# Publications

2023
[1]
A. Abboud, K. Bringmann, and N. Fischer, “Stronger 3-SUM Lower Bounds for Approximate Distance Oracles via Additive Combinatorics,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023), Orlando, FL, USA. (Accepted/in press)
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@inproceedings{Abboud_STOC23, TITLE = {Stronger 3-{SUM} Lower Bounds for Approximate Distance Oracles via Additive Combinatorics}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Fischer, Nick}, LANGUAGE = {eng}, PUBLISHER = {ACM}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023)}, ADDRESS = {Orlando, FL, USA}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Fischer, Nick %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Stronger 3-SUM Lower Bounds for Approximate Distance Oracles via Additive Combinatorics : %G eng %U http://hdl.handle.net/21.11116/0000-000C-8C13-1 %D 2023 %B 55th Annual ACM Symposium on Theory of Computing %Z date of event: 2023-06-20 - 2023-06-23 %C Orlando, FL, USA %B Proceedings of the 55th Annual ACM Symposium on Theory of Computing %I ACM
[2]
P. S. Ardra, R. Krithika, S. Saurabh, and R. Sharma, “Balanced Substructures in Bicolored Graphs,” in SOFSEM 2023: Theory and Practice of Computer Science, Nový Smokovec, Slovakia, 2023.
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@inproceedings{Ardra_SOFSEM23, TITLE = {Balanced Substructures in Bicolored Graphs}, AUTHOR = {Ardra, P. S. and Krithika, R. and Saurabh, Saket and Sharma, Roohani}, LANGUAGE = {eng}, ISBN = {978-3-031-23100-1}, DOI = {10.1007/978-3-031-23101-8_12}, PUBLISHER = {Springer}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, DATE = {2023}, BOOKTITLE = {SOFSEM 2023: Theory and Practice of Computer Science}, EDITOR = {G{\c a}sieniec, Leszek}, PAGES = {177--191}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13878}, ADDRESS = {Nov{\'y} Smokovec, Slovakia}, }
Endnote
%0 Conference Proceedings %A Ardra, P. S. %A Krithika, R. %A Saurabh, Saket %A Sharma, Roohani %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Balanced Substructures in Bicolored Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1D8F-4 %R 10.1007/978-3-031-23101-8_12 %D 2023 %B 48th International Conference on Current Trends in Theory and Practice of Computer Science %Z date of event: 2023-01-15 - 2023-01-18 %C Nov&#253; Smokovec, Slovakia %B SOFSEM 2023: Theory and Practice of Computer Science %E G&#261;sieniec, Leszek %P 177 - 191 %I Springer %@ 978-3-031-23100-1 %B Lecture Notes in Computer Science %N 13878 %U https://rdcu.be/c2Gfk
[3]
M. Beck, J. Spoerhase, and S. Storandt, “Mind the Gap: Edge Facility Location Problems in Theory and Practice,” in Algorithms and Discrete Applied Mathematics (CALDAM 2023), Gandhinagar, India, 2023.
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@inproceedings{beck-etal23:mind-the-gap, TITLE = {Mind the Gap: {E}dge Facility Location Problems in Theory and Practice}, AUTHOR = {Beck, Moritz and Spoerhase, Joachim and Storandt, Sabine}, LANGUAGE = {eng}, ISBN = {978-3-031-25210-5}, DOI = {10.1007/978-3-031-25211-2_25}, PUBLISHER = {Springer}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, DATE = {2023}, BOOKTITLE = {Algorithms and Discrete Applied Mathematics (CALDAM 2023)}, EDITOR = {Bagchi, Amitabha and Muthu, Rahul}, PAGES = {321--334}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13947}, ADDRESS = {Gandhinagar, India}, }
Endnote
%0 Conference Proceedings %A Beck, Moritz %A Spoerhase, Joachim %A Storandt, Sabine %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Mind the Gap: Edge Facility Location Problems in Theory and Practice : %G eng %U http://hdl.handle.net/21.11116/0000-000C-992D-6 %R 10.1007/978-3-031-25211-2_25 %D 2023 %B 9th International Conference on Algorithms and Discrete Applied Mathematics %Z date of event: 2023-02-09 - 2023-02-11 %C Gandhinagar, India %B Algorithms and Discrete Applied Mathematics %E Bagchi, Amitabha; Muthu, Rahul %P 321 - 334 %I Springer %@ 978-3-031-25210-5 %B Lecture Notes in Computer Science %N 13947 %U https://rdcu.be/c5J8c
[4]
S. Bhattacharya, P. Kiss, and T. Saranurak, “Sublinear Algorithms for (1.5+Epsilon)-Approximate Matching,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023), Orlando, FL, USA. (Accepted/in press)
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@inproceedings{Bhattacharya_STOC23, TITLE = {Sublinear Algorithms for $(1.5+\epsilon)$-Approximate Matching}, AUTHOR = {Bhattacharya, Sayan and Kiss, Peter and Saranurak, Thatchaphol}, LANGUAGE = {eng}, PUBLISHER = {ACM}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023)}, ADDRESS = {Orlando, FL, USA}, }
Endnote
%0 Conference Proceedings %A Bhattacharya, Sayan %A Kiss, Peter %A Saranurak, Thatchaphol %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Sublinear Algorithms for (1.5+Epsilon)-Approximate Matching : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9BA1-F %D 2023 %B 55th Annual ACM Symposium on Theory of Computing %Z date of event: 2023-06-20 - 2023-06-23 %C Orlando, FL, USA %B Proceedings of the 55th Annual ACM Symposium on Theory of Computing %I ACM
[5]
S. Bhattacharya, P. Kiss, and T. Saranurak, “Dynamic (1.5+Epsilon)-Approximate Matching Size in Truly Sublinear Update Time,” 2023. [Online]. Available: https://arxiv.org/abs/2302.05030. (arXiv: 2302.05030)
Abstract
We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate<br>\emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges<br>using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial<br>improvement over the long-standing $O(n)$ update time, which can be trivially<br>obtained by periodic recomputation. Thus, we resolve the value version of a<br>major open question of the dynamic graph algorithms literature (see, e.g.,<br>[Gupta and Peng FOCS'13], [Bernstein and Stein SODA'16],[Behnezhad and Khanna<br>SODA'22]).<br> Our key technical component is the first sublinear algorithm for $(1,\epsilon<br>n)$-approximate maximum matching with sublinear running time on dense graphs.<br>All previous algorithms suffered a multiplicative approximation factor of at<br>least $1.499$ or assumed that the graph has a very small maximum degree.<br>
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@online{Bhattacharya2302.05030, TITLE = {Dynamic $(1+\epsilon)$-Approximate Matching Size in Truly Sublinear Update Time}, AUTHOR = {Bhattacharya, Sayan and Kiss, Peter and Saranurak, Thatchaphol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2302.05030}, EPRINT = {2302.05030}, EPRINTTYPE = {arXiv}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate<br>\emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges<br>using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial<br>improvement over the long-standing $O(n)$ update time, which can be trivially<br>obtained by periodic recomputation. Thus, we resolve the value version of a<br>major open question of the dynamic graph algorithms literature (see, e.g.,<br>[Gupta and Peng FOCS'13], [Bernstein and Stein SODA'16],[Behnezhad and Khanna<br>SODA'22]).<br> Our key technical component is the first sublinear algorithm for $(1,\epsilon<br>n)$-approximate maximum matching with sublinear running time on dense graphs.<br>All previous algorithms suffered a multiplicative approximation factor of at<br>least $1.499$ or assumed that the graph has a very small maximum degree.<br>}, }
Endnote
%0 Report %A Bhattacharya, Sayan %A Kiss, Peter %A Saranurak, Thatchaphol %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Dynamic (1.5+Epsilon)-Approximate Matching Size in Truly Sublinear Update Time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9BA8-8 %U https://arxiv.org/abs/2302.05030 %D 2023 %X We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate<br>\emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges<br>using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial<br>improvement over the long-standing $O(n)$ update time, which can be trivially<br>obtained by periodic recomputation. Thus, we resolve the value version of a<br>major open question of the dynamic graph algorithms literature (see, e.g.,<br>[Gupta and Peng FOCS'13], [Bernstein and Stein SODA'16],[Behnezhad and Khanna<br>SODA'22]).<br> Our key technical component is the first sublinear algorithm for $(1,\epsilon<br>n)$-approximate maximum matching with sublinear running time on dense graphs.<br>All previous algorithms suffered a multiplicative approximation factor of at<br>least $1.499$ or assumed that the graph has a very small maximum degree.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[6]
S. Bhattacharya, P. Kiss, and T. Saranurak, “Dynamic Algorithms for Packing-Covering LPs via Multiplicative Weight,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{BhattacharyaSODA23, TITLE = {Dynamic Algorithms for Packing-Covering {LPs} via Multiplicative Weight}, AUTHOR = {Bhattacharya, Sayan and Kiss, Peter and Saranurak, Thatchaphol}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch1}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {1--47}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Bhattacharya, Sayan %A Kiss, Peter %A Saranurak, Thatchaphol %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Dynamic Algorithms for Packing-Covering LPs via Multiplicative Weight : %G eng %U http://hdl.handle.net/21.11116/0000-000C-4333-F %R 10.1137/1.9781611977554.ch1 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 1 - 47 %I SIAM %@ 978-1-61197-755-4
[7]
S. Bhattacharya, P. Kiss, T. Saranurak, and D. Wajc, “Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{BhattacharyaSODA23b, TITLE = {Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time}, AUTHOR = {Bhattacharya, Sayan and Kiss, Peter and Saranurak, Thatchaphol and Wajc, David}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch5}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {100--128}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Bhattacharya, Sayan %A Kiss, Peter %A Saranurak, Thatchaphol %A Wajc, David %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-4336-C %R 10.1137/1.9781611977554.ch5 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 100 - 128 %I SIAM %@ 978-1-61197-755-4
[8]
J. Blikstad, T.-W. Tu, D. Nanongkai, and S. Mukhopadhyay, “Fast Algorithms via Dynamic-Oracle Matroids,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023), Orlando, FL, USA. (Accepted/in press)
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@inproceedings{Blikstad_STOC23, TITLE = {Fast Algorithms via Dynamic-Oracle Matroids}, AUTHOR = {Blikstad, Joakim and Tu, Ta-Wei and Nanongkai, Danupon and Mukhopadhyay, Sagnik}, LANGUAGE = {eng}, PUBLISHER = {ACM}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023)}, ADDRESS = {Orlando, FL, USA}, }
Endnote
%0 Conference Proceedings %A Blikstad, Joakim %A Tu, Ta-Wei %A Nanongkai, Danupon %A Mukhopadhyay, Sagnik %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Fast Algorithms via Dynamic-Oracle Matroids : %G eng %U http://hdl.handle.net/21.11116/0000-000C-8C18-C %D 2023 %B 55th Annual ACM Symposium on Theory of Computing %Z date of event: 2023-06-20 - 2023-06-23 %C Orlando, FL, USA %B Proceedings of the 55th Annual ACM Symposium on Theory of Computing %I ACM
[9]
J. Blikstad and P. Kiss, “Incremental (1 - ε)-approximate dynamic matching in O(poly(1/ε)) update time,” 2023. [Online]. Available: https://arxiv.org/abs/2302.08432. (arXiv: 2302.08432)
Abstract
In the dynamic approximate maximum bipartite matching problem we are given<br>bipartite graph $G$ undergoing updates and our goal is to maintain a matching<br>of $G$ which is large compared the maximum matching size $\mu(G)$. We define a<br>dynamic matching algorithm to be $\alpha$ (respectively $(\alpha,<br>\beta)$)-approximate if it maintains matching $M$ such that at all times $|M |<br>\geq \mu(G) \cdot \alpha$ (respectively $|M| \geq \mu(G) \cdot \alpha -<br>\beta$).<br> We present the first deterministic $(1-\epsilon )$-approximate dynamic<br>matching algorithm with $O(poly(\epsilon ^{-1}))$ amortized update time for<br>graphs undergoing edge insertions. Previous solutions either required<br>super-constant [Gupta FSTTCS'14, Bhattacharya-Kiss-Saranurak SODA'23] or<br>exponential in $1/\epsilon$<br>[Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA'19] update time. Our<br>implementation is arguably simpler than the mentioned algorithms and its<br>description is self contained. Moreover, we show that if we allow for additive<br>$(1, \epsilon \cdot n)$-approximation our algorithm seamlessly extends to also<br>handle vertex deletions, on top of edge insertions. This makes our algorithm<br>one of the few small update time algorithms for $(1-\epsilon )$-approximate<br>dynamic matching allowing for updates both increasing and decreasing the<br>maximum matching size of $G$ in a fully dynamic manner.<br>
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@online{Blikstad2302.08432, TITLE = {Incremental $(1-\epsilon)$-approximate dynamic matching in $O(poly(1/\epsilon))$ update time}, AUTHOR = {Blikstad, Joakim and Kiss, Peter}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2302.08432}, EPRINT = {2302.08432}, EPRINTTYPE = {arXiv}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the dynamic approximate maximum bipartite matching problem we are given<br>bipartite graph $G$ undergoing updates and our goal is to maintain a matching<br>of $G$ which is large compared the maximum matching size $\mu(G)$. We define a<br>dynamic matching algorithm to be $\alpha$ (respectively $(\alpha,<br>\beta)$)-approximate if it maintains matching $M$ such that at all times $|M |<br>\geq \mu(G) \cdot \alpha$ (respectively $|M| \geq \mu(G) \cdot \alpha -<br>\beta$).<br> We present the first deterministic $(1-\epsilon )$-approximate dynamic<br>matching algorithm with $O(poly(\epsilon ^{-1}))$ amortized update time for<br>graphs undergoing edge insertions. Previous solutions either required<br>super-constant [Gupta FSTTCS'14, Bhattacharya-Kiss-Saranurak SODA'23] or<br>exponential in $1/\epsilon$<br>[Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA'19] update time. Our<br>implementation is arguably simpler than the mentioned algorithms and its<br>description is self contained. Moreover, we show that if we allow for additive<br>$(1, \epsilon \cdot n)$-approximation our algorithm seamlessly extends to also<br>handle vertex deletions, on top of edge insertions. This makes our algorithm<br>one of the few small update time algorithms for $(1-\epsilon )$-approximate<br>dynamic matching allowing for updates both increasing and decreasing the<br>maximum matching size of $G$ in a fully dynamic manner.<br>}, }
Endnote
%0 Report %A Blikstad, Joakim %A Kiss, Peter %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Incremental (1 - &#949;)-approximate dynamic matching in O(poly(1/&#949;)) update time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-A006-8 %U https://arxiv.org/abs/2302.08432 %D 2023 %X In the dynamic approximate maximum bipartite matching problem we are given<br>bipartite graph $G$ undergoing updates and our goal is to maintain a matching<br>of $G$ which is large compared the maximum matching size $\mu(G)$. We define a<br>dynamic matching algorithm to be $\alpha$ (respectively $(\alpha,<br>\beta)$)-approximate if it maintains matching $M$ such that at all times $|M |<br>\geq \mu(G) \cdot \alpha$ (respectively $|M| \geq \mu(G) \cdot \alpha -<br>\beta$).<br> We present the first deterministic $(1-\epsilon )$-approximate dynamic<br>matching algorithm with $O(poly(\epsilon ^{-1}))$ amortized update time for<br>graphs undergoing edge insertions. Previous solutions either required<br>super-constant [Gupta FSTTCS'14, Bhattacharya-Kiss-Saranurak SODA'23] or<br>exponential in $1/\epsilon$<br>[Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA'19] update time. Our<br>implementation is arguably simpler than the mentioned algorithms and its<br>description is self contained. Moreover, we show that if we allow for additive<br>$(1, \epsilon \cdot n)$-approximation our algorithm seamlessly extends to also<br>handle vertex deletions, on top of edge insertions. This makes our algorithm<br>one of the few small update time algorithms for $(1-\epsilon )$-approximate<br>dynamic matching allowing for updates both increasing and decreasing the<br>maximum matching size of $G$ in a fully dynamic manner.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[10]
M. Briański, G. Joret, K. Majewski, P. Micek, M. T. Seweryn, and R. Sharma, “Treedepth Vs Circumference,” Combinatorica. (Accepted/in press)
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@article{Brianski23, TITLE = {Treedepth Vs Circumference}, AUTHOR = {Bria{\'n}ski, Marcin and Joret, Gwena{\"e}l and Majewski, Konrad and Micek, Piotr and Seweryn, Micha{\l} T. and Sharma, Roohani}, LANGUAGE = {eng}, ISSN = {0209-9683}, PUBLISHER = {Springer}, ADDRESS = {Heidelberg}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, JOURNAL = {Combinatorica}, }
Endnote
%0 Journal Article %A Bria&#324;ski, Marcin %A Joret, Gwena&#235;l %A Majewski, Konrad %A Micek, Piotr %A Seweryn, Micha&#322; T. %A Sharma, Roohani %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Treedepth Vs Circumference : %G eng %U http://hdl.handle.net/21.11116/0000-000C-8E4E-E %D 2023 %J Combinatorica %I Springer %C Heidelberg %@ false
[11]
K. Bringmann, M. Kapralov, M. Makarov, V. Nakos, A. Yagudin, and A. Zandieh, “Traversing the FFT Computation Tree for Dimension-Independent Sparse Fourier Transforms,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{BringmannSODA23, TITLE = {Traversing the {FFT} Computation Tree for Dimension-Independent Sparse {F}ourier Transforms}, AUTHOR = {Bringmann, Karl and Kapralov, Michael and Makarov, Mikhail and Nakos, Vasileios and Yagudin, Amir and Zandieh, Amir}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch177}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {4768--4845}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Kapralov, Michael %A Makarov, Mikhail %A Nakos, Vasileios %A Yagudin, Amir %A Zandieh, Amir %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society 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 Traversing the FFT Computation Tree for Dimension-Independent Sparse Fourier Transforms : %G eng %U http://hdl.handle.net/21.11116/0000-000C-26DB-3 %R 10.1137/1.9781611977554.ch177 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 4768 - 4845 %I SIAM %@ 978-1-61197-755-4
[12]
K. Bringmann, V. Cohen-Addad, and D. Das, “A Linear-Time n0.4-Approximation for Longest Common Subsequence,” ACM Transactions on Algorithms, vol. 19, no. 1, 2023.
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@article{Bringmann_TOA23, TITLE = {A Linear-Time $n^{0.4}$-Approximation for Longest Common Subsequence}, AUTHOR = {Bringmann, Karl and Cohen-Addad, Vincent and Das, Debarati}, LANGUAGE = {eng}, ISSN = {1549-6325}, DOI = {10.1145/3568398}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {19}, NUMBER = {1}, PAGES = {1--24}, EID = {9}, }
Endnote
%0 Journal Article %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/21.11116/0000-000C-A7EC-E %R 10.1145/3568398 %7 2023 %D 2023 %J ACM Transactions on Algorithms %V 19 %N 1 %& 1 %P 1 - 24 %Z sequence number: 9 %I ACM %C New York, NY %@ false
[13]
C. Coupette, S. Dalleiger, and B. Rieck, “Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework,” in Eleventh International Conference on Learning Representations (ICLR 2023), Kigali, Rwanda. (Accepted/in press)
Abstract
Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of hypergraphs has remained largely unexplored. On graphs, Ollivier-Ricci curvature measures differences between random walks via Wasserstein distances, thus grounding a geometric concept in ideas from probability and optimal transport. We develop ORCHID, a flexible framework generalizing Ollivier-Ricci curvature to hypergraphs, and prove that the resulting curvatures have favorable theoretical properties. Through extensive experiments on synthetic and real-world hypergraphs from different domains, we demonstrate that ORCHID curvatures are both scalable and useful to perform a variety of hypergraph tasks in practice.
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@inproceedings{Coupette_ICLR23, TITLE = {{Ollivier-Ricc}i Curvature for Hypergraphs: {A} Unified Framework}, AUTHOR = {Coupette, Corinna and Dalleiger, Sebastian and Rieck, Bastian}, LANGUAGE = {eng}, PUBLISHER = {OpenReview.net}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of hypergraphs has remained largely unexplored. On graphs, Ollivier-Ricci curvature measures differences between random walks via Wasserstein distances, thus grounding a geometric concept in ideas from probability and optimal transport. We develop ORCHID, a flexible framework generalizing Ollivier-Ricci curvature to hypergraphs, and prove that the resulting curvatures have favorable theoretical properties. Through extensive experiments on synthetic and real-world hypergraphs from different domains, we demonstrate that ORCHID curvatures are both scalable and useful to perform a variety of hypergraph tasks in practice.}, BOOKTITLE = {Eleventh International Conference on Learning Representations (ICLR 2023)}, ADDRESS = {Kigali, Rwanda}, }
Endnote
%0 Conference Proceedings %A Coupette, Corinna %A Dalleiger, Sebastian %A Rieck, Bastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework : %G eng %U http://hdl.handle.net/21.11116/0000-000C-10CD-B %D 2023 %B Eleventh International Conference on Learning Representations %Z date of event: 2023-05-01 - 2023-05-05 %C Kigali, Rwanda %X Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of hypergraphs has remained largely unexplored. On graphs, Ollivier-Ricci curvature measures differences between random walks via Wasserstein distances, thus grounding a geometric concept in ideas from probability and optimal transport. We develop ORCHID, a flexible framework generalizing Ollivier-Ricci curvature to hypergraphs, and prove that the resulting curvatures have favorable theoretical properties. Through extensive experiments on synthetic and real-world hypergraphs from different domains, we demonstrate that ORCHID curvatures are both scalable and useful to perform a variety of hypergraph tasks in practice. %K Computer Science, Learning, cs.LG,cs.SI,Statistics, Machine Learning, stat.ML %B Eleventh International Conference on Learning Representations %I OpenReview.net %U https://openreview.net/forum?id=sPCKNl5qDps
[14]
D. Das, J. Gilbert, M. Hajiaghayi, T. Kociumaka, and B. Saha, “Weighted Edit Distance Computation: Strings, Trees, and Dyck,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023), Orlando, FL, USA. (Accepted/in press)
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@inproceedings{Debarati_STOC23, TITLE = {Weighted Edit Distance Computation: {S}trings, Trees, and {Dyck}}, AUTHOR = {Das, Debarati and Gilbert, Jacob and Hajiaghayi, MohammadTaghi and Kociumaka, Tomasz and Saha, Barna}, LANGUAGE = {eng}, PUBLISHER = {ACM}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023)}, ADDRESS = {Orlando, FL, USA}, }
Endnote
%0 Conference Proceedings %A Das, Debarati %A Gilbert, Jacob %A Hajiaghayi, MohammadTaghi %A Kociumaka, Tomasz %A Saha, Barna %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Weighted Edit Distance Computation: Strings, Trees, and Dyck : %G eng %U http://hdl.handle.net/21.11116/0000-000C-8B20-3 %D 2023 %B 55th Annual ACM Symposium on Theory of Computing %Z date of event: 2023-06-20 - 2023-06-23 %C Orlando, FL, USA %B Proceedings of the 55th Annual ACM Symposium on Theory of Computing %I ACM
[15]
F. Dross, K. Fleszar, K. Węgrzycki, and A. Zych-Pawlewicz, “Gap-ETH-Tight Approximation Schemes for Red-Green-Blue Separation and Bicolored Noncrossing Euclidean Travelling Salesman Tours,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{DrossSODA23, TITLE = {Gap-{ETH}-Tight Approximation Schemes for Red-Green-Blue Separation and Bicolored Noncrossing {E}uclidean Travelling Salesman Tours}, AUTHOR = {Dross, Fran{\c c}ois and Fleszar, Krzysztof and W{\c e}grzycki, Karol and Zych-Pawlewicz, Anna}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch52}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {1433--1463}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Dross, Fran&#231;ois %A Fleszar, Krzysztof %A W&#281;grzycki, Karol %A Zych-Pawlewicz, Anna %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Gap-ETH-Tight Approximation Schemes for Red-Green-Blue Separation and Bicolored Noncrossing Euclidean Travelling Salesman Tours : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F6C-A %R 10.1137/1.9781611977554.ch52 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 1433 - 1463 %I SIAM %@ 978-1-61197-755-4
[16]
S. Fallat, D. Kirkpatrick, H. U. Simon, A. Soltani, and S. Zilles, “On Batch Teaching Without Collusion,” Journal of Machine Learning Research, vol. 24, 2023.
