ contains a $k$-edge subgraph that satisfies $\Phi$. Specifically, we study the parameterized complexity of $\mathtt{EdgeSub}(\Phi)$ and of its counting problem $\#\mathtt{EdgeSub}(\Phi)$ with respect to both approximate and exact counting. We obtain a complete picture for minor-closed properties $\Phi$: the decision problem $\mathtt{EdgeSub}(\Phi)$ always admits an FPT algorithm and the counting problem $\#\mathtt{EdgeSub}(\Phi)$ always admits an FPTRAS. For exact counting, we present an exhaustive and explicit criterion on the property $\Phi$ which, if satisfied, yields fixed-parameter tractability and otherwise $\#\mathsf{W[1]}$-hardness. Additionally, most of our hardness results come with an almost tight conditional lower bound under the so-called Exponential Time Hypothesis, ruling out algorithms for $\#\mathtt{EdgeSub}(\Phi)$ that run in time $f(k)\cdot|G|^{o(k/\log k)}$ for any computable function $f$. As a main technical result, we gain a complete understanding of the coefficients of toroidal grids and selected Cayley graph expanders in the homomorphism basis of $\#\mathtt{EdgeSub}(\Phi)$. This allows us to establish hardness of exact counting using the Complexity Monotonicity framework due to Curticapean, Dell and Marx (STOC'17). Our methods can also be applied to a parameterized variant of the Tutte Polynomial $T^k_G$ of a graph $G$, to which many known combinatorial interpretations of values of the (classical) Tutte Polynomial can be extended. As an example, $T^k_G(2,1)$ corresponds to the number of $k$-forests in the graph $G$. Our techniques allow us to completely understand the parametrized complexity of computing the evaluation of $T^k_G$ at every pair of rational coordinates $(x,y)$. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[149]
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), Tórshavn, 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}, MARGINALMARK = {$\bullet$}, 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 = {T{\'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 T&#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/
[150]
S. Saurabh and P. Tale, “On the Parameterized Complexity of Maximum Degree Contraction Problem,” in 15th International Symposium on Parameterized and Exact Computation (IPEC 2020), Hong Kong, China (Virtual Conference), 2020.
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@inproceedings{saurabh_et_al:LIPIcs:2020:13329, TITLE = {On the Parameterized Complexity of Maximum Degree Contraction Problem}, AUTHOR = {Saurabh, Saket and Tale, Prafullkumar}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-172-6}, URL = {urn:nbn:de:0030-drops-133297}, DOI = {10.4230/LIPIcs.IPEC.2020.26}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {15th International Symposium on Parameterized and Exact Computation (IPEC 2020)}, EDITOR = {Cao, Yixin and Pilipczuk, Marcin}, EID = {26}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {180}, ADDRESS = {Hong Kong, China (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Saurabh, Saket %A Tale, Prafullkumar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Parameterized Complexity of Maximum Degree Contraction Problem : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D6AB-7 %R 10.4230/LIPIcs.IPEC.2020.26 %U urn:nbn:de:0030-drops-133297 %D 2020 %B 15th International Symposium on Parameterized and Exact Computation %Z date of event: 2020-12-14 - 2020-12-18 %C Hong Kong, China (Virtual Conference) %B 15th International Symposium on Parameterized and Exact Computation %E Cao, Yixin; Pilipczuk, Marcin %Z sequence number: 26 %I Schloss Dagstuhl %@ 978-3-95977-172-6 %B Leibniz International Proceedings in Informatics %N 180 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/13329/https://creativecommons.org/licenses/by/3.0/legalcode
[151]
P. Schepper, “Fine-Grained Complexity of Regular Expression Pattern Matching and Membership,” in 28th Annual European Symposium on Algorithms (ESA 2020), Pisa, Italy (Virtual Conference), 2020.