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@article{Fallat23, TITLE = {On Batch Teaching Without Collusion}, AUTHOR = {Fallat, Shaun and Kirkpatrick, David and Simon, Hans U. and Soltani, Abolghasem and Zilles, Sandra}, LANGUAGE = {eng}, ISSN = {1532-4435}, URL = {http://jmlr.org/papers/v24/22-0330.html}, PUBLISHER = {Microtome Publishing}, ADDRESS = {Brookline, MA}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Machine Learning Research}, VOLUME = {24}, PAGES = {1--33}, }
Endnote
%0 Journal Article %A Fallat, Shaun %A Kirkpatrick, David %A Simon, Hans U. %A Soltani, Abolghasem %A Zilles, Sandra %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T On Batch Teaching Without Collusion : %G eng %U http://hdl.handle.net/21.11116/0000-000C-7CCF-1 %U http://jmlr.org/papers/v24/22-0330.html %7 2023 %D 2023 %J Journal of Machine Learning Research %V 24 %& 1 %P 1 - 33 %I Microtome Publishing %C Brookline, MA %@ false
[17]
J. Focke, D. Marx, F. M. Inerney, D. Neuen, G. S. Sankar, P. Schepper, and P. Wellnitz, “Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{FockeSODA23, TITLE = {Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs}, AUTHOR = {Focke, Jacob and Marx, D{\'a}niel and Inerney, Fionn Mc and Neuen, Daniel and Sankar, Govind S. and Schepper, Philipp and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch140}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {3664--3683}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Focke, Jacob %A Marx, D&#225;niel %A Inerney, Fionn Mc %A Neuen, Daniel %A Sankar, Govind S. %A Schepper, Philipp %A Wellnitz, Philip %+ External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1EA4-A %R 10.1137/1.9781611977554.ch140 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 3664 - 3683 %I SIAM %@ 978-1-61197-755-4
[18]
Y. Gao, R. Kyng, and D. A. Spielman, “Robust and Practical Solution of Laplacian Equations by Approximate Elimination,” 2023. [Online]. Available: https://arxiv.org/abs/2303.00709. (arXiv: 2303.00709)
Abstract
We introduce a new algorithm and software for solving linear equations in<br>symmetric diagonally dominant matrices with non-positive off-diagonal entries<br>(SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate<br>gradient (PCG) to solve the system of linear equations. Our preconditioner is a<br>variant of the Approximate Cholesky factorization of Kyng and Sachdeva (FOCS<br>2016). Our factorization approach is simple: we eliminate matrix rows/columns<br>one at a time and update the remaining matrix using sampling to approximate the<br>outcome of complete Cholesky factorization. Unlike earlier approaches, our<br>sampling always maintains a connectivity in the remaining non-zero structure.<br>Our algorithm comes with a tuning parameter that upper bounds the number of<br>samples made per original entry. We implement our algorithm in Julia, providing<br>two versions, AC and AC2, that respectively use 1 and 2 samples per original<br>entry. We compare their single-threaded performance to that of current<br>state-of-the-art solvers Combinatorial Multigrid (CMG),<br>BoomerAMG-preconditioned Krylov solvers from HyPre and PETSc, Lean Algebraic<br>Multigrid (LAMG), and MATLAB's with Incomplete Cholesky Factorization (ICC).<br>Our evaluation uses a broad class of problems, including all large SDDM<br>matrices from the SuiteSparse collection and diverse programmatically generated<br>instances. Our experiments suggest that our algorithm attains a level of<br>robustness and reliability not seen before in SDDM solvers, while retaining<br>good performance across all instances. Our code and data are public, and we<br>provide a tutorial on how to replicate our tests. We hope that others will<br>adopt this suite of tests as a benchmark, which we refer to as SDDM2023. Our<br>solver code is available at: https://github.com/danspielman/Laplacians.jl/ Our<br>benchmarking data and tutorial are available at:<br>https://rjkyng.github.io/SDDM2023/<br>
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@online{Yuan_2303.00709, TITLE = {Robust and Practical Solution of Laplacian Equations by Approximate Elimination}, AUTHOR = {Gao, Yuan and Kyng, Rasmus and Spielman, Daniel A.}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2303.00709}, EPRINT = {2303.00709}, EPRINTTYPE = {arXiv}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We introduce a new algorithm and software for solving linear equations in<br>symmetric diagonally dominant matrices with non-positive off-diagonal entries<br>(SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate<br>gradient (PCG) to solve the system of linear equations. Our preconditioner is a<br>variant of the Approximate Cholesky factorization of Kyng and Sachdeva (FOCS<br>2016). Our factorization approach is simple: we eliminate matrix rows/columns<br>one at a time and update the remaining matrix using sampling to approximate the<br>outcome of complete Cholesky factorization. Unlike earlier approaches, our<br>sampling always maintains a connectivity in the remaining non-zero structure.<br>Our algorithm comes with a tuning parameter that upper bounds the number of<br>samples made per original entry. We implement our algorithm in Julia, providing<br>two versions, AC and AC2, that respectively use 1 and 2 samples per original<br>entry. We compare their single-threaded performance to that of current<br>state-of-the-art solvers Combinatorial Multigrid (CMG),<br>BoomerAMG-preconditioned Krylov solvers from HyPre and PETSc, Lean Algebraic<br>Multigrid (LAMG), and MATLAB's with Incomplete Cholesky Factorization (ICC).<br>Our evaluation uses a broad class of problems, including all large SDDM<br>matrices from the SuiteSparse collection and diverse programmatically generated<br>instances. Our experiments suggest that our algorithm attains a level of<br>robustness and reliability not seen before in SDDM solvers, while retaining<br>good performance across all instances. Our code and data are public, and we<br>provide a tutorial on how to replicate our tests. We hope that others will<br>adopt this suite of tests as a benchmark, which we refer to as SDDM2023. Our<br>solver code is available at: https://github.com/danspielman/Laplacians.jl/ Our<br>benchmarking data and tutorial are available at:<br>https://rjkyng.github.io/SDDM2023/<br>}, }
Endnote
%0 Report %A Gao, Yuan %A Kyng, Rasmus %A Spielman, Daniel A. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Robust and Practical Solution of Laplacian Equations by Approximate Elimination : %G eng %U http://hdl.handle.net/21.11116/0000-000C-B1C8-A %U https://arxiv.org/abs/2303.00709 %D 2023 %X We introduce a new algorithm and software for solving linear equations in<br>symmetric diagonally dominant matrices with non-positive off-diagonal entries<br>(SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate<br>gradient (PCG) to solve the system of linear equations. Our preconditioner is a<br>variant of the Approximate Cholesky factorization of Kyng and Sachdeva (FOCS<br>2016). Our factorization approach is simple: we eliminate matrix rows/columns<br>one at a time and update the remaining matrix using sampling to approximate the<br>outcome of complete Cholesky factorization. Unlike earlier approaches, our<br>sampling always maintains a connectivity in the remaining non-zero structure.<br>Our algorithm comes with a tuning parameter that upper bounds the number of<br>samples made per original entry. We implement our algorithm in Julia, providing<br>two versions, AC and AC2, that respectively use 1 and 2 samples per original<br>entry. We compare their single-threaded performance to that of current<br>state-of-the-art solvers Combinatorial Multigrid (CMG),<br>BoomerAMG-preconditioned Krylov solvers from HyPre and PETSc, Lean Algebraic<br>Multigrid (LAMG), and MATLAB's with Incomplete Cholesky Factorization (ICC).<br>Our evaluation uses a broad class of problems, including all large SDDM<br>matrices from the SuiteSparse collection and diverse programmatically generated<br>instances. Our experiments suggest that our algorithm attains a level of<br>robustness and reliability not seen before in SDDM solvers, while retaining<br>good performance across all instances. Our code and data are public, and we<br>provide a tutorial on how to replicate our tests. We hope that others will<br>adopt this suite of tests as a benchmark, which we refer to as SDDM2023. Our<br>solver code is available at: https://github.com/danspielman/Laplacians.jl/ Our<br>benchmarking data and tutorial are available at:<br>https://rjkyng.github.io/SDDM2023/<br> %K Mathematics, Numerical Analysis, math.NA,Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Mathematical Software, cs.MS,Computer Science, Numerical Analysis, cs.NA
[19]
A. Gionis, K. Khodamoradi, B. Ordozgoiti, B. Riegel, and J. Spoerhase, “A Constant-Factor Approximation Algorithm for Reconciliation k-Median,” in Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS 2023), Valencia, Spain. (Accepted/in press)
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@inproceedings{Gionis_AISTATS2023, TITLE = {A Constant-Factor Approximation Algorithm for Reconciliation $k$-Median}, AUTHOR = {Gionis, Aristides and Khodamoradi, Kamyar and Ordozgoiti, Bruno and Riegel, Benedikt and Spoerhase, Joachim}, LANGUAGE = {eng}, PUBLISHER = {PMLR}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS 2023)}, SERIES = {Proceedings of the Machine Learning Research}, ADDRESS = {Valencia, Spain}, }
Endnote
%0 Conference Proceedings %A Gionis, Aristides %A Khodamoradi, Kamyar %A Ordozgoiti, Bruno %A Riegel, Benedikt %A Spoerhase, Joachim %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Constant-Factor Approximation Algorithm for Reconciliation k-Median : %G eng %U http://hdl.handle.net/21.11116/0000-000C-739D-2 %D 2023 %B 26th International Conference on Artificial Intelligence and Statistics %Z date of event: 2023-04-25 - 2023-04-27 %C Valencia, Spain %B Proceedings of the 26th International Conference on Artificial Intelligence and Statistics %I PMLR %B Proceedings of the Machine Learning Research
[20]
E. Goldenberg, T. Kociumaka, R. Krauthgamer, and B. Saha, “An Algorithmic Bridge Between Hamming and Levenshtein Distances,” in 14th Innovations in Theoretical Computer Science Conference (ITCS 2023), Cambridge, MA, USA, 2023.
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@inproceedings{Goldenberg_ITCS23, TITLE = {An Algorithmic Bridge Between {H}amming and {L}evenshtein Distances}, AUTHOR = {Goldenberg, Elazar and Kociumaka, Tomasz and Krauthgamer, Robert and Saha, Barna}, LANGUAGE = {eng}, ISBN = {978-3-95977-263-1}, URL = {urn:nbn:de:0030-drops-175615}, DOI = {10.4230/LIPIcs.ITCS.2023.58}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, EDITOR = {Tauman Kalai, Yael}, PAGES = {1--23}, EID = {58}, SERIES = {Leibniz International Proceedings in Informatics}, ADDRESS = {Cambridge, MA, USA}, }
Endnote
%0 Conference Proceedings %A Goldenberg, Elazar %A Kociumaka, Tomasz %A Krauthgamer, Robert %A Saha, Barna %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T An Algorithmic Bridge Between Hamming and Levenshtein Distances : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1588-3 %R 10.4230/LIPIcs.ITCS.2023.58 %U urn:nbn:de:0030-drops-175615 %D 2023 %B 14th Innovations in Theoretical Computer Science Conference %Z date of event: 2023-01-10 - 2023-01-13 %C Cambridge, MA, USA %B 14th Innovations in Theoretical Computer Science Conference %E Tauman Kalai, Yael %P 1 - 23 %Z sequence number: 58 %I Schloss Dagstuhl %@ 978-3-95977-263-1 %B Leibniz International Proceedings in Informatics %U https://drops.dagstuhl.de/opus/volltexte/2023/17561/
[21]
G. Goranci, M. Henzinger, D. Nanongkai, T. Saranurak, M. Thorup, and C. Wulff, “Fully Dynamic Exact Edge Connectivity in Sublinear Time,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{GoranciSODA23, TITLE = {Fully Dynamic Exact Edge Connectivity in Sublinear Time}, AUTHOR = {Goranci, Gramoz and Henzinger, Monika and Nanongkai, Danupon and Saranurak, Thatchaphol and Thorup, Mikkel and Wulff, Christian}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch3}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {70--86}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Goranci, Gramoz %A Henzinger, Monika %A Nanongkai, Danupon %A Saranurak, Thatchaphol %A Thorup, Mikkel %A Wulff, Christian %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Fully Dynamic Exact Edge Connectivity in Sublinear Time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9383-9 %R 10.1137/1.9781611977554.ch3 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 70 - 86 %I SIAM %@ 978-1-61197-755-4 %U https://epubs.siam.org/doi/reader/10.1137/1.9781611977554.ch3
[22]
T. Gouleakis, K. Lakis, and G. Shahkarami, “Learning-Augmented Algorithms for Online TSP on the Line,” in Proceedings of the 37th AAAI Conference on Artificial Intelligence, Washington, DC, USA. (Accepted/in press)
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@inproceedings{Gouleakis_AAAI23, TITLE = {Learning-Augmented Algorithms for Online {TSP} on the Line}, AUTHOR = {Gouleakis, Themis and Lakis, Konstantinos and Shahkarami, Golnoosh}, LANGUAGE = {eng}, PUBLISHER = {AAAI}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 37th AAAI Conference on Artificial Intelligence}, ADDRESS = {Washington, DC, USA}, }
Endnote
%0 Conference Proceedings %A Gouleakis, Themis %A Lakis, Konstantinos %A Shahkarami, Golnoosh %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Learning-Augmented Algorithms for Online TSP on the Line : %G eng %U http://hdl.handle.net/21.11116/0000-000C-466C-D %D 2023 %B 37th AAAI Conference on Artificial Intelligence %Z date of event: 2023-02-07 - 2023-02-14 %C Washington, DC, USA %B Proceedings of the 37th AAAI Conference on Artificial Intelligence %I AAAI
[23]
G. Gutowski, F. Mittelstädt, I. Rutter, J. Spoerhase, A. Wolff, and J. Zink, “Coloring Mixed and Directional Interval Graphs,” in Graph Drawing and Network Visualization (GD 2022), Tokyo, Japan, 2023.
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@inproceedings{gutowski-etal22:gd, TITLE = {Coloring Mixed and Directional Interval Graphs}, AUTHOR = {Gutowski, Grzegorz and Mittelst{\"a}dt, Florian and Rutter, Ignaz and Spoerhase, Joachim and Wolff, Alexander and Zink, Johannes}, LANGUAGE = {eng}, ISBN = {978-3-031-22202-3}, DOI = {10.1007/978-3-031-22203-0_30}, PUBLISHER = {Springer}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2023}, BOOKTITLE = {Graph Drawing and Network Visualization (GD 2022)}, EDITOR = {Angelini, Patrizio and von Hanxleden, Reinhard}, PAGES = {418--431}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13764}, ADDRESS = {Tokyo, Japan}, }
Endnote
%0 Conference Proceedings %A Gutowski, Grzegorz %A Mittelst&#228;dt, Florian %A Rutter, Ignaz %A Spoerhase, Joachim %A Wolff, Alexander %A Zink, Johannes %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Coloring Mixed and Directional Interval Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-26A4-0 %R 10.1007/978-3-031-22203-0_30 %D 2023 %B 30th International Symposium on Graph Drawing and Network Visualization %Z date of event: 2022-09-13 - 2022-09-16 %C Tokyo, Japan %B Graph Drawing and Network Visualization %E Angelini, Patrizio; von Hanxleden, Reinhard %P 418 - 431 %I Springer %@ 978-3-031-22202-3 %B Lecture Notes in Computer Science %N 13764
[24]
M. Hatzel, L. Jaffke, P. T. Lima, T. Masařík, M. Pilipczuk, R. Sharma, and M. Sorge, “Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parameterized by the Size of the Cutset: Twin-width Meets Flow-Augmentation,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{Hatzel_SODA23, TITLE = {Fixed-parameter tractability of {DIRECTED MULTICUT} with three terminal pairs parameterized by the size of the cutset: {T}win-width meets flow-augmentation}, AUTHOR = {Hatzel, Meike and Jaffke, Lars and Lima, Paloma T. and Masa{\v r}{\'i}k, Tom{\'a}{\v s} and Pilipczuk, Marcin and Sharma, Roohani and Sorge, Manuel}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch123}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {3229--3244}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Hatzel, Meike %A Jaffke, Lars %A Lima, Paloma T. %A Masa&#345;&#237;k, Tom&#225;&#353; %A Pilipczuk, Marcin %A Sharma, Roohani %A Sorge, Manuel %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parameterized by the Size of the Cutset: Twin-width Meets Flow-Augmentation : %G eng %U http://hdl.handle.net/21.11116/0000-000C-8E4C-0 %R 10.1137/1.9781611977554.ch123 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 3229 - 3244 %I SIAM %@ 978-1-61197-755-4
[25]
Y. Jiang and S. Mukhopadhyay, “Finding a Small Vertex Cut on Distributed Networks,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023), Orlando, FL, USA. (Accepted/in press)
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@inproceedings{Jiang_STOC23, TITLE = {Finding a Small Vertex Cut on Distributed Networks}, AUTHOR = {Jiang, Yonggang and Mukhopadhyay, Sagnik}, LANGUAGE = {eng}, PUBLISHER = {ACM}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC 2023)}, ADDRESS = {Orlando, FL, USA}, }
Endnote
%0 Conference Proceedings %A Jiang, Yonggang %A Mukhopadhyay, Sagnik %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Finding a Small Vertex Cut on Distributed Networks : %G eng %U http://hdl.handle.net/21.11116/0000-000C-947A-4 %D 2023 %B 55th Annual ACM Symposium on Theory of Computing %Z date of event: 2023-06-20 - 2023-06-23 %C Orlando, FL, USA %B Proceedings of the 55th Annual ACM Symposium on Theory of Computing %I ACM
[26]
D. Kempa and T. Kociumaka, “Breaking the O(n)-Barrier in the Construction of Compressed Suffix Arrays,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{KempaSODA23, TITLE = {Breaking the {$O(n)$}-{B}arrier in the Construction of Compressed Suffix Arrays}, AUTHOR = {Kempa, Dominik and Kociumaka, Tomasz}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch187}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {5122--5202}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Kempa, Dominik %A Kociumaka, Tomasz %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Breaking the O(n)-Barrier in the Construction of Compressed Suffix Arrays : %G eng %U http://hdl.handle.net/21.11116/0000-000C-158F-C %R 10.1137/1.9781611977554.ch187 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 5122 - 5202 %I SIAM %@ 978-1-61197-755-4
[27]
P. Kleer and H. U. Simon, “Primal and Dual Combinatorial Dimensions,” Discrete Applied Mathematics, vol. 327, 2023.
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@article{Kleer2023, TITLE = {Primal and Dual Combinatorial Dimensions}, AUTHOR = {Kleer, Pieter and Simon, Hans U.}, LANGUAGE = {eng}, ISSN = {0166-218X}, DOI = {10.1016/j.dam.2022.11.010}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, JOURNAL = {Discrete Applied Mathematics}, VOLUME = {327}, PAGES = {185--196}, }
Endnote
%0 Journal Article %A Kleer, Pieter %A Simon, Hans U. %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Primal and Dual Combinatorial Dimensions : %G eng %U http://hdl.handle.net/21.11116/0000-000C-15FE-F %R 10.1016/j.dam.2022.11.010 %7 2023 %D 2023 %J Discrete Applied Mathematics %V 327 %& 185 %P 185 - 196 %I Elsevier %C Amsterdam %@ false
[28]
J. Li, D. Nanongkai, D. Panigrahi, and T. Saranurak, “Near-Linear Time Approximations for Cut Problems via Fair Cuts,” in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023), Florence, Italy, 2023.
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@inproceedings{LiSODA23, TITLE = {Near-Linear Time Approximations for Cut Problems via Fair Cuts}, AUTHOR = {Li, Jason and Nanongkai, Danupon and Panigrahi, Debmalya and Saranurak, Thatchaphol}, LANGUAGE = {eng}, ISBN = {978-1-61197-755-4}, DOI = {10.1137/1.9781611977554.ch10}, PUBLISHER = {SIAM}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2023)}, EDITOR = {Bansal, Nikhil and Nagarajan, Viswanath}, PAGES = {240--257}, ADDRESS = {Florence, Italy}, }
Endnote
%0 Conference Proceedings %A Li, Jason %A Nanongkai, Danupon %A Panigrahi, Debmalya %A Saranurak, Thatchaphol %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Near-Linear Time Approximations for Cut Problems via Fair Cuts : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9381-B %R 10.1137/1.9781611977554.ch10 %D 2023 %B Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2023-01-22 - 2023-01-25 %C Florence, Italy %B Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms %E Bansal, Nikhil; Nagarajan, Viswanath %P 240 - 257 %I SIAM %@ 978-1-61197-755-4 %U https://epubs.siam.org/doi/pdf/10.1137/1.9781611977554.ch10?download=true
[29]
F. Mazowiecki, H. Sinclair-Banks, and K. Węgrzycki, “Coverability in 2-VASS with One Unary Counter is in NP,” in 26th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2023), Paris, France. (Accepted/in press)
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@inproceedings{Mazowieckie_FoSSaCS23, TITLE = {Coverability in 2-{VASS} with One Unary Counter is in {NP}}, AUTHOR = {Mazowiecki, Filip and Sinclair-Banks, Henry and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, PUBLISHER = {Springer}, YEAR = {2023}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {26th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2023)}, ADDRESS = {Paris, France}, }
Endnote
%0 Conference Proceedings %A Mazowiecki, Filip %A Sinclair-Banks, Henry %A W&#281;grzycki, Karol %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Coverability in 2-VASS with One Unary Counter is in NP : Coverability in 2-{VASS} with One Unary Counter is in {NP} %G eng %U http://hdl.handle.net/21.11116/0000-000C-4678-F %D 2023 %B 26th International Conference on Foundations of Software Science and Computation Structures %Z date of event: 2023-04-22 - 2023-04-27 %C Paris, France %B 26th International Conference on Foundations of Software Science and Computation Structures %I Springer
[30]
P. Misra, S. Saket, R. Sharma, and M. Zehavi, “Sub-exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number,” Algorithmica, 2023.
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@article{Misra23b, TITLE = {Sub-exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number}, AUTHOR = {Misra, Pranabendu and Saket, Saurabh and Sharma, Roohani and Zehavi, Meirav}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-022-01093-w}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, }
Endnote
%0 Journal Article %A Misra, Pranabendu %A Saket, Saurabh %A Sharma, Roohani %A Zehavi, Meirav %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Sub-exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9037-3 %R 10.1007/s00453-022-01093-w %7 2023 %D 2023 %J Algorithmica %I Springer-Verlag %C New York %@ false
[31]
J. Olkowski, M. Pilipczuk, M. Rychlicki, K. Węgrzycki, and A. Zych-Pawlewicz, “Dynamic Data Structures for Parameterized String Problems,” in 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023), Hamburg, Germany, 2023.
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@inproceedings{OlkowskiSTACS23, TITLE = {Dynamic Data Structures for Parameterized String Problems}, AUTHOR = {Olkowski, J{\c e}drzej and Pilipczuk, Micha{\l} and Rychlicki, Mateusz and W{\c e}grzycki, Karol and Zych-Pawlewicz, Anna}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-266-2}, URL = {urn:nbn:de:0030-drops-177026}, DOI = {10.4230/LIPIcs.STACS.2023.50}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)}, EDITOR = {Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant{\'e}, Mamadou Moustapha}, PAGES = {1--22}, EID = {50}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {254}, ADDRESS = {Hamburg, Germany}, }
Endnote
%0 Conference Proceedings %A Olkowski, J&#281;drzej %A Pilipczuk, Micha&#322; %A Rychlicki, Mateusz %A W&#281;grzycki, Karol %A Zych-Pawlewicz, Anna %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Dynamic Data Structures for Parameterized String Problems : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F0E-4 %R 10.4230/LIPIcs.STACS.2023.50 %U urn:nbn:de:0030-drops-177026 %D 2023 %B 40th International Symposium on Theoretical Aspects of Computer Science %Z date of event: 2023-03-07 - 2023-03-09 %C Hamburg, Germany %B 40th International Symposium on Theoretical Aspects of Computer Science %E Berenbrink, Petra; Bouyer, Patricia; Dawar, Anuj; Kant&#233;, Mamadou Moustapha %P 1 - 22 %Z sequence number: 50 %I Schloss Dagstuhl %@ 978-3-95977-266-2 %B Leibniz International Proceedings in Informatics %N 254 %@ false
[32]
H. U. Simon, “Tournaments, Johnson Graphs, and NC-Teaching,” in Proceedings of the 34th International Conference on Algorithmic Learning Theory (ALT 2023), Singapore, Singapore, 2023.
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@inproceedings{SimonALT23, TITLE = {Tournaments, {Johnson} Graphs, and {NC}-Teaching}, AUTHOR = {Simon, Hans U.}, LANGUAGE = {eng}, PUBLISHER = {PMLR}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 34th International Conference on Algorithmic Learning Theory (ALT 2023)}, EDITOR = {Agrawal, Shipra and Orabona, Francesco}, PAGES = {1411--1428}, SERIES = {Proceedings of the Machine Learning Research}, VOLUME = {201}, ADDRESS = {Singapore, Singapore}, }
Endnote
%0 Conference Proceedings %A Simon, Hans U. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tournaments, Johnson Graphs, and NC-Teaching : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1606-5 %D 2023 %B The 34th International Conference on Algorithmic Learning Theory %Z date of event: 2023-02-20 - 2023-02-23 %C Singapore, Singapore %B Proceedings of the 34th International Conference on Algorithmic Learning Theory %E Agrawal, Shipra; Orabona, Francesco %P 1411 - 1428 %I PMLR %B Proceedings of the Machine Learning Research %N 201
[33]
A. Zandieh, I. Han, M. Daliri, and A. Karbasi, “KDEformer: Accelerating Transformers via Kernel Density Estimation,” 2023. [Online]. Available: https://arxiv.org/abs/2302.02451. (arXiv: 2302.02451)
Abstract
Dot-product attention mechanism plays a crucial role in modern deep<br>architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact<br>computation of this model incurs quadratic time and memory complexities in<br>sequence length, hindering the training of long-sequence models. Critical<br>bottlenecks are due to the computation of partition functions in the<br>denominator of softmax function as well as the multiplication of the softmax<br>matrix with the matrix of values. Our key observation is that the former can be<br>reduced to a variant of the kernel density estimation (KDE) problem, and an<br>efficient KDE solver can be further utilized to accelerate the latter via<br>subsampling-based fast matrix products. Our proposed KDEformer can approximate<br>the attention in sub-quadratic time with provable spectral norm bounds, while<br>all prior results merely provide entry-wise error bounds. Empirically, we<br>verify that KDEformer outperforms other attention approximations in terms of<br>accuracy, memory, and runtime on various pre-trained models. On BigGAN image<br>generation, we achieve better generative scores than the exact computation with<br>over $4\times$ speedup. For ImageNet classification with T2T-ViT, KDEformer<br>shows over $18\times$ speedup while the accuracy drop is less than $0.5\%$.<br>
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@online{zandieh2302.02451, TITLE = {{KDEformer}: Accelerating Transformers via Kernel Density Estimation}, AUTHOR = {Zandieh, Amir and Han, Insu and Daliri, Majid and Karbasi, Amin}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2302.02451}, EPRINT = {2302.02451}, EPRINTTYPE = {arXiv}, YEAR = {2023}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Dot-product attention mechanism plays a crucial role in modern deep<br>architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact<br>computation of this model incurs quadratic time and memory complexities in<br>sequence length, hindering the training of long-sequence models. Critical<br>bottlenecks are due to the computation of partition functions in the<br>denominator of softmax function as well as the multiplication of the softmax<br>matrix with the matrix of values. Our key observation is that the former can be<br>reduced to a variant of the kernel density estimation (KDE) problem, and an<br>efficient KDE solver can be further utilized to accelerate the latter via<br>subsampling-based fast matrix products. Our proposed KDEformer can approximate<br>the attention in sub-quadratic time with provable spectral norm bounds, while<br>all prior results merely provide entry-wise error bounds. Empirically, we<br>verify that KDEformer outperforms other attention approximations in terms of<br>accuracy, memory, and runtime on various pre-trained models. On BigGAN image<br>generation, we achieve better generative scores than the exact computation with<br>over $4\times$ speedup. For ImageNet classification with T2T-ViT, KDEformer<br>shows over $18\times$ speedup while the accuracy drop is less than $0.5\%$.<br>}, }
Endnote
%0 Report %A Zandieh, Amir %A Han, Insu %A Daliri, Majid %A Karbasi, Amin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T KDEformer: Accelerating Transformers via Kernel Density Estimation : %G eng %U http://hdl.handle.net/21.11116/0000-000C-90F7-A %U https://arxiv.org/abs/2302.02451 %D 2023 %X Dot-product attention mechanism plays a crucial role in modern deep<br>architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact<br>computation of this model incurs quadratic time and memory complexities in<br>sequence length, hindering the training of long-sequence models. Critical<br>bottlenecks are due to the computation of partition functions in the<br>denominator of softmax function as well as the multiplication of the softmax<br>matrix with the matrix of values. Our key observation is that the former can be<br>reduced to a variant of the kernel density estimation (KDE) problem, and an<br>efficient KDE solver can be further utilized to accelerate the latter via<br>subsampling-based fast matrix products. Our proposed KDEformer can approximate<br>the attention in sub-quadratic time with provable spectral norm bounds, while<br>all prior results merely provide entry-wise error bounds. Empirically, we<br>verify that KDEformer outperforms other attention approximations in terms of<br>accuracy, memory, and runtime on various pre-trained models. On BigGAN image<br>generation, we achieve better generative scores than the exact computation with<br>over $4\times$ speedup. For ImageNet classification with T2T-ViT, KDEformer<br>shows over $18\times$ speedup while the accuracy drop is less than $0.5\%$.<br> %K Computer Science, Learning, cs.LG,Computer Science, Computer Vision and Pattern Recognition, cs.CV,Computer Science, Data Structures and Algorithms, cs.DS
2022
[34]
A. Abboud, K. Bringmann, S. Khoury, and O. Zamir, “Hardness of Approximation in p via Short Cycle Removal: Cycle Detection, Distance Oracles, and Beyond,” in STOC ’22, 54th Annual ACM Symposium on Theory of Computing, Rome, Italy, 2022.
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@inproceedings{AbboudSTOC22, TITLE = {Hardness of Approximation in {P} via Short Cycle Removal: {C}ycle Detection, Distance Oracles, and Beyond}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Khoury, Seri and Zamir, Or}, LANGUAGE = {eng}, ISBN = {978-1-4503-9264-8}, DOI = {10.1145/3519935.3520066}, PUBLISHER = {ACM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '22, 54th Annual ACM Symposium on Theory of Computing}, EDITOR = {Leonardi, Stefano and Gupta, Anupam}, PAGES = {1487--1500}, ADDRESS = {Rome, Italy}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Khoury, Seri %A Zamir, Or %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Hardness of Approximation in p via Short Cycle Removal: Cycle Detection, Distance Oracles, and Beyond : %G eng %U http://hdl.handle.net/21.11116/0000-000B-4797-B %R 10.1145/3519935.3520066 %D 2022 %B 54th Annual ACM Symposium on Theory of Computing %Z date of event: 2022-06-20 - 2022-06-24 %C Rome, Italy %B STOC '22 %E Leonardi, Stefano; Gupta, Anupam %P 1487 - 1500 %I ACM %@ 978-1-4503-9264-8
[35]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “Scheduling Lower Bounds via AND Subset Sum,” Journal of Computer and System Sciences, vol. 127, 2022.
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@article{Abboud22, TITLE = {Scheduling Lower Bounds via {AND} Subset Sum}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, ISSN = {0022-0000}, DOI = {10.1016/j.jcss.2022.01.005}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Journal of Computer and System Sciences}, VOLUME = {127}, PAGES = {29--40}, }
Endnote
%0 Journal Article %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/21.11116/0000-000B-153C-B %R 10.1016/j.jcss.2022.01.005 %7 2022 %D 2022 %J Journal of Computer and System Sciences %V 127 %& 29 %P 29 - 40 %I Elsevier %C Amsterdam %@ false
[36]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “SETH-Based Lower Bounds for Subset Sum and Bicriteria Path,” ACM Transactions on Algorithms, vol. 18, no. 1, 2022.
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@article{Abboud22a, 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}, ISSN = {1549-6325}, DOI = {10.1145/3450524}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Transactions on Algorithms}, VOLUME = {18}, NUMBER = {1}, PAGES = {1--22}, EID = {6}, }
Endnote
%0 Journal Article %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/21.11116/0000-000B-1543-2 %R 10.1145/3450524 %7 2022 %D 2022 %J ACM Transactions on Algorithms %V 18 %N 1 %& 1 %P 1 - 22 %Z sequence number: 6 %I ACM %C New York, NY %@ false
[37]
A. Agrawal, D. Lokshtanov, P. Misra, S. Saurabh, and M. Zehavi, “Erdős–Pósa Property of Obstructions to Interval Graphs,” Journal of Graph Theory, vol. 102, no. 4, 2022.
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@article{Agrawal2022, TITLE = {{Erd{\H o}s-{P}{\'o}sa} Property of Obstructions to Interval Graphs}, AUTHOR = {Agrawal, Akanksha and Lokshtanov, Daniel and Misra, Pranabendu and Saurabh, Saket and Zehavi, Meirav}, LANGUAGE = {eng}, ISSN = {0364-9024}, DOI = {10.1002/jgt.22895}, PUBLISHER = {John Wiley \& Sons.}, ADDRESS = {New York}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Graph Theory}, VOLUME = {102}, NUMBER = {4}, PAGES = {702--727}, }
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 Erd&#337;s&#8211;P&#243;sa Property of Obstructions to Interval Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000B-589A-5 %R 10.1002/jgt.22895 %7 2022 %D 2022 %J Journal of Graph Theory %V 102 %N 4 %& 702 %P 702 - 727 %I John Wiley & Sons. %C New York %@ false
[38]
H. Akrami, N. Alon, B. Ray Chaudhury, J. Garg, K. Mehlhorn, and R. Mehta, “EFX Allocations: Simplifications and Improvements,” 2022. [Online]. Available: https://arxiv.org/abs/2205.07638. (arXiv: 2205.07638)
Abstract
The existence of EFX allocations is a fundamental open problem in discrete<br>fair division. Given a set of agents and indivisible goods, the goal is to<br>determine the existence of an allocation where no agent envies another<br>following the removal of any single good from the other agent's bundle. Since<br>the general problem has been illusive, progress is made on two fronts: $(i)$<br>proving existence when the number of agents is small, $(ii)$ proving existence<br>of relaxations of EFX. In this paper, we improve results on both fronts (and<br>simplify in one of the cases).<br> We prove the existence of EFX allocations with three agents, restricting only<br>one agent to have an MMS-feasible valuation function (a strict generalization<br>of nice-cancelable valuation functions introduced by Berger et al. which<br>subsumes additive, budget-additive and unit demand valuation functions). The<br>other agents may have any monotone valuation functions. Our proof technique is<br>significantly simpler and shorter than the proof by Chaudhury et al. on<br>existence of EFX allocations when there are three agents with additive<br>valuation functions and therefore more accessible.<br> Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX<br>allocations and EFX allocations with few unallocated goods (charity). Chaudhury<br>et al. showed the existence of $(1-\epsilon)$-EFX allocation with<br>$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to a<br>problem in extremal combinatorics. We improve their result and prove the<br>existence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/<br>\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used<br>to prove improved upper-bounds on a problem in zero-sum combinatorics<br>introduced by Alon and Krivelevich.<br>
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@online{Akrami2205.07638, TITLE = {{EFX} Allocations: Simplifications and Improvements}, AUTHOR = {Akrami, Hannaneh and Alon, Noga and Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2205.07638}, EPRINT = {2205.07638}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The existence of EFX allocations is a fundamental open problem in discrete<br>fair division. Given a set of agents and indivisible goods, the goal is to<br>determine the existence of an allocation where no agent envies another<br>following the removal of any single good from the other agent's bundle. Since<br>the general problem has been illusive, progress is made on two fronts: $(i)$<br>proving existence when the number of agents is small, $(ii)$ proving existence<br>of relaxations of EFX. In this paper, we improve results on both fronts (and<br>simplify in one of the cases).<br> We prove the existence of EFX allocations with three agents, restricting only<br>one agent to have an MMS-feasible valuation function (a strict generalization<br>of nice-cancelable valuation functions introduced by Berger et al. which<br>subsumes additive, budget-additive and unit demand valuation functions). The<br>other agents may have any monotone valuation functions. Our proof technique is<br>significantly simpler and shorter than the proof by Chaudhury et al. on<br>existence of EFX allocations when there are three agents with additive<br>valuation functions and therefore more accessible.<br> Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX<br>allocations and EFX allocations with few unallocated goods (charity). Chaudhury<br>et al. showed the existence of $(1-\epsilon)$-EFX allocation with<br>$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to a<br>problem in extremal combinatorics. We improve their result and prove the<br>existence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/<br>\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used<br>to prove improved upper-bounds on a problem in zero-sum combinatorics<br>introduced by Alon and Krivelevich.<br>}, }
Endnote
%0 Report %A Akrami, Hannaneh %A Alon, Noga %A Ray Chaudhury, Bhaskar %A Garg, Jugal %A Mehlhorn, Kurt %A Mehta, Ruta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T EFX Allocations: Simplifications and Improvements : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FEB-A %U https://arxiv.org/abs/2205.07638 %D 2022 %X The existence of EFX allocations is a fundamental open problem in discrete<br>fair division. Given a set of agents and indivisible goods, the goal is to<br>determine the existence of an allocation where no agent envies another<br>following the removal of any single good from the other agent's bundle. Since<br>the general problem has been illusive, progress is made on two fronts: $(i)$<br>proving existence when the number of agents is small, $(ii)$ proving existence<br>of relaxations of EFX. In this paper, we improve results on both fronts (and<br>simplify in one of the cases).<br> We prove the existence of EFX allocations with three agents, restricting only<br>one agent to have an MMS-feasible valuation function (a strict generalization<br>of nice-cancelable valuation functions introduced by Berger et al. which<br>subsumes additive, budget-additive and unit demand valuation functions). The<br>other agents may have any monotone valuation functions. Our proof technique is<br>significantly simpler and shorter than the proof by Chaudhury et al. on<br>existence of EFX allocations when there are three agents with additive<br>valuation functions and therefore more accessible.<br> Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX<br>allocations and EFX allocations with few unallocated goods (charity). Chaudhury<br>et al. showed the existence of $(1-\epsilon)$-EFX allocation with<br>$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to a<br>problem in extremal combinatorics. We improve their result and prove the<br>existence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/<br>\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used<br>to prove improved upper-bounds on a problem in zero-sum combinatorics<br>introduced by Alon and Krivelevich.<br> %K Computer Science, Computer Science and Game Theory, cs.GT
[39]
H. Akrami, B. Ray Chaudhury, M. Hoefer, K. Mehlhorn, M. Schmalhofer, G. Shahkarami, G. Varricchio, Q. Vermande, and E. van Wijland, “Maximizing Nash Social Welfare in 2-Value Instances,” in Proceedings of the 36th AAAI Conference on Artificial Intelligence, Virtual Conference, 2022.
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BibTeX
@inproceedings{AkramiAAAI22, TITLE = {Maximizing {N}ash Social Welfare in 2-Value Instances}, AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Hoefer, Martin and Mehlhorn, Kurt and Schmalhofer, Marco and Shahkarami, Golnoosh and Varricchio, Giovanna and Vermande, Quentin and van Wijland, Ernest}, LANGUAGE = {eng}, ISBN = {978-1-57735-876-3}, DOI = {10.1609/aaai.v36i5.20402}, PUBLISHER = {AAAI}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 36th AAAI Conference on Artificial Intelligence}, PAGES = {4760--4767}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Akrami, Hannaneh %A Ray Chaudhury, Bhaskar %A Hoefer, Martin %A Mehlhorn, Kurt %A Schmalhofer, Marco %A Shahkarami, Golnoosh %A Varricchio, Giovanna %A Vermande, Quentin %A van Wijland, Ernest %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society 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 External Organizations %T Maximizing Nash Social Welfare in 2-Value Instances : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FC6-3 %R 10.1609/aaai.v36i5.20402 %D 2022 %B 36th AAAI Conference on Artificial Intelligence %Z date of event: 2022-02-22 - 2022-03-01 %C Virtual Conference %B Proceedings of the 36th AAAI Conference on Artificial Intelligence %P 4760 - 4767 %I AAAI %@ 978-1-57735-876-3 %U https://ojs.aaai.org/index.php/AAAI/article/view/20402
[40]
H. Akrami, B. Ray Chaudhury, M. Hoefer, K. Mehlhorn, M. Schmalhofer, G. Shahkarami, G. Varricchio, Q. Vermande, and E. van Wijland, “Maximizing Nash Social Welfare in 2-Value Instances: The Half-Integer Case,” 2022. [Online]. Available: https://arxiv.org/abs/2207.10949. (arXiv: 2207.10949)
Abstract
We consider the problem of maximizing the Nash social welfare when allocating<br>a set $G$ of indivisible goods to a set $N$ of agents. We study instances, in<br>which all agents have 2-value additive valuations: The value of a good $g \in<br>G$ for an agent $i \in N$ is either $1$ or $s$, where $s$ is an odd multiple of<br>$\frac{1}{2}$ larger than one. We show that the problem is solvable in<br>polynomial time. Akrami et at. showed that this problem is solvable in<br>polynomial time if $s$ is integral and is NP-hard whenever $s = \frac{p}{q}$,<br>$p \in \mathbb{N}$ and $q\in \mathbb{N}$ are co-prime and $p > q \ge 3$. For<br>the latter situation, an approximation algorithm was also given. It obtains an<br>approximation ratio of at most $1.0345$. Moreover, the problem is APX-hard,<br>with a lower bound of $1.000015$ achieved at $\frac{p}{q} = \frac{5}{4}$. The<br>case $q = 2$ and odd $p$ was left open.<br> In the case of integral $s$, the problem is separable in the sense that the<br>optimal allocation of the heavy goods (= value $s$ for some agent) is<br>independent of the number of light goods (= value $1$ for all agents). This<br>leads to an algorithm that first computes an optimal allocation of the heavy<br>goods and then adds the light goods greedily. This separation no longer holds<br>for $s = \frac{3}{2}$; a simple example is given in the introduction. Thus an<br>algorithm has to consider heavy and light goods together. This complicates<br>matters considerably. Our algorithm is based on a collection of improvement<br>rules that transfers any allocation into an optimal allocation and exploits a<br>connection to matchings with parity constraints.<br>
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@online{Akrami2207.10949, TITLE = {Maximizing Nash Social Welfare in 2-Value Instances: The Half-Integer Case}, AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Hoefer, Martin and Mehlhorn, Kurt and Schmalhofer, Marco and Shahkarami, Golnoosh and Varricchio, Giovanna and Vermande, Quentin and van Wijland, Ernest}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2207.10949}, EPRINT = {2207.10949}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the problem of maximizing the Nash social welfare when allocating<br>a set $G$ of indivisible goods to a set $N$ of agents. We study instances, in<br>which all agents have 2-value additive valuations: The value of a good $g \in<br>G$ for an agent $i \in N$ is either $1$ or $s$, where $s$ is an odd multiple of<br>$\frac{1}{2}$ larger than one. We show that the problem is solvable in<br>polynomial time. Akrami et at. showed that this problem is solvable in<br>polynomial time if $s$ is integral and is NP-hard whenever $s = \frac{p}{q}$,<br>$p \in \mathbb{N}$ and $q\in \mathbb{N}$ are co-prime and $p > q \ge 3$. For<br>the latter situation, an approximation algorithm was also given. It obtains an<br>approximation ratio of at most $1.0345$. Moreover, the problem is APX-hard,<br>with a lower bound of $1.000015$ achieved at $\frac{p}{q} = \frac{5}{4}$. The<br>case $q = 2$ and odd $p$ was left open.<br> In the case of integral $s$, the problem is separable in the sense that the<br>optimal allocation of the heavy goods (= value $s$ for some agent) is<br>independent of the number of light goods (= value $1$ for all agents). This<br>leads to an algorithm that first computes an optimal allocation of the heavy<br>goods and then adds the light goods greedily. This separation no longer holds<br>for $s = \frac{3}{2}$; a simple example is given in the introduction. Thus an<br>algorithm has to consider heavy and light goods together. This complicates<br>matters considerably. Our algorithm is based on a collection of improvement<br>rules that transfers any allocation into an optimal allocation and exploits a<br>connection to matchings with parity constraints.<br>}, }
Endnote
%0 Report %A Akrami, Hannaneh %A Ray Chaudhury, Bhaskar %A Hoefer, Martin %A Mehlhorn, Kurt %A Schmalhofer, Marco %A Shahkarami, Golnoosh %A Varricchio, Giovanna %A Vermande, Quentin %A van Wijland, Ernest %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society 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 External Organizations %T Maximizing Nash Social Welfare in 2-Value Instances: The Half-Integer Case : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FD5-2 %U https://arxiv.org/abs/2207.10949 %D 2022 %X We consider the problem of maximizing the Nash social welfare when allocating<br>a set $G$ of indivisible goods to a set $N$ of agents. We study instances, in<br>which all agents have 2-value additive valuations: The value of a good $g \in<br>G$ for an agent $i \in N$ is either $1$ or $s$, where $s$ is an odd multiple of<br>$\frac{1}{2}$ larger than one. We show that the problem is solvable in<br>polynomial time. Akrami et at. showed that this problem is solvable in<br>polynomial time if $s$ is integral and is NP-hard whenever $s = \frac{p}{q}$,<br>$p \in \mathbb{N}$ and $q\in \mathbb{N}$ are co-prime and $p > q \ge 3$. For<br>the latter situation, an approximation algorithm was also given. It obtains an<br>approximation ratio of at most $1.0345$. Moreover, the problem is APX-hard,<br>with a lower bound of $1.000015$ achieved at $\frac{p}{q} = \frac{5}{4}$. The<br>case $q = 2$ and odd $p$ was left open.<br> In the case of integral $s$, the problem is separable in the sense that the<br>optimal allocation of the heavy goods (= value $s$ for some agent) is<br>independent of the number of light goods (= value $1$ for all agents). This<br>leads to an algorithm that first computes an optimal allocation of the heavy<br>goods and then adds the light goods greedily. This separation no longer holds<br>for $s = \frac{3}{2}$; a simple example is given in the introduction. Thus an<br>algorithm has to consider heavy and light goods together. This complicates<br>matters considerably. Our algorithm is based on a collection of improvement<br>rules that transfers any allocation into an optimal allocation and exploits a<br>connection to matchings with parity constraints.<br> %K Computer Science, Computer Science and Game Theory, cs.GT
[41]
H. Akrami, R. Rezvan, and M. Seddighin, “An EF2X Allocation Protocol for Restricted Additive Valuations,” in Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI 2022), Vienna, Austria, 2022.
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@inproceedings{AkramiIJCAI22, TITLE = {An {EF2X} Allocation Protocol for Restricted Additive Valuations}, AUTHOR = {Akrami, Hannaneh and Rezvan, Rojin and Seddighin, Masoud}, LANGUAGE = {eng}, ISBN = {978-1-956792-00-3}, DOI = {10.24963/ijcai.2022/3}, PUBLISHER = {IJCAI}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI 2022)}, EDITOR = {de Raedt, Luc}, PAGES = {17--23}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Akrami, Hannaneh %A Rezvan, Rojin %A Seddighin, Masoud %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T An EF2X Allocation Protocol for Restricted Additive Valuations : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FFA-9 %R 10.24963/ijcai.2022/3 %D 2022 %B Thirty-First International Joint Conference on Artificial Intelligence %Z date of event: 2022-07-23 - 2022-07-29 %C Vienna, Austria %B Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence %E de Raedt, Luc %P 17 - 23 %I IJCAI %@ 978-1-956792-00-3
[42]
H. Akrami, R. Rezvan, and M. Seddighin, “An EF2X Allocation Protocol for Restricted Additive Valuations,” 2022. [Online]. Available: https://arxiv.org/abs/2202.13676. (arXiv: 2202.13676)
Abstract
We study the problem of fairly allocating a set of $m$ indivisible goods to a<br>set of $n$ agents. Envy-freeness up to any good (EFX) criteria -- which<br>requires that no agent prefers the bundle of another agent after removal of any<br>single good -- is known to be a remarkable analogous of envy-freeness when the<br>resource is a set of indivisible goods. In this paper, we investigate EFX<br>notion for the restricted additive valuations, that is, every good has some<br>non-negative value, and every agent is interested in only some of the goods.<br> We introduce a natural relaxation of EFX called EFkX which requires that no<br>agent envies another agent after removal of any $k$ goods. Our main<br>contribution is an algorithm that finds a complete (i.e., no good is discarded)<br>EF2X allocation for the restricted additive valuations. In our algorithm we<br>devise new concepts, namely "configuration" and "envy-elimination" that might<br>be of independent interest.<br> We also use our new tools to find an EFX allocation for restricted additive<br>valuations that discards at most $\lfloor n/2 \rfloor -1$ goods. This improves<br>the state of the art for the restricted additive valuations by a factor of $2$.<br>
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@online{Akrami2202.13676, TITLE = {An {EF2X} Allocation Protocol for Restricted Additive Valuations}, AUTHOR = {Akrami, Hannaneh and Rezvan, Rojin and Seddighin, Masoud}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2202.13676}, EPRINT = {2202.13676}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the problem of fairly allocating a set of $m$ indivisible goods to a<br>set of $n$ agents. Envy-freeness up to any good (EFX) criteria -- which<br>requires that no agent prefers the bundle of another agent after removal of any<br>single good -- is known to be a remarkable analogous of envy-freeness when the<br>resource is a set of indivisible goods. In this paper, we investigate EFX<br>notion for the restricted additive valuations, that is, every good has some<br>non-negative value, and every agent is interested in only some of the goods.<br> We introduce a natural relaxation of EFX called EFkX which requires that no<br>agent envies another agent after removal of any $k$ goods. Our main<br>contribution is an algorithm that finds a complete (i.e., no good is discarded)<br>EF2X allocation for the restricted additive valuations. In our algorithm we<br>devise new concepts, namely "configuration" and "envy-elimination" that might<br>be of independent interest.<br> We also use our new tools to find an EFX allocation for restricted additive<br>valuations that discards at most $\lfloor n/2 \rfloor -1$ goods. This improves<br>the state of the art for the restricted additive valuations by a factor of $2$.<br>}, }
Endnote
%0 Report %A Akrami, Hannaneh %A Rezvan, Rojin %A Seddighin, Masoud %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T An EF2X Allocation Protocol for Restricted Additive Valuations : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FF3-0 %U https://arxiv.org/abs/2202.13676 %D 2022 %X We study the problem of fairly allocating a set of $m$ indivisible goods to a<br>set of $n$ agents. Envy-freeness up to any good (EFX) criteria -- which<br>requires that no agent prefers the bundle of another agent after removal of any<br>single good -- is known to be a remarkable analogous of envy-freeness when the<br>resource is a set of indivisible goods. In this paper, we investigate EFX<br>notion for the restricted additive valuations, that is, every good has some<br>non-negative value, and every agent is interested in only some of the goods.<br> We introduce a natural relaxation of EFX called EFkX which requires that no<br>agent envies another agent after removal of any $k$ goods. Our main<br>contribution is an algorithm that finds a complete (i.e., no good is discarded)<br>EF2X allocation for the restricted additive valuations. In our algorithm we<br>devise new concepts, namely "configuration" and "envy-elimination" that might<br>be of independent interest.<br> We also use our new tools to find an EFX allocation for restricted additive<br>valuations that discards at most $\lfloor n/2 \rfloor -1$ goods. This improves<br>the state of the art for the restricted additive valuations by a factor of $2$.<br> %K Computer Science, Computer Science and Game Theory, cs.GT
[43]
G. Amanatidis and P. Kleer, “Rapid Mixing of the Switch Markov Chain for 2-Class Joint Degree Matrices,” SIAM Journal on Discrete Mathematics, vol. 36, no. 1, 2022.
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@article{Amanatidis2022, TITLE = {Rapid Mixing of the Switch {M}arkov Chain for 2-Class Joint Degree Matrices}, AUTHOR = {Amanatidis, Georgios and Kleer, Pieter}, LANGUAGE = {eng}, ISSN = {0895-4801}, DOI = {10.1137/20M1352697}, PUBLISHER = {The Society}, ADDRESS = {Philadelphia, Pa.}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {36}, NUMBER = {1}, PAGES = {118--146}, }
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 2-Class Joint Degree Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-000A-567A-D %R 10.1137/20M1352697 %7 2022 %D 2022 %J SIAM Journal on Discrete Mathematics %V 36 %N 1 %& 118 %P 118 - 146 %I The Society %C Philadelphia, Pa. %@ false
[44]
S. A. Amiri and B. Wiederhake, “Distributed Distance-r Dominating Set on Sparse High-Girth Graphs,” Theoretical Computer Science, vol. 906, 2022.
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@article{Amiri22, TITLE = {Distributed Distance-$r$ Dominating Set on Sparse High-Girth Graphs}, AUTHOR = {Amiri, Saeed Akhoondian and Wiederhake, Ben}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2022.01.001}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Theoretical Computer Science}, VOLUME = {906}, PAGES = {18--31}, }
Endnote
%0 Journal Article %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/21.11116/0000-000A-9DFE-8 %R 10.1016/j.tcs.2022.01.001 %7 2022 %D 2022 %J Theoretical Computer Science %V 906 %& 18 %P 18 - 31 %I Elsevier %C Amsterdam %@ false
[45]
I. Anagnostides, C. Lenzen, B. Haeupler, G. Zuzic, and T. Gouleakis, “Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts,” in 36th International Symposium on Distributed Computing (DISC 2022), Augusta, GA, USA, 2022.
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@inproceedings{Anagnostides_DISC22, TITLE = {Almost Universally Optimal Distributed {L}aplacian Solvers via Low-Congestion Shortcuts}, AUTHOR = {Anagnostides, Ioannis and Lenzen, Christoph and Haeupler, Bernhard and Zuzic, Goran and Gouleakis, Themis}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-210-5}, URL = {urn:nbn:de:0030-drops-171978}, DOI = {10.4230/LIPIcs.DISC.2022.6}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {36th International Symposium on Distributed Computing (DISC 2022)}, EDITOR = {Scheideler, Christian}, PAGES = {1--20}, EID = {6}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {246}, ADDRESS = {Augusta, GA, USA}, }
Endnote
%0 Conference Proceedings %A Anagnostides, Ioannis %A Lenzen, Christoph %A Haeupler, Bernhard %A Zuzic, Goran %A Gouleakis, Themis %+ External Organizations 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 %T Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts : %G eng %U http://hdl.handle.net/21.11116/0000-000C-7314-C %R 10.4230/LIPIcs.DISC.2022.6 %U urn:nbn:de:0030-drops-171978 %D 2022 %B 36th International Symposium on Distributed Computing %Z date of event: 2022-10-25 - 2022-10-27 %C Augusta, GA, USA %B 36th International Symposium on Distributed Computing %E Scheideler, Christian %P 1 - 20 %Z sequence number: 6 %I Schloss Dagstuhl %@ 978-3-95977-210-5 %B Leibniz International Proceedings in Informatics %N 246 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2022/17197/https://creativecommons.org/licenses/by/4.0/legalcode
[46]
H. An, M. Gurumukhani, R. Impagliazzo, M. Jaber, M. Künnemann, and M. P. Parga Nina, “The Fine-Grained Complexity of Multi-Dimensional Ordering Properties,” Algorithmica, vol. 84, 2022.
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@article{An22, TITLE = {The Fine-Grained Complexity of Multi-Dimensional Ordering Properties}, AUTHOR = {An, Haozhe and Gurumukhani, Mohit and Impagliazzo, Russell and Jaber, Michael and K{\"u}nnemann, Marvin and Parga Nina, Maria Paula}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-022-01014-x}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, VOLUME = {84}, PAGES = {3156--3191}, }
Endnote
%0 Journal Article %A An, Haozhe %A Gurumukhani, Mohit %A Impagliazzo, Russell %A Jaber, Michael %A K&#252;nnemann, Marvin %A Parga Nina, Maria Paula %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T The Fine-Grained Complexity of Multi-Dimensional Ordering Properties : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F9C-3 %R 10.1007/s00453-022-01014-x %7 2022 %D 2022 %J Algorithmica %V 84 %& 3156 %P 3156 - 3191 %I Springer-Verlag %C New York %@ false
[47]
A. Antoniadis, P. Jabbarzade, and G. Shahkarami, “A Novel Prediction Setup for Online Speed-Scaling,” in 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022), Tórshavn, Faroe Islands, 2022.
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@inproceedings{AntoniadisSWAT22, TITLE = {A Novel Prediction Setup for Online Speed-Scaling}, AUTHOR = {Antoniadis, Antonios and Jabbarzade, Peyman and Shahkarami, Golnoosh}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-236-5}, URL = {urn:nbn:de:0030-drops-161693; https://drops.dagstuhl.de/opus/volltexte/2022/16169/}, DOI = {10.4230/LIPIcs.SWAT.2022.9}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)}, EDITOR = {Czumai, Artur and Xin, Qin}, PAGES = {1--20}, EID = {9}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {227}, ADDRESS = {T{\'o}rshavn, Faroe Islands}, }
Endnote
%0 Conference Proceedings %A Antoniadis, Antonios %A Jabbarzade, Peyman %A Shahkarami, Golnoosh %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Novel Prediction Setup for Online Speed-Scaling : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FBA-1 %R 10.4230/LIPIcs.SWAT.2022.9 %U urn:nbn:de:0030-drops-161693 %U https://drops.dagstuhl.de/opus/volltexte/2022/16169/ %D 2022 %B 18th Scandinavian Symposium and Workshops on Algorithm Theory %Z date of event: 2022-06-27 - 2022-06-29 %C T&#243;rshavn, Faroe Islands %B 18th Scandinavian Symposium and Workshops on Algorithm Theory %E Czumai, Artur; Xin, Qin %P 1 - 20 %Z sequence number: 9 %I Schloss Dagstuhl %@ 978-3-95977-236-5 %B Leibniz International Proceedings in Informatics %N 227 %@ false
[48]
A. Antoniadis, P. Jabbarzade Ganje, and G. Shahkarami, “A Novel Prediction Setup for Online Speed-Scaling,” 2022. [Online]. Available: https://arxiv.org/abs/2112.03082. (arXiv: 2112.03082)
Abstract
Given the rapid rise in energy demand by data centers and computing systems<br>in general, it is fundamental to incorporate energy considerations when<br>designing (scheduling) algorithms. Machine learning can be a useful approach in<br>practice by predicting the future load of the system based on, for example,<br>historical data. However, the effectiveness of such an approach highly depends<br>on the quality of the predictions and can be quite far from optimal when<br>predictions are sub-par. On the other hand, while providing a worst-case<br>guarantee, classical online algorithms can be pessimistic for large classes of<br>inputs arising in practice.<br> This paper, in the spirit of the new area of machine learning augmented<br>algorithms, attempts to obtain the best of both worlds for the classical,<br>deadline based, online speed-scaling problem: Based on the introduction of a<br>novel prediction setup, we develop algorithms that (i) obtain provably low<br>energy-consumption in the presence of adequate predictions, and (ii) are robust<br>against inadequate predictions, and (iii) are smooth, i.e., their performance<br>gradually degrades as the prediction error increases.<br>
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@online{Antoniadis2112.03082, TITLE = {A Novel Prediction Setup for Online Speed-Scaling}, AUTHOR = {Antoniadis, Antonios and Jabbarzade Ganje, Peyman and Shahkarami, Golnoosh}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2112.03082}, EPRINT = {2112.03082}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Given the rapid rise in energy demand by data centers and computing systems<br>in general, it is fundamental to incorporate energy considerations when<br>designing (scheduling) algorithms. Machine learning can be a useful approach in<br>practice by predicting the future load of the system based on, for example,<br>historical data. However, the effectiveness of such an approach highly depends<br>on the quality of the predictions and can be quite far from optimal when<br>predictions are sub-par. On the other hand, while providing a worst-case<br>guarantee, classical online algorithms can be pessimistic for large classes of<br>inputs arising in practice.<br> This paper, in the spirit of the new area of machine learning augmented<br>algorithms, attempts to obtain the best of both worlds for the classical,<br>deadline based, online speed-scaling problem: Based on the introduction of a<br>novel prediction setup, we develop algorithms that (i) obtain provably low<br>energy-consumption in the presence of adequate predictions, and (ii) are robust<br>against inadequate predictions, and (iii) are smooth, i.e., their performance<br>gradually degrades as the prediction error increases.<br>}, }
Endnote
%0 Report %A Antoniadis, Antonios %A Jabbarzade Ganje, Peyman %A Shahkarami, Golnoosh %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Novel Prediction Setup for Online Speed-Scaling : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FBE-D %U https://arxiv.org/abs/2112.03082 %D 2022 %X Given the rapid rise in energy demand by data centers and computing systems<br>in general, it is fundamental to incorporate energy considerations when<br>designing (scheduling) algorithms. Machine learning can be a useful approach in<br>practice by predicting the future load of the system based on, for example,<br>historical data. However, the effectiveness of such an approach highly depends<br>on the quality of the predictions and can be quite far from optimal when<br>predictions are sub-par. On the other hand, while providing a worst-case<br>guarantee, classical online algorithms can be pessimistic for large classes of<br>inputs arising in practice.<br> This paper, in the spirit of the new area of machine learning augmented<br>algorithms, attempts to obtain the best of both worlds for the classical,<br>deadline based, online speed-scaling problem: Based on the introduction of a<br>novel prediction setup, we develop algorithms that (i) obtain provably low<br>energy-consumption in the presence of adequate predictions, and (ii) are robust<br>against inadequate predictions, and (iii) are smooth, i.e., their performance<br>gradually degrades as the prediction error increases.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Learning, cs.LG
[49]
S. Apers, Y. Efron, P. Gawrychowski, T. Lee, S. Mukhopadhyay, and D. Nanongkai, “Cut Query Algorithms with Star Contraction,” in FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science, Denver, CO, USA, 2022.