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@inproceedings{Schepper_ESA2020, TITLE = {Fine-Grained Complexity of Regular Expression Pattern Matching and Membership}, AUTHOR = {Schepper, Philipp}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-162-7}, URL = {urn:nbn:de:0030-drops-129464}, DOI = {10.4230/LIPIcs.ESA.2020.80}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {28th Annual European Symposium on Algorithms (ESA 2020)}, EDITOR = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, EID = {80}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {173}, ADDRESS = {Pisa, Italy (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Schepper, Philipp %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity of Regular Expression Pattern Matching and Membership : %G eng %U http://hdl.handle.net/21.11116/0000-0007-DBC1-8 %R 10.4230/LIPIcs.ESA.2020.80 %U urn:nbn:de:0030-drops-129464 %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: 80 %I Schloss Dagstuhl %@ 978-3-95977-162-7 %B Leibniz International Proceedings in Informatics %N 173 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12946/https://creativecommons.org/licenses/by/3.0/legalcode
[152]
D. Vaz, “Approximation Algorithms for Network Design and Cut Problems in Bounded-Treewidth,” Universität des Saarlandes, Saarbrücken, 2020.
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@phdthesis{Vaz_2020, TITLE = {Approximation Algorithms for Network Design and Cut Problems in Bounded-Treewidth}, AUTHOR = {Vaz, Daniel}, LANGUAGE = {eng}, DOI = {10.22028/D291-32983}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2020}, MARGINALMARK = {$\bullet$}, DATE = {2020}, }
Endnote
%0 Thesis %A Vaz, Daniel %Y Mehlhorn, Kurt %A referee: Chalermsook, Parinya %A referee: Krauthgamer, Robert %+ 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 External Organizations %T Approximation Algorithms for Network Design and Cut Problems in Bounded-Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D8D7-3 %R 10.22028/D291-32983 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2020 %P 175 p. %V phd %9 phd %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/30394
2019
[153]
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
[154]
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
[155]
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
[156]
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
[157]
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 {R}omeo 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
[158]
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{Ahn2019b, 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
[159]
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
[160]
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
[161]
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
[162]
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
[163]
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
[164]
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
[165]
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{Antoniadis2019b, 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
[166]
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
[167]
A. Antoniadis, F. Biermeier, A. Cristi, C. Damerius, R. Hoeksma, D. Kaaser, P. Kling, and L. 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, Lukas}, 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, Lukas %+ 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
[168]
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
[169]
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
[170]
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
[171]
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
[172]
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
[173]
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
[174]
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
[175]
R. Becker, Y. Emek, M. Ghaffari, and C. Lenzen, “Distributed Algorithms for Low Stretch Spanning Trees,” in 33rd International Symposium on 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 Symposium on 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 Symposium on Distributed Computing %Z date of event: 2019-10-14 - 2019-10-18 %C Budapest, Hungary %B 33rd International Symposium on 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
[176]
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
[177]
B. A. Berendsohn, L. Kozma, and D. Marx, “Finding and Counting Permutations via CSPs,” in 14th International Symposium on Parameterized and Exact Computation (IPEC 2019), Munich, Germany, 2019.
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@inproceedings{berendsohn_et_al:LIPIcs:2019:11462, TITLE = {Finding and Counting Permutations via {CSPs}}, AUTHOR = {Berendsohn, Benjamin Aram and Kozma, L{\'a}szl{\'o} and Marx, D{\'a}niel}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-129-0}, URL = {urn:nbn:de:0030-drops-114627}, DOI = {10.4230/LIPIcs.IPEC.2019.1}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {14th International Symposium on Parameterized and Exact Computation (IPEC 2019)}, EDITOR = {Jansen, Bart M. P. and Telle, Jan Arne}, PAGES = {1--16}, EID = {1}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {148}, ADDRESS = {Munich, Germany}, }
Endnote
%0 Conference Proceedings %A Berendsohn, Benjamin Aram %A Kozma, L&#225;szl&#243; %A Marx, D&#225;niel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Finding and Counting Permutations via CSPs : %G eng %U http://hdl.handle.net/21.11116/0000-0007-D297-1 %R 10.4230/LIPIcs.IPEC.2019.1 %U urn:nbn:de:0030-drops-114627 %D 2019 %B 14th International Symposium on Parameterized and Exact Computation %Z date of event: 2019-09-11 - 2019-09-13 %C Munich, Germany %B 14th International Symposium on Parameterized and Exact Computation %E Jansen, Bart M. P.; Telle, Jan Arne %P 1 - 16 %Z sequence number: 1 %I Schloss Dagstuhl %@ 978-3-95977-129-0 %B Leibniz International Proceedings in Informatics %N 148 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2019/11462/https://creativecommons.org/licenses/by/3.0/legalcode
[178]
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
[179]
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
[180]
D. Bilò, L. Gualà, S. Leucci, and G. Proietti, “Tracking Routes in Communication Networks,” in Structural Information and Communication Complexity (SIROCCO 2019), L’Aquila, Italy, 2019.