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@inproceedings{Apers_FOCS22, TITLE = {Cut Query Algorithms with Star Contraction}, AUTHOR = {Apers, Simon and Efron, Yuval and Gawrychowski, Pawe{\l} and Lee, Troy and Mukhopadhyay, Sagnik and Nanongkai, Danupon}, LANGUAGE = {eng}, ISBN = {978-1-6654-5519-0}, DOI = {10.1109/FOCS54457.2022.00055}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science}, PAGES = {507--518}, ADDRESS = {Denver, CO, USA}, }
Endnote
%0 Conference Proceedings %A Apers, Simon %A Efron, Yuval %A Gawrychowski, Pawe&#322; %A Lee, Troy %A Mukhopadhyay, Sagnik %A Nanongkai, Danupon %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Cut Query Algorithms with Star Contraction : %G eng %U http://hdl.handle.net/21.11116/0000-000C-26C5-B %R 10.1109/FOCS54457.2022.00055 %D 2022 %B IEEE 63rd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-10-31 - 2022-11-03 %C Denver, CO, USA %B FOCS 2022 %P 507 - 518 %I IEEE %@ 978-1-6654-5519-0
[50]
B. Banyassady, M. de Berg, K. Bringmann, K. Buchin, H. Fernau, D. Halperin, I. Kostitsyna, Y. Okamoto, and S. Slot, “Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds,” in 38th International Symposium on Computational Geometry (SoCG 2022), Berlin, Germany, 2022.
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@inproceedings{Banyassady_SoCG2022, TITLE = {Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds}, AUTHOR = {Banyassady, Bahareh and de Berg, Mark and Bringmann, Karl and Buchin, Kevin and Fernau, Henning and Halperin, Dan and Kostitsyna, Irina and Okamoto, Yoshio and Slot, Stijn}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-227-3}, URL = {urn:nbn:de:0030-drops-160203}, DOI = {10.4230/LIPIcs.SoCG.2022.12}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {38th International Symposium on Computational Geometry (SoCG 2022)}, EDITOR = {Goaoc, Xavier and Kerber, Michael}, PAGES = {1--16}, EID = {12}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {224}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Banyassady, Bahareh %A de Berg, Mark %A Bringmann, Karl %A Buchin, Kevin %A Fernau, Henning %A Halperin, Dan %A Kostitsyna, Irina %A Okamoto, Yoshio %A Slot, Stijn %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations %T Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds : %G eng %U http://hdl.handle.net/21.11116/0000-000B-1553-0 %R 10.4230/LIPIcs.SoCG.2022.12 %U urn:nbn:de:0030-drops-160203 %D 2022 %B 38th International Symposium on Computational Geometry %Z date of event: 2022-06-07 - 2022-06-10 %C Berlin, Germany %B 38th International Symposium on Computational Geometry %E Goaoc, Xavier; Kerber, Michael %P 1 - 16 %Z sequence number: 12 %I Schloss Dagstuhl %@ 978-3-95977-227-3 %B Leibniz International Proceedings in Informatics %N 224 %@ false
[51]
R. Beier, H. Röglin, C. Rösner, and B. Vöcking, “The Smoothed Number of Pareto-optimal Solutions in Bicriteria Integer Optimization,” Mathematical Programming / A, 2022.
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@article{Beier2022, TITLE = {The smoothed number of {P}areto-optimal solutions in bicriteria integer optimization}, AUTHOR = {Beier, Ren{\'e} and R{\"o}glin, Heiko and R{\"o}sner, Clemens and V{\"o}cking, Berthold}, LANGUAGE = {eng}, ISSN = {0025-5610}, DOI = {10.1007/s10107-022-01885-6}, PUBLISHER = {Springer}, ADDRESS = {Heidelberg}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Mathematical Programming / A}, }
Endnote
%0 Journal Article %A Beier, Ren&#233; %A R&#246;glin, Heiko %A R&#246;sner, Clemens %A V&#246;cking, Berthold %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T The Smoothed Number of Pareto-optimal Solutions in Bicriteria Integer Optimization : %G eng %U http://hdl.handle.net/21.11116/0000-000B-58A2-B %R 10.1007/s10107-022-01885-6 %7 2022 %D 2022 %J Mathematical Programming / A %I Springer %C Heidelberg %@ false
[52]
A. Bernstein, D. Nanongkai, and C. Wulff-Nilsen, “Negative-Weight Single-Source Shortest Paths in Near-linear Time,” in FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science, Denver, CO, USA, 2022.
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@inproceedings{Bernstein_FOCS22, TITLE = {Negative-Weight Single-Source Shortest Paths in Near-linear Time}, AUTHOR = {Bernstein, Aaron and Nanongkai, Danupon and Wulff-Nilsen, Christian}, LANGUAGE = {eng}, ISBN = {978-1-6654-5519-0}, DOI = {10.1109/FOCS54457.2022.00063}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science}, PAGES = {600--611}, ADDRESS = {Denver, CO, USA}, }
Endnote
%0 Conference Proceedings %A Bernstein, Aaron %A Nanongkai, Danupon %A Wulff-Nilsen, Christian %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Negative-Weight Single-Source Shortest Paths in Near-linear Time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-26C9-7 %R 10.1109/FOCS54457.2022.00063 %D 2022 %B IEEE 63rd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-10-31 - 2022-11-03 %C Denver, CO, USA %B FOCS 2022 %P 600 - 611 %I IEEE %@ 978-1-6654-5519-0
[53]
S. Bhattacharya, P. Kiss, and T. Saranurak, “Sublinear Algorithms for (1.5+Epsilon)-Approximate Matching,” 2022. [Online]. Available: https://arxiv.org/abs/2212.00189. (arXiv: 2212.00189)
Abstract
We study sublinear time algorithms for estimating the size of maximum<br>matching. After a long line of research, the problem was finally settled by<br>Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation<br>factor of $2$. Very recently, Behnezhad et al.[SODA'23] improved the<br>approximation factor to $(2-\frac{1}{2^{O(1/\gamma)}})$ using $n^{1+\gamma}$<br>time. This improvement over the factor $2$ is, however, minuscule and they<br>asked if even $1.99$-approximation is possible in $n^{2-\Omega(1)}$ time. We<br>give a strong affirmative answer to this open problem by showing<br>$(1.5+\epsilon)$-approximation algorithms that run in<br>$n^{2-\Theta(\epsilon^{2})}$ time. Our approach is conceptually simple and<br>diverges from all previous sublinear-time matching algorithms: we show a<br>sublinear time algorithm for computing a variant of the edge-degree constrained<br>subgraph (EDCS), a concept that has previously been exploited in dynamic<br>[Bernstein Stein ICALP'15, SODA'16], distributed [Assadi et al. SODA'19] and<br>streaming [Bernstein ICALP'20] settings, but never before in the sublinear<br>setting. Independent work: Behnezhad, Roghani and Rubinstein [BRR'23]<br>independently showed sublinear algorithms similar to our Theorem 1.2 in both<br>adjacency list and matrix models. Furthermore, in [BRR'23], they show<br>additional results on strictly better-than-1.5 approximate matching algorithms<br>in both upper and lower bound sides.<br>
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@online{Bhattacharya2212.00189, TITLE = {Sublinear Algorithms for $(1.5+\epsilon)$-Approximate Matching}, AUTHOR = {Bhattacharya, Sayan and Kiss, Peter and Saranurak, Thatchaphol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2212.00189}, EPRINT = {2212.00189}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study sublinear time algorithms for estimating the size of maximum<br>matching. After a long line of research, the problem was finally settled by<br>Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation<br>factor of $2$. Very recently, Behnezhad et al.[SODA'23] improved the<br>approximation factor to $(2-\frac{1}{2^{O(1/\gamma)}})$ using $n^{1+\gamma}$<br>time. This improvement over the factor $2$ is, however, minuscule and they<br>asked if even $1.99$-approximation is possible in $n^{2-\Omega(1)}$ time. We<br>give a strong affirmative answer to this open problem by showing<br>$(1.5+\epsilon)$-approximation algorithms that run in<br>$n^{2-\Theta(\epsilon^{2})}$ time. Our approach is conceptually simple and<br>diverges from all previous sublinear-time matching algorithms: we show a<br>sublinear time algorithm for computing a variant of the edge-degree constrained<br>subgraph (EDCS), a concept that has previously been exploited in dynamic<br>[Bernstein Stein ICALP'15, SODA'16], distributed [Assadi et al. SODA'19] and<br>streaming [Bernstein ICALP'20] settings, but never before in the sublinear<br>setting. Independent work: Behnezhad, Roghani and Rubinstein [BRR'23]<br>independently showed sublinear algorithms similar to our Theorem 1.2 in both<br>adjacency list and matrix models. Furthermore, in [BRR'23], they show<br>additional results on strictly better-than-1.5 approximate matching algorithms<br>in both upper and lower bound sides.<br>}, }
Endnote
%0 Report %A Bhattacharya, Sayan %A Kiss, Peter %A Saranurak, Thatchaphol %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Sublinear Algorithms for (1.5+Epsilon)-Approximate Matching : %G eng %U http://hdl.handle.net/21.11116/0000-000C-2696-0 %U https://arxiv.org/abs/2212.00189 %D 2022 %X We study sublinear time algorithms for estimating the size of maximum<br>matching. After a long line of research, the problem was finally settled by<br>Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation<br>factor of $2$. Very recently, Behnezhad et al.[SODA'23] improved the<br>approximation factor to $(2-\frac{1}{2^{O(1/\gamma)}})$ using $n^{1+\gamma}$<br>time. This improvement over the factor $2$ is, however, minuscule and they<br>asked if even $1.99$-approximation is possible in $n^{2-\Omega(1)}$ time. We<br>give a strong affirmative answer to this open problem by showing<br>$(1.5+\epsilon)$-approximation algorithms that run in<br>$n^{2-\Theta(\epsilon^{2})}$ time. Our approach is conceptually simple and<br>diverges from all previous sublinear-time matching algorithms: we show a<br>sublinear time algorithm for computing a variant of the edge-degree constrained<br>subgraph (EDCS), a concept that has previously been exploited in dynamic<br>[Bernstein Stein ICALP'15, SODA'16], distributed [Assadi et al. SODA'19] and<br>streaming [Bernstein ICALP'20] settings, but never before in the sublinear<br>setting. Independent work: Behnezhad, Roghani and Rubinstein [BRR'23]<br>independently showed sublinear algorithms similar to our Theorem 1.2 in both<br>adjacency list and matrix models. Furthermore, in [BRR'23], they show<br>additional results on strictly better-than-1.5 approximate matching algorithms<br>in both upper and lower bound sides.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[54]
J. Blikstad, J. V. D. Brand, Y. Efron, S. Mukhopadhyay, and D. Nanongkai, “Nearly Optimal Communication and Query Complexity of Bipartite Matching,” in FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science, Denver, CO, USA, 2022.
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@inproceedings{Blikstad_FOCS22, TITLE = {Nearly Optimal Communication and Query Complexity of Bipartite Matching}, AUTHOR = {Blikstad, Joakim and Brand, Jan Van Den and Efron, Yuval and Mukhopadhyay, Sagnik and Nanongkai, Danupon}, LANGUAGE = {eng}, ISBN = {978-1-6654-5519-0}, DOI = {10.1109/FOCS54457.2022.00113}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science}, PAGES = {1174--1185}, ADDRESS = {Denver, CO, USA}, }
Endnote
%0 Conference Proceedings %A Blikstad, Joakim %A Brand, Jan Van Den %A Efron, Yuval %A Mukhopadhyay, Sagnik %A Nanongkai, Danupon %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Nearly Optimal Communication and Query Complexity of Bipartite Matching : %G eng %U http://hdl.handle.net/21.11116/0000-000C-26CF-1 %R 10.1109/FOCS54457.2022.00113 %D 2022 %B IEEE 63rd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-10-31 - 2022-11-03 %C Denver, CO, USA %B FOCS 2022 %P 1174 - 1185 %I IEEE %@ 978-1-6654-5519-0
[55]
V. Bonifaci, E. Facca, F. Folz, A. Karrenbauer, P. Kolev, K. Mehlhorn, G. Morigi, G. Shahkarami, and Q. Vermande, “Physarum-inspired Multi-commodity Flow Dynamics,” Theoretical Computer Science, vol. 920, 2022.
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@article{Bonifaci2022, TITLE = {Physarum-inspired 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}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2022.02.001}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Theoretical Computer Science}, VOLUME = {920}, PAGES = {1--20}, }
Endnote
%0 Journal Article %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-inspired Multi-commodity Flow Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-000A-28A1-3 %R 10.1016/j.tcs.2022.02.001 %7 2022 %D 2022 %J Theoretical Computer Science %V 920 %& 1 %P 1 - 20 %I Elsevier %C Amsterdam %@ false
[56]
S. Boodaghians, B. Ray Chaudhury, and R. Mehta, “Polynomial Time Algorithms to Find an Approximate Competitive Equilibrium for Chores,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022), Virtual, 2022.
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@inproceedings{Boodaghians_SODA22b, TITLE = {Polynomial Time Algorithms to Find an Approximate Competitive Equilibrium for Chores}, AUTHOR = {Boodaghians, Shant and Ray Chaudhury, Bhaskar and Mehta, Ruta}, LANGUAGE = {eng}, ISBN = {978-1-61197-707-3}, DOI = {10.1137/1.9781611977073}, PUBLISHER = {SIAM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022)}, EDITOR = {Naor, Seffi and Buchbinder, Niv}, PAGES = {2285--2302}, ADDRESS = {Virtual}, }
Endnote
%0 Conference Proceedings %A Boodaghians, Shant %A Ray Chaudhury, Bhaskar %A Mehta, Ruta %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Polynomial Time Algorithms to Find an Approximate Competitive Equilibrium for Chores : %G eng %U http://hdl.handle.net/21.11116/0000-000C-A3BB-9 %R 10.1137/1.9781611977073 %D 2022 %B Thirty-Third Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2022-01-09 - 2022-01-12 %C Virtual %B Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms %E Naor, Seffi; Buchbinder, Niv %P 2285 - 2302 %I SIAM %@ 978-1-61197-707-3
[57]
M. Briański, G. Joret, K. Majewski, P. Micek, M. T. Seweryn, and R. Sharma, “Treedepth Vs Circumference,” 2022. [Online]. Available: https://arxiv.org/abs/2211.11410. (arXiv: 2211.11410)
Abstract
The circumference of a graph $G$ is the length of a longest cycle in $G$, or<br>$+\infty$ if $G$ has no cycle. Birmel\'e (2003) showed that the treewidth of a<br>graph $G$ is at most its circumference minus one. We strengthen this result for<br>$2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth is<br>at most its circumference. The bound is best possible and improves on an<br>earlier quadratic upper bound due to Marshall and Wood (2015).<br>
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@online{Brianski2211.11410, TITLE = {Treedepth Vs Circumference}, AUTHOR = {Bria{\'n}ski, Marcin and Joret, Gwena{\"e}l and Majewski, Konrad and Micek, Piotr and Seweryn, Micha{\l} T. and Sharma, Roohani}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2211.11410}, EPRINT = {2211.11410}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The circumference of a graph $G$ is the length of a longest cycle in $G$, or<br>$+\infty$ if $G$ has no cycle. Birmel\'e (2003) showed that the treewidth of a<br>graph $G$ is at most its circumference minus one. We strengthen this result for<br>$2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth is<br>at most its circumference. The bound is best possible and improves on an<br>earlier quadratic upper bound due to Marshall and Wood (2015).<br>}, }
Endnote
%0 Report %A Bria&#324;ski, Marcin %A Joret, Gwena&#235;l %A Majewski, Konrad %A Micek, Piotr %A Seweryn, Micha&#322; T. %A Sharma, Roohani %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Treedepth Vs Circumference : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1E81-1 %U https://arxiv.org/abs/2211.11410 %D 2022 %X The circumference of a graph $G$ is the length of a longest cycle in $G$, or<br>$+\infty$ if $G$ has no cycle. Birmel\'e (2003) showed that the treewidth of a<br>graph $G$ is at most its circumference minus one. We strengthen this result for<br>$2$-connected graphs as follows: If $G$ is $2$-connected, then its treedepth is<br>at most its circumference. The bound is best possible and improves on an<br>earlier quadratic upper bound due to Marshall and Wood (2015).<br> %K Mathematics, Combinatorics, math.CO,Computer Science, Discrete Mathematics, cs.DM
[58]
K. Bringmann, A. Cassis, N. Fischer, and V. Nakos, “Almost-Optimal Sublinear-Time Edit Distance in the Low Distance Regime,” in STOC ’22, 54th Annual ACM Symposium on Theory of Computing, Rome, Italy, 2022.
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@inproceedings{BringmannSTOC22, TITLE = {Almost-Optimal Sublinear-Time Edit Distance in the Low Distance Regime}, AUTHOR = {Bringmann, Karl and Cassis, Alejandro and Fischer, Nick and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {978-1-4503-9264-8}, DOI = {10.1145/3519935.3519990}, PUBLISHER = {ACM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '22, 54th Annual ACM Symposium on Theory of Computing}, EDITOR = {Leonardi, Stefano and Gupta, Anupam}, PAGES = {1102--1115}, ADDRESS = {Rome, Italy}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Cassis, Alejandro %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 External Organizations %T Almost-Optimal Sublinear-Time Edit Distance in the Low Distance Regime : %G eng %U http://hdl.handle.net/21.11116/0000-000B-588D-4 %R 10.1145/3519935.3519990 %D 2022 %B 54th Annual ACM Symposium on Theory of Computing %Z date of event: 2022-06-20 - 2022-06-24 %C Rome, Italy %B STOC '22 %E Leonardi, Stefano; Gupta, Anupam %P 1102 - 1115 %I ACM %@ 978-1-4503-9264-8
[59]
K. Bringmann, A. Driemel, A. Nusser, and I. Psarros, “Tight Bounds for Approximate Near Neighbor Searching for Time Series under the Fréchet Distance,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022), Virtual, 2022.
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@inproceedings{Bringmann_SODA22, TITLE = {Tight Bounds for Approximate Near Neighbor Searching for Time Series under the {F}r\'{e}chet Distance}, AUTHOR = {Bringmann, Karl and Driemel, Anne and Nusser, Andr{\'e} and Psarros, Ioannis}, LANGUAGE = {eng}, ISBN = {978-1-61197-707-3}, DOI = {10.1137/1.9781611977073.25}, PUBLISHER = {SIAM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022)}, EDITOR = {Naor, Seffi and Buchbinder, Niv}, PAGES = {517--550}, ADDRESS = {Virtual}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Driemel, Anne %A Nusser, Andr&#233; %A Psarros, Ioannis %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Tight Bounds for Approximate Near Neighbor Searching for Time Series under the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1D7D-9 %R 10.1137/1.9781611977073.25 %D 2022 %B Thirty-Third Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2022-01-09 - 2022-01-12 %C Virtual %B Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms %E Naor, Seffi; Buchbinder, Niv %P 517 - 550 %I SIAM %@ 978-1-61197-707-3
[60]
K. Bringmann, N. Fischer, and V. Nakos, “Deterministic and Las Vegas Algorithms for Sparse Nonnegative Convolution,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022), Virtual, 2022.
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@inproceedings{Bringmann_SODA22b, TITLE = {Deterministic and {Las Vegas} Algorithms for Sparse Nonnegative Convolution}, AUTHOR = {Bringmann, Karl and Fischer, Nick and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {978-1-61197-707-3}, DOI = {10.1137/1.9781611977073.119}, PUBLISHER = {SIAM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022)}, EDITOR = {Naor, Seffi and Buchbinder, Niv}, PAGES = {3069--3090}, ADDRESS = {Virtual}, }
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 Deterministic and Las Vegas Algorithms for Sparse Nonnegative Convolution : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1D81-2 %R 10.1137/1.9781611977073.119 %D 2022 %B Thirty-Third Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2022-01-09 - 2022-01-12 %C Virtual %B Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms %E Naor, Seffi; Buchbinder, Niv %P 3069 - 3090 %I SIAM %@ 978-1-61197-707-3
[61]
K. Bringmann, R. Keusch, J. Lengler, Y. Maus, and A. R. Molla, “Greedy Routing and the Algorithmic Small-World Phenomenon,” Journal of Computer and System Sciences, vol. 125, 2022.
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@article{Bringmann22, TITLE = {Greedy Routing and the Algorithmic Small-World Phenomenon}, AUTHOR = {Bringmann, Karl and Keusch, Ralph and Lengler, Johannes and Maus, Yannic and Molla, Anisur Rahaman}, LANGUAGE = {eng}, ISSN = {0022-0000}, DOI = {10.1016/j.jcss.2021.11.003}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Computer and System Sciences}, VOLUME = {125}, PAGES = {59--105}, }
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%0 Journal Article %A Bringmann, Karl %A Keusch, Ralph %A Lengler, Johannes %A Maus, Yannic %A Molla, Anisur Rahaman %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Greedy Routing and the Algorithmic Small-World Phenomenon : %G eng %U http://hdl.handle.net/21.11116/0000-000A-9DD0-A %R 10.1016/j.jcss.2021.11.003 %7 2022 %D 2022 %J Journal of Computer and System Sciences %V 125 %& 59 %P 59 - 105 %I Elsevier %C Amsterdam %@ false
[62]
K. Bringmann, N. Fischer, D. Hermelin, D. Shabtay, and P. Wellnitz, “Faster Minimization of Tardy Processing Time on a Single Machine,” Algorithmica, vol. 84, 2022.
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@article{Bringmann2022, 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 = {0178-4617}, DOI = {10.1007/s00453-022-00928-w}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Algorithmica}, VOLUME = {84}, PAGES = {1341--1356}, }
Endnote
%0 Journal Article %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/21.11116/0000-0009-FAD4-E %R 10.1007/s00453-022-00928-w %7 2022 %D 2022 %J Algorithmica %V 84 %& 1341 %P 1341 - 1356 %I Springer %C New York %@ false %U https://rdcu.be/cG2A9
[63]
K. Bringmann, S. Kisfaludi-Bak, M. Künnemann, D. Marx, and A. Nusser, “Dynamic Time Warping Under Translation: Approximation Guided by Space-Filling Curves,” in 38th International Symposium on Computational Geometry (SoCG 2022), Berlin, Germany, 2022.
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@inproceedings{Bringmann_SoCG2022, TITLE = {Dynamic Time Warping Under Translation: Approximation Guided by Space-Filling Curves}, AUTHOR = {Bringmann, Karl and Kisfaludi-Bak, S{\'a}ndor and K{\"u}nnemann, Marvin and Marx, D{\'a}niel and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-227-3}, URL = {urn:nbn:de:0030-drops-160287}, DOI = {10.4230/LIPIcs.SoCG.2022.20}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {38th International Symposium on Computational Geometry (SoCG 2022)}, EDITOR = {Goaoc, Xavier and Kerber, Michael}, PAGES = {1--17}, EID = {20}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {224}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Kisfaludi-Bak, S&#225;ndor %A K&#252;nnemann, Marvin %A Marx, D&#225;niel %A Nusser, Andr&#233; %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Dynamic Time Warping Under Translation: Approximation Guided by Space-Filling Curves : %G eng %U http://hdl.handle.net/21.11116/0000-000B-1560-1 %R 10.4230/LIPIcs.SoCG.2022.20 %U urn:nbn:de:0030-drops-160287 %D 2022 %B 38th International Symposium on Computational Geometry %Z date of event: 2022-06-07 - 2022-06-10 %C Berlin, Germany %B 38th International Symposium on Computational Geometry %E Goaoc, Xavier; Kerber, Michael %P 1 - 17 %Z sequence number: 20 %I Schloss Dagstuhl %@ 978-3-95977-227-3 %B Leibniz International Proceedings in Informatics %N 224 %@ false
[64]
K. Bringmann, S. Kisfaludi-Bak, M. Künnemann, A. Nusser, and Z. Parsaeian, “Towards Sub-Quadratic Diameter Computation in Geometric Intersection Graphs,” in 38th International Symposium on Computational Geometry (SoCG 2022), Berlin, Germany, 2022.
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@inproceedings{Bringmann_SoCG2022b, TITLE = {Towards Sub-Quadratic Diameter Computation in Geometric Intersection Graphs}, AUTHOR = {Bringmann, Karl and Kisfaludi-Bak, S{\'a}ndor and K{\"u}nnemann, Marvin and Nusser, Andr{\'e} and Parsaeian, Zahra}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-227-3}, URL = {urn:nbn:de:0030-drops-160294}, DOI = {10.4230/LIPIcs.SoCG.2022.21}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {38th International Symposium on Computational Geometry (SoCG 2022)}, EDITOR = {Goaoc, Xavier and Kerber, Michael}, PAGES = {1--16}, EID = {21}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {224}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Kisfaludi-Bak, S&#225;ndor %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %A Parsaeian, Zahra %+ 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 Towards Sub-Quadratic Diameter Computation in Geometric Intersection Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000B-1572-D %R 10.4230/LIPIcs.SoCG.2022.21 %U urn:nbn:de:0030-drops-160294 %D 2022 %B 38th International Symposium on Computational Geometry %Z date of event: 2022-06-07 - 2022-06-10 %C Berlin, Germany %B 38th International Symposium on Computational Geometry %E Goaoc, Xavier; Kerber, Michael %P 1 - 16 %Z sequence number: 21 %I Schloss Dagstuhl %@ 978-3-95977-227-3 %B Leibniz International Proceedings in Informatics %N 224 %@ false
[65]
K. Bringmann, A. Cassis, N. Fischer, and M. Künnemann, “A Structural Investigation of the Approximability of Polynomial-Time Problems,” in 49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022), Paris, France, 2022.
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@inproceedings{Bringmann_ICALP22, TITLE = {A Structural Investigation of the Approximability of Polynomial-Time Problems}, AUTHOR = {Bringmann, Karl and Cassis, Alejandro and Fischer, Nick and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, ISBN = {978-3-95977-235-8{\textbraceright}}, URL = {urn:nbn:de:0030-drops-163713}, DOI = {10.4230/LIPIcs.ICALP.2022.30}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022)}, EDITOR = {Boja{\'n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, PAGES = {1--20}, EID = {30}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {229}, ADDRESS = {Paris, France}, }
Endnote
%0 Conference Proceedings %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 A Structural Investigation of the Approximability of Polynomial-Time Problems : %G eng %U http://hdl.handle.net/21.11116/0000-000B-15B5-1 %R 10.4230/LIPIcs.ICALP.2022.30 %U urn:nbn:de:0030-drops-163713 %D 2022 %B 49th International Colloquium on Automata, Languages, and Programming %Z date of event: 2022-07-04 - 2022-07-08 %C Paris, France %B 49th EATCS International Conference on Automata, Languages, and Programming %E Boja&#324;czyk, Miko&#322;aj; Merelli, Emanuela; Woodruff, David P. %P 1 - 20 %Z sequence number: 30 %I Schloss Dagstuhl %@ 978-3-95977-235-8} %B Leibniz International Proceedings in Informatics %N 229
[66]
K. Bringmann, A. Cassis, N. Fischer, and V. Nakos, “Improved Sublinear-Time Edit Distance for Preprocessed Strings,” in 49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022), Paris, France, 2022.
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@inproceedings{Bringmann_ICALP22c, TITLE = {Improved Sublinear-Time Edit Distance for Preprocessed Strings}, AUTHOR = {Bringmann, Karl and Cassis, Alejandro and Fischer, Nick and Nakos, Vasileios}, LANGUAGE = {eng}, ISBN = {978-3-95977-235-8{\textbraceright}}, URL = {urn:nbn:de:0030-drops-163734}, DOI = {10.4230/LIPIcs.ICALP.2022.32}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022)}, EDITOR = {Boja{\'n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, PAGES = {1--20}, EID = {32}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {229}, ADDRESS = {Paris, France}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Cassis, Alejandro %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 External Organizations %T Improved Sublinear-Time Edit Distance for Preprocessed Strings : %G eng %U http://hdl.handle.net/21.11116/0000-000B-163A-C %R 10.4230/LIPIcs.ICALP.2022.32 %U urn:nbn:de:0030-drops-163734 %D 2022 %B 49th International Colloquium on Automata, Languages, and Programming %Z date of event: 2022-07-04 - 2022-07-08 %C Paris, France %B 49th EATCS International Conference on Automata, Languages, and Programming %E Boja&#324;czyk, Miko&#322;aj; Merelli, Emanuela; Woodruff, David P. %P 1 - 20 %Z sequence number: 32 %I Schloss Dagstuhl %@ 978-3-95977-235-8} %B Leibniz International Proceedings in Informatics %N 229
[67]
K. Bringmann and A. Cassis, “Faster Knapsack Algorithms via Bounded Monotone Min-Plus-Convolution,” in 49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022), Paris, France, 2022.
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@inproceedings{Bringmann_ICALP22b, TITLE = {Faster {K}napsack Algorithms via Bounded Monotone {Min-Plus-Convolution}}, AUTHOR = {Bringmann, Karl and Cassis, Alejandro}, LANGUAGE = {eng}, ISBN = {978-3-95977-235-8{\textbraceright}}, URL = {urn:nbn:de:0030-drops-163727}, DOI = {10.4230/LIPIcs.ICALP.2022.31}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022)}, EDITOR = {Boja{\'n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, PAGES = {1--21}, EID = {31}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {229}, ADDRESS = {Paris, France}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Cassis, Alejandro %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Knapsack Algorithms via Bounded Monotone Min-Plus-Convolution : %G eng %U http://hdl.handle.net/21.11116/0000-000B-1622-6 %R 10.4230/LIPIcs.ICALP.2022.31 %U urn:nbn:de:0030-drops-163727 %D 2022 %B 49th International Colloquium on Automata, Languages, and Programming %Z date of event: 2022-07-04 - 2022-07-08 %C Paris, France %B 49th EATCS International Conference on Automata, Languages, and Programming %E Boja&#324;czyk, Miko&#322;aj; Merelli, Emanuela; Woodruff, David P. %P 1 - 21 %Z sequence number: 31 %I Schloss Dagstuhl %@ 978-3-95977-235-8} %B Leibniz International Proceedings in Informatics %N 229
[68]
K. Bringmann, N. Carmeli, and S. Mengel, “Tight Fine-Grained Bounds for Direct Access on Join Queries,” in PODS ’22, 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, Philadelphia, PA, USA, 2022.
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@inproceedings{Bringmann_PODS22, TITLE = {Tight Fine-Grained Bounds for Direct Access on Join Queries}, AUTHOR = {Bringmann, Karl and Carmeli, Nofar and Mengel, Stefan}, LANGUAGE = {eng}, ISBN = {978-1-4503-9260-0}, DOI = {10.1145/3517804.3526234}, PUBLISHER = {ACM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {PODS '22, 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems}, EDITOR = {Libkin, Leonid and Barcel{\'o}, Pablo and Grez, Alejandro}, PAGES = {427--436}, ADDRESS = {Philadelphia, PA, USA}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Carmeli, Nofar %A Mengel, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Tight Fine-Grained Bounds for Direct Access on Join Queries : %G eng %U http://hdl.handle.net/21.11116/0000-000B-2037-3 %R 10.1145/3517804.3526234 %D 2022 %B 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems %Z date of event: 2022-06-12 - 2022-06-17 %C Philadelphia, PA, USA %B PODS '22 %E Libkin, Leonid; Barcel&#243;, Pablo; Grez, Alejandro %P 427 - 436 %I ACM %@ 978-1-4503-9260-0
[69]
K. Buchin, A. Nusser, and S. Wong, “Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time,” in 38th International Symposium on Computational Geometry (SoCG 2022), Berlin, Germany, 2022.
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@inproceedings{Buchin_SoCG2022a, TITLE = {Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time}, AUTHOR = {Buchin, Kevin and Nusser, Andr{\'e} and Wong, Sampson}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-227-3}, URL = {urn:nbn:de:0030-drops-160307}, DOI = {10.4230/LIPIcs.SoCG.2022.22}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {38th International Symposium on Computational Geometry (SoCG 2022)}, EDITOR = {Goaoc, Xavier and Kerber, Michael}, PAGES = {1--16}, EID = {22}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {224}, ADDRESS = {Berlin, Germany}, }
Endnote
%0 Conference Proceedings %A Buchin, Kevin %A Nusser, Andr&#233; %A Wong, Sampson %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-268B-D %R 10.4230/LIPIcs.SoCG.2022.22 %U urn:nbn:de:0030-drops-160307 %D 2022 %B 38th International Symposium on Computational Geometry %Z date of event: 2022-06-07 - 2022-06-10 %C Berlin, Germany %B 38th International Symposium on Computational Geometry %E Goaoc, Xavier; Kerber, Michael %P 1 - 16 %Z sequence number: 22 %I Schloss Dagstuhl %@ 978-3-95977-227-3 %B Leibniz International Proceedings in Informatics %N 224 %@ false
[70]
M. Caoduro, J. Cslovjecsek, M. Pilipczuk, and K. Węgrzycki, “Independence Number of Intersection Graphs of Axis-Parallel Segments,” 2022. [Online]. Available: https://arxiv.org/abs/2205.15189. (arXiv: 2205.15189)
Abstract
We prove that for any triangle-free intersection graph of $n$ axis-parallel<br>segments in the plane, the independence number $\alpha$ of this graph is at<br>least $\alpha \ge n/4 + \Omega(\sqrt{n})$. We complement this with a<br>construction of a graph in this class satisfying $\alpha \le n/4 + c \sqrt{n}$<br>for an absolute constant $c$, which demonstrates the optimality of our result.<br>
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@online{Caoduro2205.15189, TITLE = {Independence Number of Intersection Graphs of Axis-Parallel Segments}, AUTHOR = {Caoduro, Marco and Cslovjecsek, Jana and Pilipczuk, Micha{\l} and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2205.15189}, EPRINT = {2205.15189}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We prove that for any triangle-free intersection graph of $n$ axis-parallel<br>segments in the plane, the independence number $\alpha$ of this graph is at<br>least $\alpha \ge n/4 + \Omega(\sqrt{n})$. We complement this with a<br>construction of a graph in this class satisfying $\alpha \le n/4 + c \sqrt{n}$<br>for an absolute constant $c$, which demonstrates the optimality of our result.<br>}, }
Endnote
%0 Report %A Caoduro, Marco %A Cslovjecsek, Jana %A Pilipczuk, Micha&#322; %A W&#281;grzycki, Karol %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Independence Number of Intersection Graphs of Axis-Parallel Segments : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F1D-3 %U https://arxiv.org/abs/2205.15189 %D 2022 %X We prove that for any triangle-free intersection graph of $n$ axis-parallel<br>segments in the plane, the independence number $\alpha$ of this graph is at<br>least $\alpha \ge n/4 + \Omega(\sqrt{n})$. We complement this with a<br>construction of a graph in this class satisfying $\alpha \le n/4 + c \sqrt{n}$<br>for an absolute constant $c$, which demonstrates the optimality of our result.<br> %K Mathematics, Combinatorics, math.CO,Computer Science, Computational Geometry, cs.CG,Computer Science, Discrete Mathematics, cs.DM,
[71]
P. Charalampopoulos, T. Kociumaka, and P. Wellnitz, “Faster Pattern Matching under Edit Distance,” 2022. [Online]. Available: https://arxiv.org/abs/2204.03087. (arXiv: 2204.03087)
Abstract
We consider the approximate pattern matching problem under the edit distance.<br>Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold<br>$k$, the task is to find the starting positions of all substrings of $T$ that<br>can be transformed to $P$ with at most $k$ edits. More than 20 years ago, Cole<br>and Hariharan [SODA'98, J. Comput.'02] gave an $\mathcal{O}(n+k^4 \cdot n/<br>m)$-time algorithm for this classic problem, and this runtime has not been<br>improved since.<br> Here, we present an algorithm that runs in time $\mathcal{O}(n+k^{3.5}<br>\sqrt{\log m \log k} \cdot n/m)$, thus breaking through this long-standing<br>barrier. In the case where $n^{1/4+\varepsilon} \leq k \leq<br>n^{2/5-\varepsilon}$ for some arbitrarily small positive constant<br>$\varepsilon$, our algorithm improves over the state-of-the-art by polynomial<br>factors: it is polynomially faster than both the algorithm of Cole and<br>Hariharan and the classic $\mathcal{O}(kn)$-time algorithm of Landau and<br>Vishkin [STOC'86, J. Algorithms'89].<br> We observe that the bottleneck case of the alternative $\mathcal{O}(n+k^4<br>\cdot n/m)$-time algorithm of Charalampopoulos, Kociumaka, and Wellnitz<br>[FOCS'20] is when the text and the pattern are (almost) periodic. Our new<br>algorithm reduces this case to a new dynamic problem (Dynamic Puzzle Matching),<br>which we solve by building on tools developed by Tiskin [SODA'10,<br>Algorithmica'15] for the so-called seaweed monoid of permutation matrices. Our<br>algorithm relies only on a small set of primitive operations on strings and<br>thus also applies to the fully-compressed setting (where text and pattern are<br>given as straight-line programs) and to the dynamic setting (where we maintain<br>a collection of strings under creation, splitting, and concatenation),<br>improving over the state of the art.<br>
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@online{Charalampopoulos2204.03087, TITLE = {Faster Pattern Matching under Edit Distance}, AUTHOR = {Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Wellnitz, Philip}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2204.03087}, EPRINT = {2204.03087}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the approximate pattern matching problem under the edit distance.<br>Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold<br>$k$, the task is to find the starting positions of all substrings of $T$ that<br>can be transformed to $P$ with at most $k$ edits. More than 20 years ago, Cole<br>and Hariharan [SODA'98, J. Comput.'02] gave an $\mathcal{O}(n+k^4 \cdot n/<br>m)$-time algorithm for this classic problem, and this runtime has not been<br>improved since.<br> Here, we present an algorithm that runs in time $\mathcal{O}(n+k^{3.5}<br>\sqrt{\log m \log k} \cdot n/m)$, thus breaking through this long-standing<br>barrier. In the case where $n^{1/4+\varepsilon} \leq k \leq<br>n^{2/5-\varepsilon}$ for some arbitrarily small positive constant<br>$\varepsilon$, our algorithm improves over the state-of-the-art by polynomial<br>factors: it is polynomially faster than both the algorithm of Cole and<br>Hariharan and the classic $\mathcal{O}(kn)$-time algorithm of Landau and<br>Vishkin [STOC'86, J. Algorithms'89].<br> We observe that the bottleneck case of the alternative $\mathcal{O}(n+k^4<br>\cdot n/m)$-time algorithm of Charalampopoulos, Kociumaka, and Wellnitz<br>[FOCS'20] is when the text and the pattern are (almost) periodic. Our new<br>algorithm reduces this case to a new dynamic problem (Dynamic Puzzle Matching),<br>which we solve by building on tools developed by Tiskin [SODA'10,<br>Algorithmica'15] for the so-called seaweed monoid of permutation matrices. Our<br>algorithm relies only on a small set of primitive operations on strings and<br>thus also applies to the fully-compressed setting (where text and pattern are<br>given as straight-line programs) and to the dynamic setting (where we maintain<br>a collection of strings under creation, splitting, and concatenation),<br>improving over the state of the art.<br>}, }
Endnote
%0 Report %A Charalampopoulos, Panagiotis %A Kociumaka, Tomasz %A Wellnitz, Philip %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Pattern Matching under Edit Distance : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1EC9-1 %U https://arxiv.org/abs/2204.03087 %D 2022 %X We consider the approximate pattern matching problem under the edit distance.<br>Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold<br>$k$, the task is to find the starting positions of all substrings of $T$ that<br>can be transformed to $P$ with at most $k$ edits. More than 20 years ago, Cole<br>and Hariharan [SODA'98, J. Comput.'02] gave an $\mathcal{O}(n+k^4 \cdot n/<br>m)$-time algorithm for this classic problem, and this runtime has not been<br>improved since.<br> Here, we present an algorithm that runs in time $\mathcal{O}(n+k^{3.5}<br>\sqrt{\log m \log k} \cdot n/m)$, thus breaking through this long-standing<br>barrier. In the case where $n^{1/4+\varepsilon} \leq k \leq<br>n^{2/5-\varepsilon}$ for some arbitrarily small positive constant<br>$\varepsilon$, our algorithm improves over the state-of-the-art by polynomial<br>factors: it is polynomially faster than both the algorithm of Cole and<br>Hariharan and the classic $\mathcal{O}(kn)$-time algorithm of Landau and<br>Vishkin [STOC'86, J. Algorithms'89].<br> We observe that the bottleneck case of the alternative $\mathcal{O}(n+k^4<br>\cdot n/m)$-time algorithm of Charalampopoulos, Kociumaka, and Wellnitz<br>[FOCS'20] is when the text and the pattern are (almost) periodic. Our new<br>algorithm reduces this case to a new dynamic problem (Dynamic Puzzle Matching),<br>which we solve by building on tools developed by Tiskin [SODA'10,<br>Algorithmica'15] for the so-called seaweed monoid of permutation matrices. Our<br>algorithm relies only on a small set of primitive operations on strings and<br>thus also applies to the fully-compressed setting (where text and pattern are<br>given as straight-line programs) and to the dynamic setting (where we maintain<br>a collection of strings under creation, splitting, and concatenation),<br>improving over the state of the art.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[72]
P. Charalampopoulos, T. Kociumaka, and P. Wellnitz, “Faster Pattern Matching under Edit Distance: A Reduction to Dynamic Puzzle Matching and the Seaweed Monoid of Permutation Matrices,” in FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science, Denver, CO, USA, 2022.
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@inproceedings{Charalampopoulos_FOCS22, TITLE = {Faster Pattern Matching under Edit Distance: {A} Reduction to Dynamic Puzzle Matching and the Seaweed Monoid of Permutation Matrices}, AUTHOR = {Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Wellnitz, Philip}, LANGUAGE = {eng}, ISBN = {978-1-6654-5519-0}, DOI = {10.1109/FOCS54457.2022.00072}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science}, PAGES = {698--707}, ADDRESS = {Denver, CO, USA}, }
Endnote
%0 Conference Proceedings %A Charalampopoulos, Panagiotis %A Kociumaka, Tomasz %A Wellnitz, Philip %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Pattern Matching under Edit Distance: A Reduction to Dynamic Puzzle Matching and the Seaweed Monoid of Permutation Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1571-D %R 10.1109/FOCS54457.2022.00072 %D 2022 %B IEEE 63rd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-10-31 - 2022-11-03 %C Denver, CO, USA %B FOCS 2022 %P 698 - 707 %I IEEE %@ 978-1-6654-5519-0
[73]
P. Charalampopoulos, T. Kociumaka, S. P. Pissis, J. Radoszewski, W. Rytter, T. Waleń, and W. Zuba, “Approximate Circular Pattern Matching,” in 30th Annual European Symposium on Algorithms (ESA 2022), Berlin/Potsdam, Germany, 2022.
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@inproceedings{CharalampopoulosESA22, TITLE = {Approximate Circular Pattern Matching}, AUTHOR = {Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Pissis, Solon P. and Radoszewski, Jakub and Rytter, Wojciech and Wale{\'n}, Tomasz and Zuba, Wiktor}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-247-1}, URL = {urn:nbn:de:0030-drops-169738; https://drops.dagstuhl.de/opus/volltexte/2022/16973/}, DOI = {10.4230/LIPIcs.ESA.2022.35}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {30th Annual European Symposium on Algorithms (ESA 2022)}, EDITOR = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz}, PAGES = {1--19}, EID = {35}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {244}, ADDRESS = {Berlin/Potsdam, Germany}, }
Endnote
%0 Conference Proceedings %A Charalampopoulos, Panagiotis %A Kociumaka, Tomasz %A Pissis, Solon P. %A Radoszewski, Jakub %A Rytter, Wojciech %A Wale&#324;, Tomasz %A Zuba, Wiktor %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Approximate Circular Pattern Matching : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1531-5 %R 10.4230/LIPIcs.ESA.2022.35 %U urn:nbn:de:0030-drops-169738 %U https://drops.dagstuhl.de/opus/volltexte/2022/16973/ %D 2022 %B 30th Annual European Symposium on Algorithms %Z date of event: 2022-09-05 - 2022-09-09 %C Berlin/Potsdam, Germany %B 30th Annual European Symposium on Algorithms %E Chechik, Shiri; Navarro, Gonzalo; Rotenberg, Eva; Herman, Grzegorz %P 1 - 19 %Z sequence number: 35 %I Schloss Dagstuhl %@ 978-3-95977-247-1 %B Leibniz International Proceedings in Informatics %N 244 %@ false
[74]
D. Coudert, A. Nusser, and L. Viennot, “Computing Graph Hyperbolicity Using Dominating Sets,” in Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX 2022), Alexandria, VA, USA, 2022.
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@inproceedings{Coudert_ALENEX22, TITLE = {Computing Graph Hyperbolicity Using Dominating Sets}, AUTHOR = {Coudert, David and Nusser, Andr{\'e} and Viennot, Laurent}, LANGUAGE = {eng}, ISBN = {978-1-61197-704-2}, DOI = {10.1137/1.9781611977042.7}, PUBLISHER = {SIAM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX 2022)}, EDITOR = {Phillips, Cynthia A. and Speckman, Bettina}, PAGES = {78--90}, ADDRESS = {Alexandria, VA, USA}, }
Endnote
%0 Conference Proceedings %A Coudert, David %A Nusser, Andr&#233; %A Viennot, Laurent %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Computing Graph Hyperbolicity Using Dominating Sets : %G eng %U http://hdl.handle.net/21.11116/0000-000C-268E-A %R 10.1137/1.9781611977042.7 %D 2022 %B Symposium on Algorithm Engineering and Experiments %Z date of event: 2022-01-09 - 2022-01-10 %C Alexandria, VA, USA %B Proceedings of the Symposium on Algorithm Engineering and Experiments %E Phillips, Cynthia A.; Speckman, Bettina %P 78 - 90 %I SIAM %@ 978-1-61197-704-2
[75]
D. Coudert, A. Nusser, and L. Viennot, “Enumeration of Far-Apart Pairs by Decreasing Distance for Faster Hyperbolicity Computation,” ACM Journal of Experimental Algorithmics, vol. 27, 2022.
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@article{Coudert22, TITLE = {Enumeration of Far-Apart Pairs by Decreasing Distance for Faster Hyperbolicity Computation}, AUTHOR = {Coudert, David and Nusser, Andr{\'e} and Viennot, Laurent}, LANGUAGE = {eng}, ISSN = {1084-6654}, DOI = {10.1145/3569169}, PUBLISHER = {ACM}, ADDRESS = {New York, NY}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {ACM Journal of Experimental Algorithmics}, VOLUME = {27}, EID = {1.15}, }
Endnote
%0 Journal Article %A Coudert, David %A Nusser, Andr&#233; %A Viennot, Laurent %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Enumeration of Far-Apart Pairs by Decreasing Distance for Faster Hyperbolicity Computation : %G eng %U http://hdl.handle.net/21.11116/0000-000B-FE19-C %R 10.1145/3569169 %7 2022 %D 2022 %J ACM Journal of Experimental Algorithmics %V 27 %Z sequence number: 1.15 %I ACM %C New York, NY %@ false
[76]
C. Coupette, J. Vreeken, and B. Rieck, “All the World’s a (Hyper)Graph: A Data Drama,” 2022. [Online]. Available: https://arxiv.org/abs/2206.08225. (arXiv: 2206.08225)
Abstract
We introduce Hyperbard, a dataset of diverse relational data representations<br>derived from Shakespeare's plays. Our representations range from simple graphs<br>capturing character co-occurrence in single scenes to hypergraphs encoding<br>complex communication settings and character contributions as hyperedges with<br>edge-specific node weights. By making multiple intuitive representations<br>readily available for experimentation, we facilitate rigorous representation<br>robustness checks in graph learning, graph mining, and network analysis,<br>highlighting the advantages and drawbacks of specific representations.<br>Leveraging the data released in Hyperbard, we demonstrate that many solutions<br>to popular graph mining problems are highly dependent on the representation<br>choice, thus calling current graph curation practices into question. As an<br>homage to our data source, and asserting that science can also be art, we<br>present all our points in the form of a play.<br>
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@online{Coupette2206.08225, TITLE = {All the World's a (Hyper)Graph: A Data Drama}, AUTHOR = {Coupette, Corinna and Vreeken, Jilles and Rieck, Bastian}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2206.08225}, EPRINT = {2206.08225}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We introduce Hyperbard, a dataset of diverse relational data representations<br>derived from Shakespeare's plays. Our representations range from simple graphs<br>capturing character co-occurrence in single scenes to hypergraphs encoding<br>complex communication settings and character contributions as hyperedges with<br>edge-specific node weights. By making multiple intuitive representations<br>readily available for experimentation, we facilitate rigorous representation<br>robustness checks in graph learning, graph mining, and network analysis,<br>highlighting the advantages and drawbacks of specific representations.<br>Leveraging the data released in Hyperbard, we demonstrate that many solutions<br>to popular graph mining problems are highly dependent on the representation<br>choice, thus calling current graph curation practices into question. As an<br>homage to our data source, and asserting that science can also be art, we<br>present all our points in the form of a play.<br>}, }
Endnote
%0 Report %A Coupette, Corinna %A Vreeken, Jilles %A Rieck, Bastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T All the World's a (Hyper)Graph: A Data Drama : %G eng %U http://hdl.handle.net/21.11116/0000-000C-10C1-7 %U https://arxiv.org/abs/2206.08225 %D 2022 %X We introduce Hyperbard, a dataset of diverse relational data representations<br>derived from Shakespeare's plays. Our representations range from simple graphs<br>capturing character co-occurrence in single scenes to hypergraphs encoding<br>complex communication settings and character contributions as hyperedges with<br>edge-specific node weights. By making multiple intuitive representations<br>readily available for experimentation, we facilitate rigorous representation<br>robustness checks in graph learning, graph mining, and network analysis,<br>highlighting the advantages and drawbacks of specific representations.<br>Leveraging the data released in Hyperbard, we demonstrate that many solutions<br>to popular graph mining problems are highly dependent on the representation<br>choice, thus calling current graph curation practices into question. As an<br>homage to our data source, and asserting that science can also be art, we<br>present all our points in the form of a play.<br> %K Computer Science, Learning, cs.LG,Computer Science, Computation and Language, cs.CL,Computer Science, Computers and Society, cs.CY,cs.SI
[77]
C. Coupette and D. Hartung, “Sharing and Caring: Creating a Culture of Constructive Criticism in Computational Legal Studies,” 2022. [Online]. Available: https://arxiv.org/abs/2205.01071. (arXiv: 2205.01071)
Abstract
We introduce seven foundational principles for creating a culture of<br>constructive criticism in computational legal studies. Beginning by challenging<br>the current perception of papers as the primary scholarly output, we call for a<br>more comprehensive interpretation of publications. We then suggest to make<br>these publications computationally reproducible, releasing all of the data and<br>all of the code all of the time, on time, and in the most functioning form<br>possible. Subsequently, we invite constructive criticism in all phases of the<br>publication life cycle. We posit that our proposals will help form our field,<br>and float the idea of marking this maturity by the creation of a modern<br>flagship publication outlet for computational legal studies.<br>
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@online{Coupette2205.01071, TITLE = {Sharing and Caring: Creating a Culture of Constructive Criticism in Computational Legal Studies}, AUTHOR = {Coupette, Corinna and Hartung, Dirk}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2205.01071}, EPRINT = {2205.01071}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We introduce seven foundational principles for creating a culture of<br>constructive criticism in computational legal studies. Beginning by challenging<br>the current perception of papers as the primary scholarly output, we call for a<br>more comprehensive interpretation of publications. We then suggest to make<br>these publications computationally reproducible, releasing all of the data and<br>all of the code all of the time, on time, and in the most functioning form<br>possible. Subsequently, we invite constructive criticism in all phases of the<br>publication life cycle. We posit that our proposals will help form our field,<br>and float the idea of marking this maturity by the creation of a modern<br>flagship publication outlet for computational legal studies.<br>}, }
Endnote
%0 Report %A Coupette, Corinna %A Hartung, Dirk %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Sharing and Caring: Creating a Culture of Constructive Criticism in Computational Legal Studies : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1083-D %U https://arxiv.org/abs/2205.01071 %D 2022 %X We introduce seven foundational principles for creating a culture of<br>constructive criticism in computational legal studies. Beginning by challenging<br>the current perception of papers as the primary scholarly output, we call for a<br>more comprehensive interpretation of publications. We then suggest to make<br>these publications computationally reproducible, releasing all of the data and<br>all of the code all of the time, on time, and in the most functioning form<br>possible. Subsequently, we invite constructive criticism in all phases of the<br>publication life cycle. We posit that our proposals will help form our field,<br>and float the idea of marking this maturity by the creation of a modern<br>flagship publication outlet for computational legal studies.<br> %K Computer Science, Computers and Society, cs.CY,Computer Science, Computation and Language, cs.CL
[78]
C. Coupette and D. Hartung, “Rechtsstrukturvergleichung,” Rabels Zeitschrift für ausländisches und internationales Privatrecht, vol. 86, no. 4, 2022.
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@article{CoupetteRabelsZ22, TITLE = {Rechtsstrukturvergleichung}, AUTHOR = {Coupette, Corinna and Hartung, Dirk}, LANGUAGE = {eng}, DOI = {10.1628/rabelsz-2022-0082}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Rabels Zeitschrift f{\"u}r ausl{\"a}ndisches und internationales Privatrecht}, VOLUME = {86}, NUMBER = {4}, PAGES = {935--975}, }
Endnote
%0 Journal Article %A Coupette, Corinna %A Hartung, Dirk %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Rechtsstrukturvergleichung : %G eng %U http://hdl.handle.net/21.11116/0000-000C-108A-6 %R 10.1628/rabelsz-2022-0082 %7 2022 %D 2022 %J Rabels Zeitschrift f&#252;r ausl&#228;ndisches und internationales Privatrecht %O RabelsZ %V 86 %N 4 %& 935 %P 935 - 975
[79]
C. Coupette, S. Dalleiger, and J. Vreeken, “Differentially Describing Groups of Graphs,” in Proceedings of the 36th AAAI Conference on Artificial Intelligence, Virtual Conference, 2022.
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@inproceedings{CoupetteAAAI22, TITLE = {Differentially Describing Groups of Graphs}, AUTHOR = {Coupette, Corinna and Dalleiger, Sebastian and Vreeken, Jilles}, LANGUAGE = {eng}, ISBN = {978-1-57735-876-3}, DOI = {10.1609/aaai.v36i4.20312}, PUBLISHER = {AAAI}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 36th AAAI Conference on Artificial Intelligence}, PAGES = {3959--3967}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Coupette, Corinna %A Dalleiger, Sebastian %A Vreeken, Jilles %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Differentially Describing Groups of Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-105C-B %R 10.1609/aaai.v36i4.20312 %D 2022 %B 36th AAAI Conference on Artificial Intelligence %Z date of event: 2022-02-22 - 2022-03-01 %C Virtual Conference %B Proceedings of the 36th AAAI Conference on Artificial Intelligence %P 3959 - 3967 %I AAAI %@ 978-1-57735-876-3 %U https://ojs.aaai.org/index.php/AAAI/article/view/20312/20071
[80]
C. Coupette, D. Hartung, J. Beckedorf, M. Bother, and D. M. Katz, “Law Smells - Defining and Detecting Problematic Patterns in Legal Drafting,” Artificial Intelligence and Law, 2022.