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@inproceedings{Bilo_SIROCCO2019, TITLE = {Tracking Routes in Communication Networks}, AUTHOR = {Bil{\o}, Davide and Gual{\`a}, Luciano and Leucci, Stefano and Proietti, Guido}, LANGUAGE = {eng}, ISBN = {978-3-030-24921-2; 978-3-030-24922-9}, DOI = {10.1007/978-3-030-24922-9_6}, PUBLISHER = {Springer}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Structural Information and Communication Complexity (SIROCCO 2019)}, EDITOR = {Censor-Hillel, Keren and Flammini, Michele}, PAGES = {81--93}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {11639}, ADDRESS = {L{\textquoteright}Aquila, Italy}, }
Endnote
%0 Conference Proceedings %A Bil&#242;, Davide %A Gual&#224;, Luciano %A Leucci, Stefano %A Proietti, Guido %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Tracking Routes in Communication Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0007-DBB8-3 %R 10.1007/978-3-030-24922-9_6 %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 81 - 93 %I Springer %@ 978-3-030-24921-2 978-3-030-24922-9 %B Lecture Notes in Computer Science %N 11639
[181]
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
[182]
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
[183]
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
[184]
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
[185]
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
[186]
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
[187]
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
[188]
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
[189]
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
[190]
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
[191]
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
[192]
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
[193]
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
[194]
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
[195]
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
[196]
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
[197]
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
[198]
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
[199]
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
[200]
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
[201]
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
[202]
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
[203]
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/
[204]
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
[205]
L. Chen, F. Eberle, N. Megow, K. Schewior, and C. Stein, “A General Framework for Handling Commitment in Online Throughput Maximization,” in Integer Programming and Combinatorial Optimization (IPCO 2019), Ann Arbor, MI, USA, 2019.
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@inproceedings{SchewiorIPCO2019, TITLE = {A General Framework for Handling Commitment in Online Throughput Maximization}, AUTHOR = {Chen, Lin and Eberle, Franziska and Megow, Nicole and Schewior, Kevin and Stein, Clifford}, LANGUAGE = {eng}, ISBN = {978-3-030-17952-6}, DOI = {10.1007/978-3-030-17953-3_11}, PUBLISHER = {Springer}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, BOOKTITLE = {Integer Programming and Combinatorial Optimization (IPCO 2019)}, EDITOR = {Lodi, Andrea and Nagarajan, Viswanath}, PAGES = {141--154}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {11480}, 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 Throughput Maximization : %G eng %U http://hdl.handle.net/21.11116/0000-0002-F4CC-5 %R 10.1007/978-3-030-17953-3_11 %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 %E Lodi, Andrea; Nagarajan, Viswanath %P 141 - 154 %I Springer %@ 978-3-030-17952-6 %B Lecture Notes in Computer Science %N 11480
[206]
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
[207]
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
[208]
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}, }
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%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
[209]
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}, }
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%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
[210]
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
[211]
A. Choudhary and A. Ghosh, “Delaunay Simplices in Diagonally Distorted Lattices,” Computational Geometry: Theory and Applications, vol. 81, 2019.
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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}, MARGINALMARK = {$\bullet$}, DATE = {2019}, JOURNAL = {Computational Geometry: Theory and Applications}, VOLUME = {81}, PAGES = {33--44}, }
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 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 81 %& 33 %P 33 - 44 %I Elsevier %C Amsterdam %@ false
[212]
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}, }
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%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
[213]
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
[214]
C. Coupette, Juristische Netzwerkforschung : Modellierung, Quantifizierung und Visualisierung relationaler Daten im Recht. Tübingen: Mohr Siebeck, 2019.