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@article{Coupette22, TITLE = {Law Smells -- Defining and Detecting Problematic Patterns in Legal Drafting}, AUTHOR = {Coupette, Corinna and Hartung, Dirk and Beckedorf, Janis and Bother, Maximilian and Katz, Daniel Martin}, LANGUAGE = {eng}, ISSN = {0924-8463}, DOI = {10.1007/s10506-022-09315-w}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Artificial Intelligence and Law}, }
Endnote
%0 Journal Article %A Coupette, Corinna %A Hartung, Dirk %A Beckedorf, Janis %A Bother, Maximilian %A Katz, Daniel Martin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Law Smells - Defining and Detecting Problematic Patterns in Legal Drafting : %G eng %U http://hdl.handle.net/21.11116/0000-000A-CD04-B %R 10.1007/s10506-022-09315-w %7 2022 %D 2022 %J Artificial Intelligence and Law %I Springer %C New York, NY %@ false
[81]
C. Coupette, S. Dalleiger, and J. Vreeken, “Differentially Describing Groups of Graphs,” 2022. [Online]. Available: https://arxiv.org/abs/2201.04064. (arXiv: 2201.04064)
Abstract
How does neural connectivity in autistic children differ from neural<br>connectivity in healthy children or autistic youths? What patterns in global<br>trade networks are shared across classes of goods, and how do these patterns<br>change over time? Answering questions like these requires us to differentially<br>describe groups of graphs: Given a set of graphs and a partition of these<br>graphs into groups, discover what graphs in one group have in common, how they<br>systematically differ from graphs in other groups, and how multiple groups of<br>graphs are related. We refer to this task as graph group analysis, which seeks<br>to describe similarities and differences between graph groups by means of<br>statistically significant subgraphs. To perform graph group analysis, we<br>introduce Gragra, which uses maximum entropy modeling to identify a<br>non-redundant set of subgraphs with statistically significant associations to<br>one or more graph groups. Through an extensive set of experiments on a wide<br>range of synthetic and real-world graph groups, we confirm that Gragra works<br>well in practice.<br>
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@online{Coupette2201.04064, TITLE = {Differentially Describing Groups of Graphs}, AUTHOR = {Coupette, Corinna and Dalleiger, Sebastian and Vreeken, Jilles}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2201.04064}, EPRINT = {2201.04064}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {How does neural connectivity in autistic children differ from neural<br>connectivity in healthy children or autistic youths? What patterns in global<br>trade networks are shared across classes of goods, and how do these patterns<br>change over time? Answering questions like these requires us to differentially<br>describe groups of graphs: Given a set of graphs and a partition of these<br>graphs into groups, discover what graphs in one group have in common, how they<br>systematically differ from graphs in other groups, and how multiple groups of<br>graphs are related. We refer to this task as graph group analysis, which seeks<br>to describe similarities and differences between graph groups by means of<br>statistically significant subgraphs. To perform graph group analysis, we<br>introduce Gragra, which uses maximum entropy modeling to identify a<br>non-redundant set of subgraphs with statistically significant associations to<br>one or more graph groups. Through an extensive set of experiments on a wide<br>range of synthetic and real-world graph groups, we confirm that Gragra works<br>well in practice.<br>}, }
Endnote
%0 Report %A Coupette, Corinna %A Dalleiger, Sebastian %A Vreeken, Jilles %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Differentially Describing Groups of Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-165D-4 %U https://arxiv.org/abs/2201.04064 %D 2022 %X How does neural connectivity in autistic children differ from neural<br>connectivity in healthy children or autistic youths? What patterns in global<br>trade networks are shared across classes of goods, and how do these patterns<br>change over time? Answering questions like these requires us to differentially<br>describe groups of graphs: Given a set of graphs and a partition of these<br>graphs into groups, discover what graphs in one group have in common, how they<br>systematically differ from graphs in other groups, and how multiple groups of<br>graphs are related. We refer to this task as graph group analysis, which seeks<br>to describe similarities and differences between graph groups by means of<br>statistically significant subgraphs. To perform graph group analysis, we<br>introduce Gragra, which uses maximum entropy modeling to identify a<br>non-redundant set of subgraphs with statistically significant associations to<br>one or more graph groups. Through an extensive set of experiments on a wide<br>range of synthetic and real-world graph groups, we confirm that Gragra works<br>well in practice.<br> %K cs.SI,Computer Science, Information Theory, cs.IT,Computer Science, Learning, cs.LG,Mathematics, Information Theory, math.IT
[82]
C. Croitoru and M. Croitoru, “Indepth Combinatorial Analysis of Admissible Sets for Abstract Argumentation,” Annals of Mathematics and Artificial Intelligence, vol. 90, 2022.
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@article{Croitoru2022, TITLE = {Indepth Combinatorial Analysis of Admissible Sets for Abstract Argumentation}, AUTHOR = {Croitoru, Cosmina and Croitoru, Madalina}, LANGUAGE = {eng}, ISSN = {1012-2443}, DOI = {10.1007/s10472-022-09785-3}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Annals of Mathematics and Artificial Intelligence}, VOLUME = {90}, PAGES = {1139--1158}, }
Endnote
%0 Journal Article %A Croitoru, Cosmina %A Croitoru, Madalina %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Indepth Combinatorial Analysis of Admissible Sets for Abstract Argumentation : %G eng %U http://hdl.handle.net/21.11116/0000-000A-5D72-E %R 10.1007/s10472-022-09785-3 %7 2022 %D 2022 %J Annals of Mathematics and Artificial Intelligence %V 90 %& 1139 %P 1139 - 1158 %I Springer %C New York, NY %@ false
[83]
Á. Cseh, Y. Faenza, T. Kavitha, and V. Powers, “Understanding Popular Matchings via Stable Matchings,” SIAM Journal on Discrete Mathematics, vol. 36, no. 1, 2022.
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@article{Cseh2022, TITLE = {Understanding Popular Matchings via Stable Matchings}, AUTHOR = {Cseh, {\'A}gnes and Faenza, Yuri and Kavitha, Telikepalli and Powers, Vladlena}, LANGUAGE = {eng}, ISSN = {0895-4801}, DOI = {10.1137/19M124770X}, PUBLISHER = {The Society}, ADDRESS = {Philadelphia, Pa.}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {36}, NUMBER = {1}, PAGES = {188--213}, }
Endnote
%0 Journal Article %A Cseh, &#193;gnes %A Faenza, Yuri %A Kavitha, Telikepalli %A Powers, Vladlena %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Understanding Popular Matchings via Stable Matchings : %G eng %U http://hdl.handle.net/21.11116/0000-000A-57C3-8 %R 10.1137/19M124770X %7 2022 %D 2022 %J SIAM Journal on Discrete Mathematics %V 36 %N 1 %& 188 %P 188 - 213 %I The Society %C Philadelphia, Pa. %@ false
[84]
J. Cslovjecsek, M. Pilipczuk, and K. Węgrzycki, “Parameterized Approximation for Maximum Weight Independent Set of Rectangles and Segments,” 2022. [Online]. Available: https://arxiv.org/abs/2212.01620. (arXiv: 2212.01620)
Abstract
In the Maximum Weight Independent Set of Rectangles problem (MWISR) we are<br>given a weighted set of $n$ axis-parallel rectangles in the plane. The task is<br>to find a subset of pairwise non-overlapping rectangles with the maximum<br>possible total weight. This problem is NP-hard and the best-known<br>polynomial-time approximation algorithm, due to by Chalermsook and Walczak<br>(SODA 2021), achieves approximation factor $O(\log\log n )$. While in the<br>unweighted setting, constant factor approximation algorithms are known, due to<br>Mitchell (FOCS 2021) and to G\'alvez et al. (SODA 2022), it remains open to<br>extend these techniques to the weighted setting.<br> In this paper, we consider MWISR through the lens of parameterized<br>approximation. Grandoni et al. (ESA 2019) gave a $(1-\epsilon)$-approximation<br>algorithm with running time $k^{O(k/\epsilon^8)} n^{O(1/\epsilon^8)}$ time,<br>where $k$ is the number of rectangles in an optimum solution. Unfortunately,<br>their algorithm works only in the unweighted setting and they left it as an<br>open problem to give a parameterized approximation scheme in the weighted<br>setting.<br> Our contribution is a partial answer to the open question of Grandoni et al.<br>(ESA 2019). We give a parameterized approximation algorithm for MWISR that<br>given a parameter $k$, finds a set of non-overlapping rectangles of weight at<br>least $(1-\epsilon) \text{opt}_k$ in $2^{O(k \log(k/\epsilon))}<br>n^{O(1/\epsilon)}$ time, where $\text{opt}_k$ is the maximum weight of a<br>solution of cardinality at most $k$. Note that thus, our algorithm may return a<br>solution consisting of more than $k$ rectangles. To complement this apparent<br>weakness, we also propose a parameterized approximation scheme with running<br>time $2^{O(k^2 \log(k/\epsilon))} n^{O(1)}$ that finds a solution with<br>cardinality at most $k$ and total weight at least $(1-\epsilon)\text{opt}_k$<br>for the special case of axis-parallel segments.<br>
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@online{Cslovjecsek2212.01620, TITLE = {Parameterized Approximation for Maximum Weight Independent Set of Rectangles and Segments}, AUTHOR = {Cslovjecsek, Jana and Pilipczuk, Micha{\l} and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2212.01620}, EPRINT = {2212.01620}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the Maximum Weight Independent Set of Rectangles problem (MWISR) we are<br>given a weighted set of $n$ axis-parallel rectangles in the plane. The task is<br>to find a subset of pairwise non-overlapping rectangles with the maximum<br>possible total weight. This problem is NP-hard and the best-known<br>polynomial-time approximation algorithm, due to by Chalermsook and Walczak<br>(SODA 2021), achieves approximation factor $O(\log\log n )$. While in the<br>unweighted setting, constant factor approximation algorithms are known, due to<br>Mitchell (FOCS 2021) and to G\'alvez et al. (SODA 2022), it remains open to<br>extend these techniques to the weighted setting.<br> In this paper, we consider MWISR through the lens of parameterized<br>approximation. Grandoni et al. (ESA 2019) gave a $(1-\epsilon)$-approximation<br>algorithm with running time $k^{O(k/\epsilon^8)} n^{O(1/\epsilon^8)}$ time,<br>where $k$ is the number of rectangles in an optimum solution. Unfortunately,<br>their algorithm works only in the unweighted setting and they left it as an<br>open problem to give a parameterized approximation scheme in the weighted<br>setting.<br> Our contribution is a partial answer to the open question of Grandoni et al.<br>(ESA 2019). We give a parameterized approximation algorithm for MWISR that<br>given a parameter $k$, finds a set of non-overlapping rectangles of weight at<br>least $(1-\epsilon) \text{opt}_k$ in $2^{O(k \log(k/\epsilon))}<br>n^{O(1/\epsilon)}$ time, where $\text{opt}_k$ is the maximum weight of a<br>solution of cardinality at most $k$. Note that thus, our algorithm may return a<br>solution consisting of more than $k$ rectangles. To complement this apparent<br>weakness, we also propose a parameterized approximation scheme with running<br>time $2^{O(k^2 \log(k/\epsilon))} n^{O(1)}$ that finds a solution with<br>cardinality at most $k$ and total weight at least $(1-\epsilon)\text{opt}_k$<br>for the special case of axis-parallel segments.<br>}, }
Endnote
%0 Report %A Cslovjecsek, Jana %A Pilipczuk, Micha&#322; %A W&#281;grzycki, Karol %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Parameterized Approximation for Maximum Weight Independent Set of Rectangles and Segments : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F75-F %U https://arxiv.org/abs/2212.01620 %D 2022 %X In the Maximum Weight Independent Set of Rectangles problem (MWISR) we are<br>given a weighted set of $n$ axis-parallel rectangles in the plane. The task is<br>to find a subset of pairwise non-overlapping rectangles with the maximum<br>possible total weight. This problem is NP-hard and the best-known<br>polynomial-time approximation algorithm, due to by Chalermsook and Walczak<br>(SODA 2021), achieves approximation factor $O(\log\log n )$. While in the<br>unweighted setting, constant factor approximation algorithms are known, due to<br>Mitchell (FOCS 2021) and to G\'alvez et al. (SODA 2022), it remains open to<br>extend these techniques to the weighted setting.<br> In this paper, we consider MWISR through the lens of parameterized<br>approximation. Grandoni et al. (ESA 2019) gave a $(1-\epsilon)$-approximation<br>algorithm with running time $k^{O(k/\epsilon^8)} n^{O(1/\epsilon^8)}$ time,<br>where $k$ is the number of rectangles in an optimum solution. Unfortunately,<br>their algorithm works only in the unweighted setting and they left it as an<br>open problem to give a parameterized approximation scheme in the weighted<br>setting.<br> Our contribution is a partial answer to the open question of Grandoni et al.<br>(ESA 2019). We give a parameterized approximation algorithm for MWISR that<br>given a parameter $k$, finds a set of non-overlapping rectangles of weight at<br>least $(1-\epsilon) \text{opt}_k$ in $2^{O(k \log(k/\epsilon))}<br>n^{O(1/\epsilon)}$ time, where $\text{opt}_k$ is the maximum weight of a<br>solution of cardinality at most $k$. Note that thus, our algorithm may return a<br>solution consisting of more than $k$ rectangles. To complement this apparent<br>weakness, we also propose a parameterized approximation scheme with running<br>time $2^{O(k^2 \log(k/\epsilon))} n^{O(1)}$ that finds a solution with<br>cardinality at most $k$ and total weight at least $(1-\epsilon)\text{opt}_k$<br>for the special case of axis-parallel segments.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Geometry, cs.CG
[85]
D. Das, T. Kociumaka, and B. Saha, “Improved Approximation Algorithms for Dyck Edit Distance and RNA Folding,” in 49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022), Paris, France, 2022.
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@inproceedings{Das_ICALP22b, TITLE = {Improved Approximation Algorithms for {D}yck Edit Distance and {RNA} Folding}, AUTHOR = {Das, Debarati and Kociumaka, Tomasz and Saha, Barna}, LANGUAGE = {eng}, ISBN = {978-3-95977-235-8}, URL = {urn:nbn:de:0030-drops-163902; https://drops.dagstuhl.de/opus/volltexte/2022/16390/}, DOI = {10.4230/LIPIcs.ICALP.2022.49}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {49th EATCS International Conference on Automata, Languages, and Programming (ICALP 2022)}, EDITOR = {Boja{\'n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, PAGES = {1--20}, EID = {49}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {229}, ADDRESS = {Paris, France}, }
Endnote
%0 Conference Proceedings %A Das, Debarati %A Kociumaka, Tomasz %A Saha, Barna %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Improved Approximation Algorithms for Dyck Edit Distance and RNA Folding : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1541-3 %R 10.4230/LIPIcs.ICALP.2022.49 %U urn:nbn:de:0030-drops-163902 %U https://drops.dagstuhl.de/opus/volltexte/2022/16390/ %D 2022 %B 49th International Colloquium on Automata, Languages, and Programming %Z date of event: 2022-07-04 - 2022-07-08 %C Paris, France %B 49th EATCS International Conference on Automata, Languages, and Programming %E Boja&#324;czyk, Miko&#322;aj; Merelli, Emanuela; Woodruff, David P. %P 1 - 20 %Z sequence number: 49 %I Schloss Dagstuhl %@ 978-3-95977-235-8 %B Leibniz International Proceedings in Informatics %N 229
[86]
D. Das, J. Gilbert, M. Hajiaghayi, T. Kociumaka, B. Saha, and H. Saleh, “Õ(n + poly(k))-time Algorithm for Bounded Tree Edit Distance,” in FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science, Denver, CO, USA, 2022.
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@inproceedings{Das_FOCS22, TITLE = {$\tilde{O}(n + \mathrm{poly}(k))$-time Algorithm for Bounded Tree Edit Distance}, AUTHOR = {Das, Debarati and Gilbert, Jacob and Hajiaghayi, MohammadTaghi and Kociumaka, Tomasz and Saha, Barna and Saleh, Hamed}, LANGUAGE = {eng}, ISBN = {978-1-6654-5519-0}, DOI = {10.1109/FOCS54457.2022.00071}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science}, PAGES = {686--697}, ADDRESS = {Denver, CO, USA}, }
Endnote
%0 Conference Proceedings %A Das, Debarati %A Gilbert, Jacob %A Hajiaghayi, MohammadTaghi %A Kociumaka, Tomasz %A Saha, Barna %A Saleh, Hamed %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T &#213;(n + poly(k))-time Algorithm for Bounded Tree Edit Distance : %G eng %U http://hdl.handle.net/21.11116/0000-000C-153D-9 %R 10.1109/FOCS54457.2022.00071 %D 2022 %B IEEE 63rd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-10-31 - 2022-11-03 %C Denver, CO, USA %B FOCS 2022 %P 686 - 697 %I IEEE %@ 978-1-6654-5519-0
[87]
B. C. Esmer, A. Kulik, D. Marx, D. Neuen, and R. Sharma, “Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search,” in 30th Annual European Symposium on Algorithms (ESA 2022), Berlin/Potsdam, Germany, 2022.
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@inproceedings{EsmerESA22, TITLE = {Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search}, AUTHOR = {Esmer, Bari{\c s} Can and Kulik, Ariel and Marx, D{\'a}niel and Neuen, Daniel and Sharma, Roohani}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-247-1}, URL = {urn:nbn:de:0030-drops-169887; https://drops.dagstuhl.de/opus/volltexte/2022/16988/}, DOI = {10.4230/LIPIcs.ESA.2022.50}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {30th Annual European Symposium on Algorithms (ESA 2022)}, EDITOR = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz}, PAGES = {1--19}, EID = {50}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {244}, ADDRESS = {Berlin/Potsdam, Germany}, }
Endnote
%0 Conference Proceedings %A Esmer, Bari&#351; Can %A Kulik, Ariel %A Marx, D&#225;niel %A Neuen, Daniel %A Sharma, Roohani %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DA2-D %R 10.4230/LIPIcs.ESA.2022.50 %U urn:nbn:de:0030-drops-169887 %U https://drops.dagstuhl.de/opus/volltexte/2022/16988/ %D 2022 %B 30th Annual European Symposium on Algorithms %Z date of event: 2022-09-05 - 2022-09-09 %C Berlin/Potsdam, Germany %B 30th Annual European Symposium on Algorithms %E Chechik, Shiri; Navarro, Gonzalo; Rotenberg, Eva; Herman, Grzegorz %P 1 - 19 %Z sequence number: 50 %I Schloss Dagstuhl %@ 978-3-95977-247-1 %B Leibniz International Proceedings in Informatics %N 244 %@ false
[88]
B. C. Esmer, A. Kulik, D. Marx, P. Schepper, and K. Węgrzycki, “Computing Generalized Convolutions Faster Than Brute Force,” in 17th International Symposium on Parameterized and Exact Computation (IPEC 2022), Potsdam, Germany, 2022.
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@inproceedings{Esmer_IPEC22, TITLE = {Computing Generalized Convolutions Faster Than Brute Force}, AUTHOR = {Esmer, Bari{\c s} Can and Kulik, Ariel and Marx, D{\'a}niel and Schepper, Philipp and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, ISBN = {978-3-95977-260-0}, URL = {urn:nbn:de:0030-drops-173685; https://drops.dagstuhl.de/opus/volltexte/2022/17368/}, DOI = {10.4230/LIPIcs.IPEC.2022.12}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)}, EDITOR = {Dell, Holger and Nederlof, Jesper}, PAGES = {1--22}, EID = {12}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {249}, ADDRESS = {Potsdam, Germany}, }
Endnote
%0 Conference Proceedings %A Esmer, Bari&#351; Can %A Kulik, Ariel %A Marx, D&#225;niel %A Schepper, Philipp %A W&#281;grzycki, Karol %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Computing Generalized Convolutions Faster Than Brute Force : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1EE6-0 %R 10.4230/LIPIcs.IPEC.2022.12 %U urn:nbn:de:0030-drops-173685 %U https://drops.dagstuhl.de/opus/volltexte/2022/17368/ %D 2022 %B 17th International Symposium on Parameterized and Exact Computation %Z date of event: 2022-09-07 - 2022-09-09 %C Potsdam, Germany %B 17th International Symposium on Parameterized and Exact Computation %E Dell, Holger; Nederlof, Jesper %P 1 - 22 %Z sequence number: 12 %I Schloss Dagstuhl %@ 978-3-95977-260-0 %B Leibniz International Proceedings in Informatics %N 249
[89]
B. C. Esmer, A. Kulik, D. Marx, D. Neuen, and R. Sharma, “Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search,” 2022. [Online]. Available: https://arxiv.org/abs/2206.13481. (arXiv: 2206.13481)
Abstract
We generalize the monotone local search approach of Fomin, Gaspers,<br>Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection between<br>parameterized approximation and exponential-time approximation algorithms for<br>monotone subset minimization problems. In a monotone subset minimization<br>problem the input implicitly describes a non-empty set family over a universe<br>of size $n$ which is closed under taking supersets. The task is to find a<br>minimum cardinality set in this family. Broadly speaking, we use approximate<br>monotone local search to show that a parameterized $\alpha$-approximation<br>algorithm that runs in $c^k \cdot n^{O(1)}$ time, where $k$ is the solution<br>size, can be used to derive an $\alpha$-approximation randomized algorithm that<br>runs in $d^n \cdot n^{O(1)}$ time, where $d$ is the unique value in $d \in<br>(1,1+\frac{c-1}{\alpha})$ such that<br>$\mathcal{D}(\frac{1}{\alpha}\|\frac{d-1}{c-1})=\frac{\ln c}{\alpha}$ and<br>$\mathcal{D}(a \|b)$ is the Kullback-Leibler divergence. This running time<br>matches that of Fomin et al. for $\alpha=1$, and is strictly better when<br>$\alpha >1$, for any $c > 1$. Furthermore, we also show that this result can be<br>derandomized at the expense of a sub-exponential multiplicative factor in the<br>running time.<br> We demonstrate the potential of approximate monotone local search by deriving<br>new and faster exponential approximation algorithms for Vertex Cover,<br>$3$-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback Vertex<br>Set, Directed Odd Cycle Transversal and Undirected Multicut. For instance, we<br>get a $1.1$-approximation algorithm for Vertex Cover with running time $1.114^n<br>\cdot n^{O(1)}$, improving upon the previously best known $1.1$-approximation<br>running in time $1.127^n \cdot n^{O(1)}$ by Bourgeois et al. [DAM 2011].<br>
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@online{Esmer2206.13481, TITLE = {Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search}, AUTHOR = {Esmer, Bar{\i}{\c s} Can and Kulik, Ariel and Marx, D{\'a}niel and Neuen, Daniel and Sharma, Roohani}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2206.13481}, EPRINT = {2206.13481}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We generalize the monotone local search approach of Fomin, Gaspers,<br>Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection between<br>parameterized approximation and exponential-time approximation algorithms for<br>monotone subset minimization problems. In a monotone subset minimization<br>problem the input implicitly describes a non-empty set family over a universe<br>of size $n$ which is closed under taking supersets. The task is to find a<br>minimum cardinality set in this family. Broadly speaking, we use approximate<br>monotone local search to show that a parameterized $\alpha$-approximation<br>algorithm that runs in $c^k \cdot n^{O(1)}$ time, where $k$ is the solution<br>size, can be used to derive an $\alpha$-approximation randomized algorithm that<br>runs in $d^n \cdot n^{O(1)}$ time, where $d$ is the unique value in $d \in<br>(1,1+\frac{c-1}{\alpha})$ such that<br>$\mathcal{D}(\frac{1}{\alpha}\|\frac{d-1}{c-1})=\frac{\ln c}{\alpha}$ and<br>$\mathcal{D}(a \|b)$ is the Kullback-Leibler divergence. This running time<br>matches that of Fomin et al. for $\alpha=1$, and is strictly better when<br>$\alpha >1$, for any $c > 1$. Furthermore, we also show that this result can be<br>derandomized at the expense of a sub-exponential multiplicative factor in the<br>running time.<br> We demonstrate the potential of approximate monotone local search by deriving<br>new and faster exponential approximation algorithms for Vertex Cover,<br>$3$-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback Vertex<br>Set, Directed Odd Cycle Transversal and Undirected Multicut. For instance, we<br>get a $1.1$-approximation algorithm for Vertex Cover with running time $1.114^n<br>\cdot n^{O(1)}$, improving upon the previously best known $1.1$-approximation<br>running in time $1.127^n \cdot n^{O(1)}$ by Bourgeois et al. [DAM 2011].<br>}, }
Endnote
%0 Report %A Esmer, Bar&#305;&#351; Can %A Kulik, Ariel %A Marx, D&#225;niel %A Neuen, Daniel %A Sharma, Roohani %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Faster Exponential-Time Approximation Algorithms Using Approximate Monotone Local Search : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1E6F-8 %U https://arxiv.org/abs/2206.13481 %D 2022 %X We generalize the monotone local search approach of Fomin, Gaspers,<br>Lokshtanov and Saurabh [J.ACM 2019], by establishing a connection between<br>parameterized approximation and exponential-time approximation algorithms for<br>monotone subset minimization problems. In a monotone subset minimization<br>problem the input implicitly describes a non-empty set family over a universe<br>of size $n$ which is closed under taking supersets. The task is to find a<br>minimum cardinality set in this family. Broadly speaking, we use approximate<br>monotone local search to show that a parameterized $\alpha$-approximation<br>algorithm that runs in $c^k \cdot n^{O(1)}$ time, where $k$ is the solution<br>size, can be used to derive an $\alpha$-approximation randomized algorithm that<br>runs in $d^n \cdot n^{O(1)}$ time, where $d$ is the unique value in $d \in<br>(1,1+\frac{c-1}{\alpha})$ such that<br>$\mathcal{D}(\frac{1}{\alpha}\|\frac{d-1}{c-1})=\frac{\ln c}{\alpha}$ and<br>$\mathcal{D}(a \|b)$ is the Kullback-Leibler divergence. This running time<br>matches that of Fomin et al. for $\alpha=1$, and is strictly better when<br>$\alpha >1$, for any $c > 1$. Furthermore, we also show that this result can be<br>derandomized at the expense of a sub-exponential multiplicative factor in the<br>running time.<br> We demonstrate the potential of approximate monotone local search by deriving<br>new and faster exponential approximation algorithms for Vertex Cover,<br>$3$-Hitting Set, Directed Feedback Vertex Set, Directed Subset Feedback Vertex<br>Set, Directed Odd Cycle Transversal and Undirected Multicut. For instance, we<br>get a $1.1$-approximation algorithm for Vertex Cover with running time $1.114^n<br>\cdot n^{O(1)}$, improving upon the previously best known $1.1$-approximation<br>running in time $1.127^n \cdot n^{O(1)}$ by Bourgeois et al. [DAM 2011].<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[90]
O. Firman and J. Spoerhase, “Hypergraph Representation via Axis-Aligned Point-Subspace Cover,” in WALCOM: Algorithms and Computation, Jember, Indonesia, 2022.
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@inproceedings{firman-spoerhase22:walcom, TITLE = {Hypergraph Representation via Axis-Aligned Point-Subspace Cover}, AUTHOR = {Firman, Oksana and Spoerhase, Joachim}, LANGUAGE = {eng}, ISBN = {978-3-030-96730-7}, DOI = {10.1007/978-3-030-96731-4_27}, PUBLISHER = {Springer}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, BOOKTITLE = {WALCOM: Algorithms and Computation}, EDITOR = {Mutzel, Petra and Rahman, Md. Saidur and Slamin}, PAGES = {328--339}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13174}, ADDRESS = {Jember, Indonesia}, }
Endnote
%0 Conference Proceedings %A Firman, Oksana %A Spoerhase, Joachim %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Hypergraph Representation via Axis-Aligned Point-Subspace Cover : %G eng %U http://hdl.handle.net/21.11116/0000-000C-26B3-F %R 10.1007/978-3-030-96731-4_27 %D 2022 %B 16th International Conference and Workshops on Algorithms and Computation %Z date of event: 2022-03-24 - 2022-03-26 %C Jember, Indonesia %B WALCOM: Algorithms and Computation %E Mutzel, Petra; Rahman, Md. Saidur; Slamin %P 328 - 339 %I Springer %@ 978-3-030-96730-7 %B Lecture Notes in Computer Science %N 13174 %U https://rdcu.be/c21qy
[91]
F. V. Fomin, P. A. Golovach, W. Lochet, P. Misra, S. Saurabh, and R. Sharma, “Parameterized Complexity of Directed Spanner Problems,” Algorithmica, vol. 84, 2022.
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@article{Formin21, TITLE = {Parameterized Complexity of Directed Spanner Problems}, AUTHOR = {Fomin, Fedor V. and Golovach, Petr A. and Lochet, William and Misra, Pranabendu and Saurabh, Saket and Sharma, Roohani}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-021-00911-x}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {Algorithmica}, VOLUME = {84}, PAGES = {2292--2308}, }
Endnote
%0 Journal Article %A Fomin, Fedor V. %A Golovach, Petr A. %A Lochet, William %A Misra, Pranabendu %A Saurabh, Saket %A Sharma, Roohani %+ 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 %T Parameterized Complexity of Directed Spanner Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0009-BAB8-6 %R 10.1007/s00453-021-00911-x %7 2021 %D 2022 %J Algorithmica %V 84 %& 2292 %P 2292 - 2308 %I Springer-Verlag %C New York %@ false
[92]
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, vol. 41, no. 8, 2022.
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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 = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, JOURNAL = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, VOLUME = {41}, NUMBER = {8}, PAGES = {2518--2531}, }
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 2022 %J IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems %V 41 %N 8 %& 2518 %P 2518 - 2531 %I IEEE %C Piscataway, NJ %@ false
[93]
E. Galby, D. Marx, P. Schepper, R. Sharma, and P. Tale, “Parameterized Complexity of Weighted Multicut in Trees,” in Graph-Theoretic Concepts in Computer Science (WG 2022), Tübingen, Germany, 2022.
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@inproceedings{GalbyWG22, TITLE = {Parameterized Complexity of Weighted Multicut in Trees}, AUTHOR = {Galby, Esther and Marx, D{\'a}niel and Schepper, Philipp and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, ISBN = {978-3-031-15913-8}, DOI = {10.1007/978-3-031-15914-5_19}, PUBLISHER = {Springer}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, BOOKTITLE = {Graph-Theoretic Concepts in Computer Science (WG 2022)}, EDITOR = {Bekos, Michael A. and Kaufmann, Michael}, PAGES = {257--270}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13453}, ADDRESS = {T{\"u}bingen, Germany}, }
Endnote
%0 Conference Proceedings %A Galby, Esther %A Marx, D&#225;niel %A Schepper, Philipp %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Parameterized Complexity of Weighted Multicut in Trees : %G eng %U http://hdl.handle.net/21.11116/0000-000B-5925-8 %R 10.1007/978-3-031-15914-5_19 %D 2022 %B 48th International Workshop on Graph-Theoretic Concepts in Computer Science %Z date of event: 2022-06-22 - 2022-06-24 %C T&#252;bingen, Germany %B Graph-Theoretic Concepts in Computer Science %E Bekos, Michael A.; Kaufmann, Michael %P 257 - 270 %I Springer %@ 978-3-031-15913-8 %B Lecture Notes in Computer Science %N 13453
[94]
E. Galby, D. Marx, P. Schepper, R. Sharma, and P. Tale, “Domination and Cut Problems on Chordal Graphs with Bounded Leafage,” in 17th International Symposium on Parameterized and Exact Computation (IPEC 2022), Potsdam, Germany, 2022.
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@inproceedings{Galby_IPEC22, TITLE = {Domination and Cut Problems on Chordal Graphs with Bounded Leafage}, AUTHOR = {Galby, Esther and Marx, D{\'a}niel and Schepper, Philipp and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, ISBN = {978-3-95977-260-0}, URL = {urn:nbn:de:0030-drops-173704; https://drops.dagstuhl.de/opus/volltexte/2022/17370/}, DOI = {10.4230/LIPIcs.IPEC.2022.14}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)}, EDITOR = {Dell, Holger and Nederlof, Jesper}, PAGES = {1--24}, EID = {14}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {249}, ADDRESS = {Potsdam, Germany}, }
Endnote
%0 Conference Proceedings %A Galby, Esther %A Marx, D&#225;niel %A Schepper, Philipp %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Domination and Cut Problems on Chordal Graphs with Bounded Leafage : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DB2-B %R 10.4230/LIPIcs.IPEC.2022.14 %U urn:nbn:de:0030-drops-173704 %U https://drops.dagstuhl.de/opus/volltexte/2022/17370/ %D 2022 %B 17th International Symposium on Parameterized and Exact Computation %Z date of event: 2022-09-07 - 2022-09-09 %C Potsdam, Germany %B 17th International Symposium on Parameterized and Exact Computation %E Dell, Holger; Nederlof, Jesper %P 1 - 24 %Z sequence number: 14 %I Schloss Dagstuhl %@ 978-3-95977-260-0 %B Leibniz International Proceedings in Informatics %N 249
[95]
E. Galby, L. Khazaliya, F. Mc Inerney, R. Sharma, and P. Tale, “Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters,” in 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Vienna, Austria, 2022.
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@inproceedings{Galby_MFCS22, TITLE = {Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters}, AUTHOR = {Galby, Esther and Khazaliya, Liana and Mc Inerney, Fionn and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, ISBN = {978-3-95977-256-3}, URL = {urn:nbn:de:0030-drops-168496; https://drops.dagstuhl.de/opus/volltexte/2022/16849/}, DOI = {10.4230/LIPIcs.MFCS.2022.51}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, EDITOR = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, PAGES = {1--15}, EID = {51}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {241}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Galby, Esther %A Khazaliya, Liana %A Mc Inerney, Fionn %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DB9-4 %R 10.4230/LIPIcs.MFCS.2022.51 %U urn:nbn:de:0030-drops-168496 %U https://drops.dagstuhl.de/opus/volltexte/2022/16849/ %D 2022 %B 47th International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2022-08-22 - 2022-08-26 %C Vienna, Austria %B 47th International Symposium on Mathematical Foundations of Computer Science %E Szeider, Stefan; Ganian, Robert; Silva, Alexandra %P 1 - 15 %Z sequence number: 51 %I Schloss Dagstuhl %@ 978-3-95977-256-3 %B Leibniz International Proceedings in Informatics %N 241
[96]
E. Galby, D. Marx, P. Schepper, R. Sharma, and P. Tale, “Parameterized Complexity of Weighted Multicut in Trees,” 2022. [Online]. Available: https://arxiv.org/abs/2205.10105. (arXiv: 2205.10105)
Abstract
The Edge Multicut problem is a classical cut problem where given an<br>undirected graph $G$, a set of pairs of vertices $\mathcal{P}$, and a budget<br>$k$, the goal is to determine if there is a set $S$ of at most $k$ edges such<br>that for each $(s,t) \in \mathcal{P}$, $G-S$ has no path from $s$ to $t$. Edge<br>Multicut has been relatively recently shown to be fixed-parameter tractable<br>(FPT), parameterized by $k$, by Marx and Razgon [SICOMP 2014], and<br>independently by Bousquet et al. [SICOMP 2018]. In the weighted version of the<br>problem, called Weighted Edge Multicut one is additionally given a weight<br>function $\mathtt{wt} : E(G) \to \mathbb{N}$ and a weight bound $w$, and the<br>goal is to determine if there is a solution of size at most $k$ and weight at<br>most $w$. Both the FPT algorithms for Edge Multicut by Marx et al. and Bousquet<br>et al. fail to generalize to the weighted setting. In fact, the weighted<br>problem is non-trivial even on trees and determining whether Weighted Edge<br>Multicut on trees is FPT was explicitly posed as an open problem by Bousquet et<br>al. [STACS 2009]. In this article, we answer this question positively by<br>designing an algorithm which uses a very recent result by Kim et al. [STOC<br>2022] about directed flow augmentation as subroutine.<br> We also study a variant of this problem where there is no bound on the size<br>of the solution, but the parameter is a structural property of the input, for<br>example, the number of leaves of the tree. We strengthen our results by stating<br>them for the more general vertex deletion version.<br>
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@online{Galby2205.10105, TITLE = {Parameterized Complexity of Weighted Multicut in Trees}, AUTHOR = {Galby, Esther and Marx, D{\'a}niel and Schepper, Philipp and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2205.10105}, EPRINT = {2205.10105}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The Edge Multicut problem is a classical cut problem where given an<br>undirected graph $G$, a set of pairs of vertices $\mathcal{P}$, and a budget<br>$k$, the goal is to determine if there is a set $S$ of at most $k$ edges such<br>that for each $(s,t) \in \mathcal{P}$, $G-S$ has no path from $s$ to $t$. Edge<br>Multicut has been relatively recently shown to be fixed-parameter tractable<br>(FPT), parameterized by $k$, by Marx and Razgon [SICOMP 2014], and<br>independently by Bousquet et al. [SICOMP 2018]. In the weighted version of the<br>problem, called Weighted Edge Multicut one is additionally given a weight<br>function $\mathtt{wt} : E(G) \to \mathbb{N}$ and a weight bound $w$, and the<br>goal is to determine if there is a solution of size at most $k$ and weight at<br>most $w$. Both the FPT algorithms for Edge Multicut by Marx et al. and Bousquet<br>et al. fail to generalize to the weighted setting. In fact, the weighted<br>problem is non-trivial even on trees and determining whether Weighted Edge<br>Multicut on trees is FPT was explicitly posed as an open problem by Bousquet et<br>al. [STACS 2009]. In this article, we answer this question positively by<br>designing an algorithm which uses a very recent result by Kim et al. [STOC<br>2022] about directed flow augmentation as subroutine.<br> We also study a variant of this problem where there is no bound on the size<br>of the solution, but the parameter is a structural property of the input, for<br>example, the number of leaves of the tree. We strengthen our results by stating<br>them for the more general vertex deletion version.<br>}, }
Endnote
%0 Report %A Galby, Esther %A Marx, D&#225;niel %A Schepper, Philipp %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Parameterized Complexity of Weighted Multicut in Trees : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DC8-3 %U https://arxiv.org/abs/2205.10105 %D 2022 %X The Edge Multicut problem is a classical cut problem where given an<br>undirected graph $G$, a set of pairs of vertices $\mathcal{P}$, and a budget<br>$k$, the goal is to determine if there is a set $S$ of at most $k$ edges such<br>that for each $(s,t) \in \mathcal{P}$, $G-S$ has no path from $s$ to $t$. Edge<br>Multicut has been relatively recently shown to be fixed-parameter tractable<br>(FPT), parameterized by $k$, by Marx and Razgon [SICOMP 2014], and<br>independently by Bousquet et al. [SICOMP 2018]. In the weighted version of the<br>problem, called Weighted Edge Multicut one is additionally given a weight<br>function $\mathtt{wt} : E(G) \to \mathbb{N}$ and a weight bound $w$, and the<br>goal is to determine if there is a solution of size at most $k$ and weight at<br>most $w$. Both the FPT algorithms for Edge Multicut by Marx et al. and Bousquet<br>et al. fail to generalize to the weighted setting. In fact, the weighted<br>problem is non-trivial even on trees and determining whether Weighted Edge<br>Multicut on trees is FPT was explicitly posed as an open problem by Bousquet et<br>al. [STACS 2009]. In this article, we answer this question positively by<br>designing an algorithm which uses a very recent result by Kim et al. [STOC<br>2022] about directed flow augmentation as subroutine.<br> We also study a variant of this problem where there is no bound on the size<br>of the solution, but the parameter is a structural property of the input, for<br>example, the number of leaves of the tree. We strengthen our results by stating<br>them for the more general vertex deletion version.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[97]
E. Galby, D. Marx, P. Schepper, R. Sharma, and P. Tale, “Domination and Cut Problems on Chordal Graphs with Bounded Leafage,” 2022. [Online]. Available: https://arxiv.org/abs/2208.02850. (arXiv: 2208.02850)
Abstract
The leafage of a chordal graph G is the minimum integer l such that G can be<br>realized as an intersection graph of subtrees of a tree with l leaves. We<br>consider structural parameterization by the leafage of classical domination and<br>cut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018,<br>Algorithmica 2020] proved, among other things, that Dominating Set on chordal<br>graphs admits an algorithm running in time $2^{O(l^2)} n^{O(1)}$. We present a<br>conceptually much simpler algorithm that runs in time $2^{O(l)} n^{O(1)}$. We<br>extend our approach to obtain similar results for Connected Dominating Set and<br>Steiner Tree. We then consider the two classical cut problems MultiCut with<br>Undeletable Terminals and Multiway Cut with Undeletable Terminals. We prove<br>that the former is W[1]-hard when parameterized by the leafage and complement<br>this result by presenting a simple $n^{O(l)}$-time algorithm. To our surprise,<br>we find that Multiway Cut with Undeletable Terminals on chordal graphs can be<br>solved, in contrast, in $n^{O(1)}$-time.<br>
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@online{Galby2208.02850, TITLE = {Domination and Cut Problems on Chordal Graphs with Bounded Leafage}, AUTHOR = {Galby, Esther and Marx, D{\'a}niel and Schepper, Philipp and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2208.02850}, EPRINT = {2208.02850}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The leafage of a chordal graph G is the minimum integer l such that G can be<br>realized as an intersection graph of subtrees of a tree with l leaves. We<br>consider structural parameterization by the leafage of classical domination and<br>cut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018,<br>Algorithmica 2020] proved, among other things, that Dominating Set on chordal<br>graphs admits an algorithm running in time $2^{O(l^2)} n^{O(1)}$. We present a<br>conceptually much simpler algorithm that runs in time $2^{O(l)} n^{O(1)}$. We<br>extend our approach to obtain similar results for Connected Dominating Set and<br>Steiner Tree. We then consider the two classical cut problems MultiCut with<br>Undeletable Terminals and Multiway Cut with Undeletable Terminals. We prove<br>that the former is W[1]-hard when parameterized by the leafage and complement<br>this result by presenting a simple $n^{O(l)}$-time algorithm. To our surprise,<br>we find that Multiway Cut with Undeletable Terminals on chordal graphs can be<br>solved, in contrast, in $n^{O(1)}$-time.<br>}, }
Endnote
%0 Report %A Galby, Esther %A Marx, D&#225;niel %A Schepper, Philipp %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Domination and Cut Problems on Chordal Graphs with Bounded Leafage : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DF6-F %U https://arxiv.org/abs/2208.02850 %D 2022 %X The leafage of a chordal graph G is the minimum integer l such that G can be<br>realized as an intersection graph of subtrees of a tree with l leaves. We<br>consider structural parameterization by the leafage of classical domination and<br>cut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018,<br>Algorithmica 2020] proved, among other things, that Dominating Set on chordal<br>graphs admits an algorithm running in time $2^{O(l^2)} n^{O(1)}$. We present a<br>conceptually much simpler algorithm that runs in time $2^{O(l)} n^{O(1)}$. We<br>extend our approach to obtain similar results for Connected Dominating Set and<br>Steiner Tree. We then consider the two classical cut problems MultiCut with<br>Undeletable Terminals and Multiway Cut with Undeletable Terminals. We prove<br>that the former is W[1]-hard when parameterized by the leafage and complement<br>this result by presenting a simple $n^{O(l)}$-time algorithm. To our surprise,<br>we find that Multiway Cut with Undeletable Terminals on chordal graphs can be<br>solved, in contrast, in $n^{O(1)}$-time.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,
[98]
E. Galby, L. Khazaliya, F. M. Inerney, R. Sharma, and P. Tale, “Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters,” 2022. [Online]. Available: https://arxiv.org/abs/2206.15424. (arXiv: 2206.15424)
Abstract
For a graph $G$, a subset $S \subseteq V(G)$ is called a \emph{resolving set}<br>if for any two vertices $u,v \in V(G)$, there exists a vertex $w \in S$ such<br>that $d(w,u) \neq d(w,v)$. The {\sc Metric Dimension} problem takes as input a<br>graph $G$ and a positive integer $k$, and asks whether there exists a resolving<br>set of size at most $k$. This problem was introduced in the 1970s and is known<br>to be NP-hard~[GT~61 in Garey and Johnson's book]. In the realm of<br>parameterized complexity, Hartung and Nichterlein~[CCC~2013] proved that the<br>problem is W[2]-hard when parameterized by the natural parameter $k$. They also<br>observed that it is FPT when parameterized by the vertex cover number and asked<br>about its complexity under \emph{smaller} parameters, in particular the<br>feedback vertex set number. We answer this question by proving that {\sc Metric<br>Dimension} is W[1]-hard when parameterized by the feedback vertex set number.<br>This also improves the result of Bonnet and Purohit~[IPEC 2019] which states<br>that the problem is W[1]-hard parameterized by the treewidth. Regarding the<br>parameterization by the vertex cover number, we prove that {\sc Metric<br>Dimension} does not admit a polynomial kernel under this parameterization<br>unless $NP\subseteq coNP/poly$. We observe that a similar result holds when the<br>parameter is the distance to clique. On the positive side, we show that {\sc<br>Metric Dimension} is FPT when parameterized by either the distance to cluster<br>or the distance to co-cluster, both of which are smaller parameters than the<br>vertex cover number.<br>
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@online{Galby2206.15424, TITLE = {Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters}, AUTHOR = {Galby, Esther and Khazaliya, Liana and Inerney, Fionn Mc and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2206.15424}, EPRINT = {2206.15424}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {For a graph $G$, a subset $S \subseteq V(G)$ is called a \emph{resolving set}<br>if for any two vertices $u,v \in V(G)$, there exists a vertex $w \in S$ such<br>that $d(w,u) \neq d(w,v)$. The {\sc Metric Dimension} problem takes as input a<br>graph $G$ and a positive integer $k$, and asks whether there exists a resolving<br>set of size at most $k$. This problem was introduced in the 1970s and is known<br>to be NP-hard~[GT~61 in Garey and Johnson's book]. In the realm of<br>parameterized complexity, Hartung and Nichterlein~[CCC~2013] proved that the<br>problem is W[2]-hard when parameterized by the natural parameter $k$. They also<br>observed that it is FPT when parameterized by the vertex cover number and asked<br>about its complexity under \emph{smaller} parameters, in particular the<br>feedback vertex set number. We answer this question by proving that {\sc Metric<br>Dimension} is W[1]-hard when parameterized by the feedback vertex set number.<br>This also improves the result of Bonnet and Purohit~[IPEC 2019] which states<br>that the problem is W[1]-hard parameterized by the treewidth. Regarding the<br>parameterization by the vertex cover number, we prove that {\sc Metric<br>Dimension} does not admit a polynomial kernel under this parameterization<br>unless $NP\subseteq coNP/poly$. We observe that a similar result holds when the<br>parameter is the distance to clique. On the positive side, we show that {\sc<br>Metric Dimension} is FPT when parameterized by either the distance to cluster<br>or the distance to co-cluster, both of which are smaller parameters than the<br>vertex cover number.<br>}, }
Endnote
%0 Report %A Galby, Esther %A Khazaliya, Liana %A Inerney, Fionn Mc %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DDF-A %U https://arxiv.org/abs/2206.15424 %D 2022 %X For a graph $G$, a subset $S \subseteq V(G)$ is called a \emph{resolving set}<br>if for any two vertices $u,v \in V(G)$, there exists a vertex $w \in S$ such<br>that $d(w,u) \neq d(w,v)$. The {\sc Metric Dimension} problem takes as input a<br>graph $G$ and a positive integer $k$, and asks whether there exists a resolving<br>set of size at most $k$. This problem was introduced in the 1970s and is known<br>to be NP-hard~[GT~61 in Garey and Johnson's book]. In the realm of<br>parameterized complexity, Hartung and Nichterlein~[CCC~2013] proved that the<br>problem is W[2]-hard when parameterized by the natural parameter $k$. They also<br>observed that it is FPT when parameterized by the vertex cover number and asked<br>about its complexity under \emph{smaller} parameters, in particular the<br>feedback vertex set number. We answer this question by proving that {\sc Metric<br>Dimension} is W[1]-hard when parameterized by the feedback vertex set number.<br>This also improves the result of Bonnet and Purohit~[IPEC 2019] which states<br>that the problem is W[1]-hard parameterized by the treewidth. Regarding the<br>parameterization by the vertex cover number, we prove that {\sc Metric<br>Dimension} does not admit a polynomial kernel under this parameterization<br>unless $NP\subseteq coNP/poly$. We observe that a similar result holds when the<br>parameter is the distance to clique. On the positive side, we show that {\sc<br>Metric Dimension} is FPT when parameterized by either the distance to cluster<br>or the distance to co-cluster, both of which are smaller parameters than the<br>vertex cover number.<br> %K Computer Science, Discrete Mathematics, cs.DM,Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[99]
E. Galby, S. Kisfaludi-Bak, D. Marx, and R. Sharma, “Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification,” 2022. [Online]. Available: https://arxiv.org/abs/2208.06015. (arXiv: 2208.06015)
Abstract
In the Directed Steiner Network problem, the input is a directed graph G, a<br>subset T of k vertices of G called the terminals, and a demand graph D on T.<br>The task is to find a subgraph H of G with the minimum number of edges such<br>that for every edge (s,t) in D, the solution H contains a directed s to t path.<br>In this paper we investigate how the complexity of the problem depends on the<br>demand pattern when G is planar. Formally, if \mathcal{D} is a class of<br>directed graphs closed under identification of vertices, then the<br>\mathcal{D}-Steiner Network (\mathcal{D}-SN) problem is the special case where<br>the demand graph D is restricted to be from \mathcal{D}. For general graphs,<br>Feldmann and Marx [ICALP 2016] characterized those families of demand graphs<br>where the problem is fixed-parameter tractable (FPT) parameterized by the<br>number k of terminals. They showed that if \mathcal{D} is a superset of one of<br>the five hard families, then \mathcal{D}-SN is W[1]-hard parameterized by k,<br>otherwise it can be solved in time f(k)n^{O(1)}.<br> For planar graphs an interesting question is whether the W[1]-hard cases can<br>be solved by subexponential parameterized algorithms. Chitnis et al. [SICOMP<br>2020] showed that, assuming the ETH, there is no f(k)n^{o(k)} time algorithm<br>for the general \mathcal{D}-SN problem on planar graphs, but the special case<br>called Strongly Connected Steiner Subgraph can be solved in time f(k)<br>n^{O(\sqrt{k})} on planar graphs. We present a far-reaching generalization and<br>unification of these two results: we give a complete characterization of the<br>behavior of every $\mathcal{D}$-SN problem on planar graphs. We show that<br>assuming ETH, either the problem is (1) solvable in time 2^{O(k)}n^{O(1)}, and<br>not in time 2^{o(k)}n^{O(1)}, or (2) solvable in time f(k)n^{O(\sqrt{k})}, but<br>not in time f(k)n^{o(\sqrt{k})}, or (3) solvable in time f(k)n^{O(k)}, but not<br>in time f(k)n^{o({k})}.<br>
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@online{Galby2208.06015, TITLE = {Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification}, AUTHOR = {Galby, Esther and Kisfaludi-Bak, S{\'a}ndor and Marx, D{\'a}niel and Sharma, Roohani}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2208.06015}, EPRINT = {2208.06015}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the Directed Steiner Network problem, the input is a directed graph G, a<br>subset T of k vertices of G called the terminals, and a demand graph D on T.<br>The task is to find a subgraph H of G with the minimum number of edges such<br>that for every edge (s,t) in D, the solution H contains a directed s to t path.<br>In this paper we investigate how the complexity of the problem depends on the<br>demand pattern when G is planar. Formally, if \mathcal{D} is a class of<br>directed graphs closed under identification of vertices, then the<br>\mathcal{D}-Steiner Network (\mathcal{D}-SN) problem is the special case where<br>the demand graph D is restricted to be from \mathcal{D}. For general graphs,<br>Feldmann and Marx [ICALP 2016] characterized those families of demand graphs<br>where the problem is fixed-parameter tractable (FPT) parameterized by the<br>number k of terminals. They showed that if \mathcal{D} is a superset of one of<br>the five hard families, then \mathcal{D}-SN is W[1]-hard parameterized by k,<br>otherwise it can be solved in time f(k)n^{O(1)}.<br> For planar graphs an interesting question is whether the W[1]-hard cases can<br>be solved by subexponential parameterized algorithms. Chitnis et al. [SICOMP<br>2020] showed that, assuming the ETH, there is no f(k)n^{o(k)} time algorithm<br>for the general \mathcal{D}-SN problem on planar graphs, but the special case<br>called Strongly Connected Steiner Subgraph can be solved in time f(k)<br>n^{O(\sqrt{k})} on planar graphs. We present a far-reaching generalization and<br>unification of these two results: we give a complete characterization of the<br>behavior of every $\mathcal{D}$-SN problem on planar graphs. We show that<br>assuming ETH, either the problem is (1) solvable in time 2^{O(k)}n^{O(1)}, and<br>not in time 2^{o(k)}n^{O(1)}, or (2) solvable in time f(k)n^{O(\sqrt{k})}, but<br>not in time f(k)n^{o(\sqrt{k})}, or (3) solvable in time f(k)n^{O(k)}, but not<br>in time f(k)n^{o({k})}.<br>}, }
Endnote
%0 Report %A Galby, Esther %A Kisfaludi-Bak, S&#225;ndor %A Marx, D&#225;niel %A Sharma, Roohani %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1E72-3 %U https://arxiv.org/abs/2208.06015 %D 2022 %X In the Directed Steiner Network problem, the input is a directed graph G, a<br>subset T of k vertices of G called the terminals, and a demand graph D on T.<br>The task is to find a subgraph H of G with the minimum number of edges such<br>that for every edge (s,t) in D, the solution H contains a directed s to t path.<br>In this paper we investigate how the complexity of the problem depends on the<br>demand pattern when G is planar. Formally, if \mathcal{D} is a class of<br>directed graphs closed under identification of vertices, then the<br>\mathcal{D}-Steiner Network (\mathcal{D}-SN) problem is the special case where<br>the demand graph D is restricted to be from \mathcal{D}. For general graphs,<br>Feldmann and Marx [ICALP 2016] characterized those families of demand graphs<br>where the problem is fixed-parameter tractable (FPT) parameterized by the<br>number k of terminals. They showed that if \mathcal{D} is a superset of one of<br>the five hard families, then \mathcal{D}-SN is W[1]-hard parameterized by k,<br>otherwise it can be solved in time f(k)n^{O(1)}.<br> For planar graphs an interesting question is whether the W[1]-hard cases can<br>be solved by subexponential parameterized algorithms. Chitnis et al. [SICOMP<br>2020] showed that, assuming the ETH, there is no f(k)n^{o(k)} time algorithm<br>for the general \mathcal{D}-SN problem on planar graphs, but the special case<br>called Strongly Connected Steiner Subgraph can be solved in time f(k)<br>n^{O(\sqrt{k})} on planar graphs. We present a far-reaching generalization and<br>unification of these two results: we give a complete characterization of the<br>behavior of every $\mathcal{D}$-SN problem on planar graphs. We show that<br>assuming ETH, either the problem is (1) solvable in time 2^{O(k)}n^{O(1)}, and<br>not in time 2^{o(k)}n^{O(1)}, or (2) solvable in time f(k)n^{O(\sqrt{k})}, but<br>not in time f(k)n^{o(\sqrt{k})}, or (3) solvable in time f(k)n^{O(k)}, but not<br>in time f(k)n^{o({k})}.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,
[100]
Y. Gao, H. Kamkari, A. Karrenbauer, K. Mehlhorn, and M. Sharifi, “Physarum Inspired Dynamics to Solve Semi-Definite Programs,” 2022. [Online]. Available: https://arxiv.org/abs/2111.02291. (arXiv: 2111.02291)
Abstract
Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br>
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@online{Kamkari_2111.02291, TITLE = {Physarum Inspired Dynamics to Solve Semi-Definite Programs}, AUTHOR = {Gao, Yuan and Kamkari, Hamidreza and Karrenbauer, Andreas and Mehlhorn, Kurt and Sharifi, Mohammadamin}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2111.02291}, EPRINT = {2111.02291}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br>}, }
Endnote
%0 Report %A Gao, Yuan %A Kamkari, Hamidreza %A Karrenbauer, Andreas %A Mehlhorn, Kurt %A Sharifi, Mohammadamin %+ 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 External Organizations %T Physarum Inspired Dynamics to Solve Semi-Definite Programs : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B656-9 %U https://arxiv.org/abs/2111.02291 %D 2022 %X Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Optimization and Control, math.OC
[101]
J. Giliberti and A. Karrenbauer, “Improved Online Algorithm for Fractional Knapsack in the Random Order Model,” in Approximation and Online Algorithms, Lisbon, Portugal, 2022.