Abstract
Netzwerke sind überall. Juristen nutzen sie auf dem Weg zur Arbeit (Infrastrukturnetzwerke), für die Suche nach Rat (Kontaktnetzwerke) und bei der juristischen Recherche (Informationsnetzwerke). Sie konstruieren sie (Zitiernetzwerke), beaufsichtigen sie (Finanznetzwerke) und bekämpfen sie (Verbrechensnetzwerke). Aus dieser Perspektive gibt es nichts, das sich nicht als Netzwerk modellieren lässt: als eine Menge von Einheiten, kombiniert mit einer Menge von Beziehungen zwischen diesen Einheiten. Corinna Coupette untersucht, wie juristische Phänomene als Netzwerke repräsentiert werden können, und ergründet, was man durch die quantitative und visuelle Analyse dieser Netzwerke für das Recht lernen kann. Dabei führt sie die juristische Netzwerkforschung in den deutschen juristischen Diskurs ein. Auf Basis eines eigens zusammengestellten Datensatzes von Entscheidungen des Bundesverfassungsgerichts entwickelt sie Werkzeuge zur Modellierung, Quantifizierung und Visualisierung des Rechts. Zur Arbeit gehört ein Online-Appendix, der unter folgender DOI abrufbar ist: https://doi.org/10.1628/978-3-16-157012-4-appendix
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@book{Coupette_Juristische2019, TITLE = {{Juristische Netzwerkforschung : Modellierung, Quantifizierung und Visualisierung relationaler Daten im Recht}}, AUTHOR = {Coupette, Corinna}, LANGUAGE = {deu}, ISBN = {978-3-16-157011-7}, DOI = {10.1628/978-3-16-157012-4}, PUBLISHER = {Mohr Siebeck}, ADDRESS = {T{\"u}bingen}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, DATE = {2019}, ABSTRACT = {Netzwerke sind {\"u}berall. Juristen nutzen sie auf dem Weg zur Arbeit (Infrastrukturnetzwerke), f{\"u}r die Suche nach Rat (Kontaktnetzwerke) und bei der juristischen Recherche (Informationsnetzwerke). Sie konstruieren sie (Zitiernetzwerke), beaufsichtigen sie (Finanznetzwerke) und bek{\"a}mpfen sie (Verbrechensnetzwerke). Aus dieser Perspektive gibt es nichts, das sich nicht als Netzwerk modellieren l{\"a}sst: als eine Menge von Einheiten, kombiniert mit einer Menge von Beziehungen zwischen diesen Einheiten. Corinna Coupette untersucht, wie juristische Ph{\"a}nomene als Netzwerke repr{\"a}sentiert werden k{\"o}nnen, und ergr{\"u}ndet, was man durch die quantitative und visuelle Analyse dieser Netzwerke f{\"u}r das Recht lernen kann. Dabei f{\"u}hrt sie die juristische Netzwerkforschung in den deutschen juristischen Diskurs ein. Auf Basis eines eigens zusammengestellten Datensatzes von Entscheidungen des Bundesverfassungsgerichts entwickelt sie Werkzeuge zur Modellierung, Quantifizierung und Visualisierung des Rechts. Zur Arbeit geh{\"o}rt ein Online-Appendix, der unter folgender DOI abrufbar ist: https://doi.org/10.1628/978-3-16-157012-4-appendix}, ABSTRACT = {Legal network science explores how legal phenomena can be represented as networks and investigates what can be gained from their quantification and visualization. Corinna Coupette introduces legal network science to the German legal discourse. Based on an original dataset of decisions by Germany's Federal Constitutional Court, she develops tools for modeling, measuring, and mapping the law.}, PAGES = {XVIII, 376 p.}, }
Endnote
%0 Book %A Coupette, Corinna %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Juristische Netzwerkforschung : Modellierung, Quantifizierung und Visualisierung relationaler Daten im Recht : %G deu %U http://hdl.handle.net/21.11116/0000-0005-613C-B %@ 978-3-16-157011-7 %R 10.1628/978-3-16-157012-4 %I Mohr Siebeck %C T&#252;bingen %D 2019 %P XVIII, 376 p. %X Netzwerke sind &#252;berall. Juristen nutzen sie auf dem Weg zur Arbeit (Infrastrukturnetzwerke), f&#252;r die Suche nach Rat (Kontaktnetzwerke) und bei der juristischen Recherche (Informationsnetzwerke). Sie konstruieren sie (Zitiernetzwerke), beaufsichtigen sie (Finanznetzwerke) und bek&#228;mpfen sie (Verbrechensnetzwerke). Aus dieser Perspektive gibt es nichts, das sich nicht als Netzwerk modellieren l&#228;sst: als eine Menge von Einheiten, kombiniert mit einer Menge von Beziehungen zwischen diesen Einheiten. Corinna Coupette untersucht, wie juristische Ph&#228;nomene als Netzwerke repr&#228;sentiert werden k&#246;nnen, und ergr&#252;ndet, was man durch die quantitative und visuelle Analyse dieser Netzwerke f&#252;r das Recht lernen kann. Dabei f&#252;hrt sie die juristische Netzwerkforschung in den deutschen juristischen Diskurs ein. Auf Basis eines eigens zusammengestellten Datensatzes von Entscheidungen des Bundesverfassungsgerichts entwickelt sie Werkzeuge zur Modellierung, Quantifizierung und Visualisierung des Rechts. Zur Arbeit geh&#246;rt ein Online-Appendix, der unter folgender DOI abrufbar ist: https://doi.org/10.1628/978-3-16-157012-4-appendix Legal network science explores how legal phenomena can be represented as networks and investigates what can be gained from their quantification and visualization. Corinna Coupette introduces legal network science to the German legal discourse. Based on an original dataset of decisions by Germany's Federal Constitutional Court, she develops tools for modeling, measuring, and mapping the law. %U https://zenodo.org/record/2617115
[215]
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
[216]
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
[217]
M. de Berg, S. Kisfaludi-Bak, and M. Mehr, “On One-Round Discrete Voronoi Games,” in 30th International Symposium on Algorithms and Computation (ISAAC 2019), Shanghai, China, 2019.
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@inproceedings{BergKM19, TITLE = {On One-Round Discrete {Voronoi} Games}, AUTHOR = {de Berg, Mark and Kisfaludi-Bak, S{\'a}ndor and Mehr, Mehran}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-130-6}, URL = {urn:nbn:de:0030-drops-115339}, DOI = {10.4230/LIPIcs.ISAAC.2019.37}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, EDITOR = {Lu, Pinyan and Zhang, Guochuan}, PAGES = {1--17}, EID = {37}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {149}, ADDRESS = {Shanghai, China}, }
Endnote
%0 Conference Proceedings %A de Berg, Mark %A Kisfaludi-Bak, S&#225;ndor %A Mehr, Mehran %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On One-Round Discrete Voronoi Games : %G eng %U http://hdl.handle.net/21.11116/0000-0007-778D-5 %R 10.4230/LIPIcs.ISAAC.2019.37 %U urn:nbn:de:0030-drops-115339 %D 2019 %B 30th International Symposium on Algorithms and Computation %Z date of event: 2019-12-08 - 2019-12-11 %C Shanghai, China %B 30th International Symposium on Algorithms and Computation %E Lu, Pinyan; Zhang, Guochuan %P 1 - 17 %Z sequence number: 37 %I Schloss Dagstuhl %@ 978-3-95977-130-6 %B Leibniz International Proceedings in Informatics %N 149 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2019/11533/https://creativecommons.org/licenses/by/3.0/legalcode
[218]
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
[219]
I. Diakonikolas, T. Gouleakis, and C. Tzamos, “Distribution-Independent PAC Learning of Halfspaces with Massart Noise,” in Advances in Neural Information Processing Systems 32 (NeurIPS 2019), Vancouver, Canada, 2019.
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@inproceedings{Diakonikolas_NeurIPs2019, TITLE = {Distribution-Independent {PAC} Learning of Halfspaces with {Massart} Noise}, AUTHOR = {Diakonikolas, Ilias and Gouleakis, Themis and Tzamos, Christos}, LANGUAGE = {eng}, URL = {https://proceedings.neurips.cc/paper/2019/file/358aee4cc897452c00244351e4d91f69-Paper.pdf}, PUBLISHER = {Curran Associates, Inc.}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 32 (NeurIPS 2019)}, EDITOR = {Wallach, H. and Larochelle, H. and Beygelzimer, A. and d'Alch{\'e}-Buc, F. and Fox, E. and Garnett, R.}, PAGES = {4749--4760}, ADDRESS = {Vancouver, Canada}, }
Endnote
%0 Conference Proceedings %A Diakonikolas, Ilias %A Gouleakis, Themis %A Tzamos, Christos %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Distribution-Independent PAC Learning of Halfspaces with Massart Noise : %G eng %U http://hdl.handle.net/21.11116/0000-0007-8B82-9 %U https://proceedings.neurips.cc/paper/2019/file/358aee4cc897452c00244351e4d91f69-Paper.pdf %D 2019 %B 33rd Conference on Neural Information Processing Systems %Z date of event: 2019-12-08 - 2019-12-14 %C Vancouver, Canada %B Advances in Neural Information Processing Systems 32 %E Wallach, H.; Larochelle, H.; Beygelzimer, A.; d'Alch&#233;-Buc, F.; Fox, E.; Garnett, R. %P 4749 - 4760 %I Curran Associates, Inc.
[220]
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
[221]
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,
[222]
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
[223]
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
[224]
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
[225]
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}, }
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%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
[226]
S. Funke, T. Rupp, A. Nusser, and S. Storandt, “PATHFINDER: Storage and Indexing of Massive Trajectory Sets,” in SSTD ’19, 16th International Symposium on Spatial 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 on Spatial 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}, }
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%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 on Spatial 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
[227]
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}, }
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%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
[228]
B. Geissmann, S. Leucci, C.-H. Liu, P. Penna, and G. Proietti, “Dual-Mode Greedy Algorithms Can Save Energy,” in 30th International Symposium on Algorithms and Computation (ISAAC 2019), Shanghai, China, 2019.
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@inproceedings{Geissmann_ISAAC19, TITLE = {Dual-Mode Greedy Algorithms Can Save Energy}, AUTHOR = {Geissmann, Barbara and Leucci, Stefano and Liu, Chih-Hung and Penna, Paolo and Proietti, Guido}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-130-6}, URL = {urn:nbn:de:0030-drops-115604}, DOI = {10.4230/LIPIcs.ISAAC.2019.64}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2019}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, EDITOR = {Lu, Pinyan and Zhang, Guochuan}, EID = {64}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {149}, ADDRESS = {Shanghai, China}, }
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%0 Conference Proceedings %A Geissmann, Barbara %A Leucci, Stefano %A Liu, Chih-Hung %A Penna, Paolo %A Proietti, Guido %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Dual-Mode Greedy Algorithms Can Save Energy : %G eng %U http://hdl.handle.net/21.11116/0000-0007-DBBA-1 %R 10.4230/LIPIcs.ISAAC.2019.64 %U urn:nbn:de:0030-drops-115604 %D 2019 %B 30th International Symposium on Algorithms and Computation %Z date of event: 2019-12-08 - 2019-12-11 %C Shanghai, China %B 30th International Symposium on Algorithms and Computation %E Lu, Pinyan; Zhang, Guochuan %Z sequence number: 64 %I Schloss Dagstuhl %@ 978-3-95977-130-6 %B Leibniz International Proceedings in Informatics %N 149 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2019/11560/https://creativecommons.org/licenses/by/3.0/legalcode
[229]
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}, }
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%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
[230]
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}, }
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%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
[231]
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}, }
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%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
[232]
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
[233]
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
[234]
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<