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@inproceedings{GilbertiGK2021, TITLE = {Improved Online Algorithm for Fractional Knapsack in the Random Order Model}, AUTHOR = {Giliberti, Jeff and Karrenbauer, Andreas}, LANGUAGE = {eng}, ISBN = {978-3-030-92701-1}, DOI = {10.1007/978-3-030-92702-8_12}, PUBLISHER = {Springer}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2022}, BOOKTITLE = {Approximation and Online Algorithms}, EDITOR = {Koenemann, Jochen and Preis, Britta}, PAGES = {188--205}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12982}, ADDRESS = {Lisbon, Portugal}, }
Endnote
%0 Conference Proceedings %A Giliberti, Jeff %A Karrenbauer, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Improved Online Algorithm for Fractional Knapsack in the Random Order Model : %G eng %U http://hdl.handle.net/21.11116/0000-000C-11BF-A %R 10.1007/978-3-030-92702-8_12 %D 2022 %B 19th Workshop on Approximation and Online Algorithms %Z date of event: 2021-09-06 - 2021-09-10 %C Lisbon, Portugal %B Approximation and Online Algorithms %E Koenemann, Jochen; Preis, Britta %P 188 - 205 %I Springer %@ 978-3-030-92701-1 %B Lecture Notes in Computer Science %N 12982
[102]
E. Goldenberg, T. Kociumaka, R. Krauthgamer, and B. Saha, “Gap Edit Distance via Non-Adaptive Queries: Simple and Optimal,” in FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science, Denver, CO, USA, 2022.
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@inproceedings{Goldenberg_FOCS22, TITLE = {Gap Edit Distance via Non-Adaptive Queries: {S}imple and Optimal}, AUTHOR = {Goldenberg, Elazar and Kociumaka, Tomasz and Krauthgamer, Robert and Saha, Barna}, LANGUAGE = {eng}, ISBN = {978-1-6654-5519-0}, DOI = {10.1109/FOCS54457.2022.00070}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2022, IEEE 63rd Annual Symposium on Foundations of Computer Science}, PAGES = {674--685}, ADDRESS = {Denver, CO, USA}, }
Endnote
%0 Conference Proceedings %A Goldenberg, Elazar %A Kociumaka, Tomasz %A Krauthgamer, Robert %A Saha, Barna %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Gap Edit Distance via Non-Adaptive Queries: Simple and Optimal : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1578-6 %R 10.1109/FOCS54457.2022.00070 %D 2022 %B IEEE 63rd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-10-31 - 2022-11-03 %C Denver, CO, USA %B FOCS 2022 %P 674 - 685 %I IEEE %@ 978-1-6654-5519-0
[103]
T. Gouleakis, K. Lakis, and G. Shahkarami, “Learning-Augmented Algorithms for Online TSP on the Line,” 2022. [Online]. Available: https://arxiv.org/abs/2206.00655. (arXiv: 2206.00655)
Abstract
We study the online Traveling Salesman Problem (TSP) on the line augmented<br>with machine-learned predictions. In the classical problem, there is a stream<br>of requests released over time along the real line. The goal is to minimize the<br>makespan of the algorithm. We distinguish between the open variant and the<br>closed one, in which we additionally require the algorithm to return to the<br>origin after serving all requests. The state of the art is a $1.64$-competitive<br>algorithm and a $2.04$-competitive algorithm for the closed and open variants,<br>respectively \cite{Bjelde:1.64}. In both cases, a tight lower bound is known<br>\cite{Ausiello:1.75, Bjelde:1.64}.<br> In both variants, our primary prediction model involves predicted positions<br>of the requests. We introduce algorithms that (i) obtain a tight 1.5<br>competitive ratio for the closed variant and a 1.66 competitive ratio for the<br>open variant in the case of perfect predictions, (ii) are robust against<br>unbounded prediction error, and (iii) are smooth, i.e., their performance<br>degrades gracefully as the prediction error increases.<br> Moreover, we further investigate the learning-augmented setting in the open<br>variant by additionally considering a prediction for the last request served by<br>the optimal offline algorithm. Our algorithm for this enhanced setting obtains<br>a 1.33 competitive ratio with perfect predictions while also being smooth and<br>robust, beating the lower bound of 1.44 we show for our original prediction<br>setting for the open variant. Also, we provide a lower bound of 1.25 for this<br>enhanced setting.<br>
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@online{Gouleakis2206.00655, TITLE = {Learning-Augmented Algorithms for Online {TSP} on the Line}, AUTHOR = {Gouleakis, Themis and Lakis, Konstantinos and Shahkarami, Golnoosh}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2206.00655}, EPRINT = {2206.00655}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the online Traveling Salesman Problem (TSP) on the line augmented<br>with machine-learned predictions. In the classical problem, there is a stream<br>of requests released over time along the real line. The goal is to minimize the<br>makespan of the algorithm. We distinguish between the open variant and the<br>closed one, in which we additionally require the algorithm to return to the<br>origin after serving all requests. The state of the art is a $1.64$-competitive<br>algorithm and a $2.04$-competitive algorithm for the closed and open variants,<br>respectively \cite{Bjelde:1.64}. In both cases, a tight lower bound is known<br>\cite{Ausiello:1.75, Bjelde:1.64}.<br> In both variants, our primary prediction model involves predicted positions<br>of the requests. We introduce algorithms that (i) obtain a tight 1.5<br>competitive ratio for the closed variant and a 1.66 competitive ratio for the<br>open variant in the case of perfect predictions, (ii) are robust against<br>unbounded prediction error, and (iii) are smooth, i.e., their performance<br>degrades gracefully as the prediction error increases.<br> Moreover, we further investigate the learning-augmented setting in the open<br>variant by additionally considering a prediction for the last request served by<br>the optimal offline algorithm. Our algorithm for this enhanced setting obtains<br>a 1.33 competitive ratio with perfect predictions while also being smooth and<br>robust, beating the lower bound of 1.44 we show for our original prediction<br>setting for the open variant. Also, we provide a lower bound of 1.25 for this<br>enhanced setting.<br>}, }
Endnote
%0 Report %A Gouleakis, Themis %A Lakis, Konstantinos %A Shahkarami, Golnoosh %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Learning-Augmented Algorithms for Online TSP on the Line : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1FCC-D %U https://arxiv.org/abs/2206.00655 %D 2022 %X We study the online Traveling Salesman Problem (TSP) on the line augmented<br>with machine-learned predictions. In the classical problem, there is a stream<br>of requests released over time along the real line. The goal is to minimize the<br>makespan of the algorithm. We distinguish between the open variant and the<br>closed one, in which we additionally require the algorithm to return to the<br>origin after serving all requests. The state of the art is a $1.64$-competitive<br>algorithm and a $2.04$-competitive algorithm for the closed and open variants,<br>respectively \cite{Bjelde:1.64}. In both cases, a tight lower bound is known<br>\cite{Ausiello:1.75, Bjelde:1.64}.<br> In both variants, our primary prediction model involves predicted positions<br>of the requests. We introduce algorithms that (i) obtain a tight 1.5<br>competitive ratio for the closed variant and a 1.66 competitive ratio for the<br>open variant in the case of perfect predictions, (ii) are robust against<br>unbounded prediction error, and (iii) are smooth, i.e., their performance<br>degrades gracefully as the prediction error increases.<br> Moreover, we further investigate the learning-augmented setting in the open<br>variant by additionally considering a prediction for the last request served by<br>the optimal offline algorithm. Our algorithm for this enhanced setting obtains<br>a 1.33 competitive ratio with perfect predictions while also being smooth and<br>robust, beating the lower bound of 1.44 we show for our original prediction<br>setting for the open variant. Also, we provide a lower bound of 1.25 for this<br>enhanced setting.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Learning, cs.LG
[104]
G. Gutowski, F. Mittelstädt, I. Rutter, J. Spoerhase, A. Wolff, and J. Zink, “Coloring Mixed and Directional Interval Graphs,” 2022. [Online]. Available: https://arxiv.org/abs/2208.14250. (arXiv: 2208.14250)
Abstract
A mixed graph has a set of vertices, a set of undirected egdes, and a set of<br>directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that<br>assigns to each vertex in $G$ a positive integer such that, for each edge $uv$<br>in $G$, $c(u) \ne c(v)$ and, for each arc $uv$ in $G$, $c(u) < c(v)$. For a<br>mixed graph $G$, the chromatic number $\chi(G)$ is the smallest number of<br>colors in any proper coloring of $G$. A directional interval graph is a mixed<br>graph whose vertices correspond to intervals on the real line. Such a graph has<br>an edge between every two intervals where one is contained in the other and an<br>arc between every two overlapping intervals, directed towards the interval that<br>starts and ends to the right.<br> Coloring such graphs has applications in routing edges in layered orthogonal<br>graph drawing according to the Sugiyama framework; the colors correspond to the<br>tracks for routing the edges. We show how to recognize directional interval<br>graphs, and how to compute their chromatic number efficiently. On the other<br>hand, for mixed interval graphs, i.e., graphs where two intersecting intervals<br>can be connected by an edge or by an arc in either direction arbitrarily, we<br>prove that computing the chromatic number is NP-hard.<br>
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@online{gutowski-etal22:arxiv, TITLE = {Coloring Mixed and Directional Interval Graphs}, AUTHOR = {Gutowski, Grzegorz and Mittelst{\"a}dt, Florian and Rutter, Ignaz and Spoerhase, Joachim and Wolff, Alexander and Zink, Johannes}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2208.14250}, EPRINT = {2208.14250}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {A mixed graph has a set of vertices, a set of undirected egdes, and a set of<br>directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that<br>assigns to each vertex in $G$ a positive integer such that, for each edge $uv$<br>in $G$, $c(u) \ne c(v)$ and, for each arc $uv$ in $G$, $c(u) < c(v)$. For a<br>mixed graph $G$, the chromatic number $\chi(G)$ is the smallest number of<br>colors in any proper coloring of $G$. A directional interval graph is a mixed<br>graph whose vertices correspond to intervals on the real line. Such a graph has<br>an edge between every two intervals where one is contained in the other and an<br>arc between every two overlapping intervals, directed towards the interval that<br>starts and ends to the right.<br> Coloring such graphs has applications in routing edges in layered orthogonal<br>graph drawing according to the Sugiyama framework; the colors correspond to the<br>tracks for routing the edges. We show how to recognize directional interval<br>graphs, and how to compute their chromatic number efficiently. On the other<br>hand, for mixed interval graphs, i.e., graphs where two intersecting intervals<br>can be connected by an edge or by an arc in either direction arbitrarily, we<br>prove that computing the chromatic number is NP-hard.<br>}, }
Endnote
%0 Report %A Gutowski, Grzegorz %A Mittelst&#228;dt, Florian %A Rutter, Ignaz %A Spoerhase, Joachim %A Wolff, Alexander %A Zink, Johannes %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Coloring Mixed and Directional Interval Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-269B-B %U https://arxiv.org/abs/2208.14250 %D 2022 %X A mixed graph has a set of vertices, a set of undirected egdes, and a set of<br>directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that<br>assigns to each vertex in $G$ a positive integer such that, for each edge $uv$<br>in $G$, $c(u) \ne c(v)$ and, for each arc $uv$ in $G$, $c(u) < c(v)$. For a<br>mixed graph $G$, the chromatic number $\chi(G)$ is the smallest number of<br>colors in any proper coloring of $G$. A directional interval graph is a mixed<br>graph whose vertices correspond to intervals on the real line. Such a graph has<br>an edge between every two intervals where one is contained in the other and an<br>arc between every two overlapping intervals, directed towards the interval that<br>starts and ends to the right.<br> Coloring such graphs has applications in routing edges in layered orthogonal<br>graph drawing according to the Sugiyama framework; the colors correspond to the<br>tracks for routing the edges. We show how to recognize directional interval<br>graphs, and how to compute their chromatic number efficiently. On the other<br>hand, for mixed interval graphs, i.e., graphs where two intersecting intervals<br>can be connected by an edge or by an arc in either direction arbitrarily, we<br>prove that computing the chromatic number is NP-hard.<br> %K Computer Science, Discrete Mathematics, cs.DM
[105]
D. Halperin, S. Har-Peled, K. Mehlhorn, E. Oh, and M. Sharir, “The Maximum-Level Vertex in an Arrangement of Lines,” Discrete & Computational Geometry, vol. 67, 2022.
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@article{Halperin2022, 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}, ISSN = {0179-5376}, DOI = {10.1007/s00454-021-00338-9}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Discrete \& Computational Geometry}, VOLUME = {67}, PAGES = {439--461}, }
Endnote
%0 Journal Article %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/21.11116/0000-0009-D020-7 %R 10.1007/s00454-021-00338-9 %7 2022 %D 2022 %J Discrete & Computational Geometry %V 67 %& 439 %P 439 - 461 %I Springer %C New York, NY %@ false %U https://rdcu.be/cFlQF
[106]
I. Han, A. Zandieh, J. Lee, R. Novak, L. Xiao, and A. Karbasi, “Fast Neural Kernel Embeddings for General Activations,” in Advances in Neural Information Processing Systems 35 (NeurIPS 2022), New Orleans, LA, USA, 2022.
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@inproceedings{Han_Neurips22, TITLE = {Fast Neural Kernel Embeddings for General Activations}, AUTHOR = {Han, Insu and Zandieh, Amir and Lee, Jaehoon and Novak, Roman and Xiao, Lechao and Karbasi, Amin}, LANGUAGE = {eng}, PUBLISHER = {Curran Associates, Inc.}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 35 (NeurIPS 2022)}, EDITOR = {Koyejo, S. and Mohamed, S. and Agarwal, A. and Belgrave, D. and Cho, K. and Oh, A.}, PAGES = {35657--35671}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Han, Insu %A Zandieh, Amir %A Lee, Jaehoon %A Novak, Roman %A Xiao, Lechao %A Karbasi, Amin %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Fast Neural Kernel Embeddings for General Activations : %G eng %U http://hdl.handle.net/21.11116/0000-000C-90F3-E %D 2022 %B 36th Conference on Neural Information Processing Systems %Z date of event: 2022-11-28 - 2022-12-09 %C New Orleans, LA, USA %B Advances in Neural Information Processing Systems 35 %E Koyejo, S.; Mohamed, S.; Agarwal, A.; Belgrave, D.; Cho, K.; Oh, A. %P 35657 - 35671 %I Curran Associates, Inc. %U https://openreview.net/pdf?id=yLilJ1vZgMe
[107]
I. Han, A. Zandieh, and H. Avron, “Random Gegenbauer Features for Scalable Kernel Methods,” in Proceedings of the 39th International Conference on Machine Learning (ICML 2022), Baltimore, MA, USA, 2022.
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@inproceedings{Han_ICML22, TITLE = {Random {Gegenbauer} Features for Scalable Kernel Methods}, AUTHOR = {Han, Insu and Zandieh, Amir and Avron, Haim}, LANGUAGE = {eng}, ISSN = {1938-7228}, URL = {https://proceedings.mlr.press/v162/han22g.html}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 39th International Conference on Machine Learning (ICML 2022)}, EDITOR = {Chaudhuri, Kamalika and Jegelka, Stefanie and Le, Song and Csaba, Szepesvari and Gang, Niu and Sabato, Sivan}, PAGES = {8330--8358}, SERIES = {Proceedings of the Machine Learning Research}, VOLUME = {162}, ADDRESS = {Baltimore, MA, USA}, }
Endnote
%0 Conference Proceedings %A Han, Insu %A Zandieh, Amir %A Avron, Haim %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Random Gegenbauer Features for Scalable Kernel Methods : %G eng %U http://hdl.handle.net/21.11116/0000-000C-90FB-6 %U https://proceedings.mlr.press/v162/han22g.html %D 2022 %B 39th International Conference on Machine Learning %Z date of event: 2022-07-17 - 2022-07-23 %C Baltimore, MA, USA %B Proceedings of the 39th International Conference on Machine Learning %E Chaudhuri, Kamalika; Jegelka, Stefanie; Le, Song; Csaba, Szepesvari; Gang, Niu; Sabato, Sivan %P 8330 - 8358 %B Proceedings of the Machine Learning Research %N 162 %@ false
[108]
M. Hatzel, L. Jaffke, P. T. Lima, T. Masařík, M. Pilipczuk, R. Sharma, and M. Sorge, “Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parameterized by the Size of the Cutset: Twin-width Meets Flow-Augmentation,” 2022. [Online]. Available: https://arxiv.org/abs/2207.07425. (arXiv: 2207.07425)
Abstract
We show fixed-parameter tractability of the Directed Multicut problem with<br>three terminal pairs (with a randomized algorithm). This problem, given a<br>directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$,<br>$(s_2,t_2)$, and $(s_3,t_3)$, and an integer $k$, asks to find a set of at most<br>$k$ non-terminal vertices in $G$ that intersect all $s_1t_1$-paths, all<br>$s_2t_2$-paths, and all $s_3t_3$-paths. The parameterized complexity of this<br>case has been open since Chitnis, Cygan, Hajiaghayi, and Marx proved<br>fixed-parameter tractability of the 2-terminal-pairs case at SODA 2012, and<br>Pilipczuk and Wahlstr\"{o}m proved the W[1]-hardness of the 4-terminal-pairs<br>case at SODA 2016.<br> On the technical side, we use two recent developments in parameterized<br>algorithms. Using the technique of directed flow-augmentation [Kim, Kratsch,<br>Pilipczuk, Wahlstr\"{o}m, STOC 2022] we cast the problem as a CSP problem with<br>few variables and constraints over a large ordered domain.We observe that this<br>problem can be in turn encoded as an FO model-checking task over a structure<br>consisting of a few 0-1 matrices. We look at this problem through the lenses of<br>twin-width, a recently introduced structural parameter [Bonnet, Kim,<br>Thomass\'{e}, Watrigant, FOCS 2020]: By a recent characterization [Bonnet,<br>Giocanti, Ossona de Mendes, Simon, Thomass\'{e}, Toru\'{n}czyk, STOC 2022] the<br>said FO model-checking task can be done in FPT time if the said matrices have<br>bounded grid rank. To complete the proof, we show an irrelevant vertex rule: If<br>any of the matrices in the said encoding has a large grid minor, a vertex<br>corresponding to the middle'' box in the grid minor can be proclaimed<br>irrelevant -- not contained in the sought solution -- and thus reduced.<br>
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BibTeX
@online{Hatzel2207.07425, TITLE = {Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parameterized by the Size of the Cutset: Twin-width Meets Flow-Augmentation}, AUTHOR = {Hatzel, Meike and Jaffke, Lars and Lima, Paloma T. and Masa{\v r}{\'i}k, Tom{\'a}{\v s} and Pilipczuk, Marcin and Sharma, Roohani and Sorge, Manuel}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2207.07425}, EPRINT = {2207.07425}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We show fixed-parameter tractability of the Directed Multicut problem with<br>three terminal pairs (with a randomized algorithm). This problem, given a<br>directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$,<br>$(s_2,t_2)$, and $(s_3,t_3)$, and an integer $k$, asks to find a set of at most<br>$k$ non-terminal vertices in $G$ that intersect all $s_1t_1$-paths, all<br>$s_2t_2$-paths, and all $s_3t_3$-paths. The parameterized complexity of this<br>case has been open since Chitnis, Cygan, Hajiaghayi, and Marx proved<br>fixed-parameter tractability of the 2-terminal-pairs case at SODA 2012, and<br>Pilipczuk and Wahlstr\"{o}m proved the W[1]-hardness of the 4-terminal-pairs<br>case at SODA 2016.<br> On the technical side, we use two recent developments in parameterized<br>algorithms. Using the technique of directed flow-augmentation [Kim, Kratsch,<br>Pilipczuk, Wahlstr\"{o}m, STOC 2022] we cast the problem as a CSP problem with<br>few variables and constraints over a large ordered domain.We observe that this<br>problem can be in turn encoded as an FO model-checking task over a structure<br>consisting of a few 0-1 matrices. We look at this problem through the lenses of<br>twin-width, a recently introduced structural parameter [Bonnet, Kim,<br>Thomass\'{e}, Watrigant, FOCS 2020]: By a recent characterization [Bonnet,<br>Giocanti, Ossona de Mendes, Simon, Thomass\'{e}, Toru\'{n}czyk, STOC 2022] the<br>said FO model-checking task can be done in FPT time if the said matrices have<br>bounded grid rank. To complete the proof, we show an irrelevant vertex rule: If<br>any of the matrices in the said encoding has a large grid minor, a vertex<br>corresponding to the middle'' box in the grid minor can be proclaimed<br>irrelevant -- not contained in the sought solution -- and thus reduced.<br>}, }
Endnote
%0 Report %A Hatzel, Meike %A Jaffke, Lars %A Lima, Paloma T. %A Masa&#345;&#237;k, Tom&#225;&#353; %A Pilipczuk, Marcin %A Sharma, Roohani %A Sorge, Manuel %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parameterized by the Size of the Cutset: Twin-width Meets Flow-Augmentation : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DE8-F %U https://arxiv.org/abs/2207.07425 %D 2022 %X We show fixed-parameter tractability of the Directed Multicut problem with<br>three terminal pairs (with a randomized algorithm). This problem, given a<br>directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$,<br>$(s_2,t_2)$, and $(s_3,t_3)$, and an integer $k$, asks to find a set of at most<br>$k$ non-terminal vertices in $G$ that intersect all $s_1t_1$-paths, all<br>$s_2t_2$-paths, and all $s_3t_3$-paths. The parameterized complexity of this<br>case has been open since Chitnis, Cygan, Hajiaghayi, and Marx proved<br>fixed-parameter tractability of the 2-terminal-pairs case at SODA 2012, and<br>Pilipczuk and Wahlstr\"{o}m proved the W[1]-hardness of the 4-terminal-pairs<br>case at SODA 2016.<br> On the technical side, we use two recent developments in parameterized<br>algorithms. Using the technique of directed flow-augmentation [Kim, Kratsch,<br>Pilipczuk, Wahlstr\"{o}m, STOC 2022] we cast the problem as a CSP problem with<br>few variables and constraints over a large ordered domain.We observe that this<br>problem can be in turn encoded as an FO model-checking task over a structure<br>consisting of a few 0-1 matrices. We look at this problem through the lenses of<br>twin-width, a recently introduced structural parameter [Bonnet, Kim,<br>Thomass\'{e}, Watrigant, FOCS 2020]: By a recent characterization [Bonnet,<br>Giocanti, Ossona de Mendes, Simon, Thomass\'{e}, Toru\'{n}czyk, STOC 2022] the<br>said FO model-checking task can be done in FPT time if the said matrices have<br>bounded grid rank. To complete the proof, we show an irrelevant vertex rule: If<br>any of the matrices in the said encoding has a large grid minor, a vertex<br>corresponding to the middle'' box in the grid minor can be proclaimed<br>irrelevant -- not contained in the sought solution -- and thus reduced.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[109]
L. Jaffke, P. T. Lima, and R. Sharma, “b-Coloring Parameterized by Pathwidth is XNLP-complete,” 2022. [Online]. Available: https://arxiv.org/abs/2209.07772. (arXiv: 2209.07772)
Abstract
We show that the $b$-Coloring problem is complete for the class XNLP when<br>parameterized by the pathwidth of the input graph. Besides determining the<br>precise parameterized complexity of this problem, this implies that b-Coloring<br>parameterized by pathwidth is $W[t]$-hard for all $t$, and resolves the<br>parameterized complexity of $b$-Coloring parameterized by treewidth.<br>
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BibTeX
@online{Jaffke2209.07772, TITLE = {$b$-Coloring Parameterized by Pathwidth is {XNLP}-complete}, AUTHOR = {Jaffke, Lars and Lima, Paloma T. and Sharma, Roohani}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2209.07772}, EPRINT = {2209.07772}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We show that the $b$-Coloring problem is complete for the class XNLP when<br>parameterized by the pathwidth of the input graph. Besides determining the<br>precise parameterized complexity of this problem, this implies that b-Coloring<br>parameterized by pathwidth is $W[t]$-hard for all $t$, and resolves the<br>parameterized complexity of $b$-Coloring parameterized by treewidth.<br>}, }
Endnote
%0 Report %A Jaffke, Lars %A Lima, Paloma T. %A Sharma, Roohani %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T b-Coloring Parameterized by Pathwidth is XNLP-complete : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1E7E-7 %U https://arxiv.org/abs/2209.07772 %D 2022 %X We show that the $b$-Coloring problem is complete for the class XNLP when<br>parameterized by the pathwidth of the input graph. Besides determining the<br>precise parameterized complexity of this problem, this implies that b-Coloring<br>parameterized by pathwidth is $W[t]$-hard for all $t$, and resolves the<br>parameterized complexity of $b$-Coloring parameterized by treewidth.<br> %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[110]
Y. Jiang and C. Zheng, “Robust and Optimal Contention Resolution without Collision Detection,” in SPAA ’22, 34th ACM Symposium on Parallelism in Algorithms and Architectures, Philadelphia, PA, USA, 2022.
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@inproceedings{Jiang_SPAA22, TITLE = {Robust and Optimal Contention Resolution without Collision Detection}, AUTHOR = {Jiang, Yonggang and Zheng, Chaodong}, LANGUAGE = {eng}, ISBN = {978-1-4503-9146-7}, DOI = {10.1145/3490148.3538592}, PUBLISHER = {ACM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {SPAA '22, 34th ACM Symposium on Parallelism in Algorithms and Architectures}, EDITOR = {Agrawal, Kunal and Lee, I-Ting Angelina}, PAGES = {107--118}, ADDRESS = {Philadelphia, PA, USA}, }
Endnote
%0 Conference Proceedings %A Jiang, Yonggang %A Zheng, Chaodong %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Robust and Optimal Contention Resolution without Collision Detection : %G eng %U http://hdl.handle.net/21.11116/0000-000C-104C-D %R 10.1145/3490148.3538592 %D 2022 %B 34th ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2022-07-11 - 2022-07-14 %C Philadelphia, PA, USA %B SPAA '22 %E Agrawal, Kunal; Lee, I-Ting Angelina %P 107 - 118 %I ACM %@ 978-1-4503-9146-7
[111]
E. J. Kim, T. Masařík, M. Pilipczuk, R. Sharma, and M. Wahlström, “On Weighted Graph Separation Problems and Flow-Augmentation,” 2022. [Online]. Available: https://arxiv.org/abs/2208.14841. (arXiv: 2208.14841)
Abstract
One of the first application of the recently introduced technique of<br>\emph{flow-augmentation} [Kim et al., STOC 2022] is a fixed-parameter algorithm<br>for the weighted version of \textsc{Directed Feedback Vertex Set}, a landmark<br>problem in parameterized complexity. In this note we explore applicability of<br>flow-augmentation to other weighted graph separation problems parameterized by<br>the size of the cutset. We show the following. -- In weighted undirected graphs<br>\textsc{Multicut} is FPT, both in the edge- and vertex-deletion version. -- The<br>weighted version of \textsc{Group Feedback Vertex Set} is FPT, even with an<br>oracle access to group operations. -- The weighted version of \textsc{Directed<br>Subset Feedback Vertex Set} is FPT. Our study reveals \textsc{Directed<br>Symmetric Multicut} as the next important graph separation problem whose<br>parameterized complexity remains unknown, even in the unweighted setting.<br>
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@online{Kim2208.14841, TITLE = {On Weighted Graph Separation Problems and Flow-Augmentation}, AUTHOR = {Kim, Eun Jung and Masa{\v r}{\'i}k, Tom{\'a}{\v s} and Pilipczuk, Marcin and Sharma, Roohani and Wahlstr{\"o}m, Magnus}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2208.14841}, EPRINT = {2208.14841}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {One of the first application of the recently introduced technique of<br>\emph{flow-augmentation} [Kim et al., STOC 2022] is a fixed-parameter algorithm<br>for the weighted version of \textsc{Directed Feedback Vertex Set}, a landmark<br>problem in parameterized complexity. In this note we explore applicability of<br>flow-augmentation to other weighted graph separation problems parameterized by<br>the size of the cutset. We show the following. -- In weighted undirected graphs<br>\textsc{Multicut} is FPT, both in the edge- and vertex-deletion version. -- The<br>weighted version of \textsc{Group Feedback Vertex Set} is FPT, even with an<br>oracle access to group operations. -- The weighted version of \textsc{Directed<br>Subset Feedback Vertex Set} is FPT. Our study reveals \textsc{Directed<br>Symmetric Multicut} as the next important graph separation problem whose<br>parameterized complexity remains unknown, even in the unweighted setting.<br>}, }
Endnote
%0 Report %A Kim, Eun Jung %A Masa&#345;&#237;k, Tom&#225;&#353; %A Pilipczuk, Marcin %A Sharma, Roohani %A Wahlstr&#246;m, Magnus %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Weighted Graph Separation Problems and Flow-Augmentation : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1E78-D %U https://arxiv.org/abs/2208.14841 %D 2022 %X One of the first application of the recently introduced technique of<br>\emph{flow-augmentation} [Kim et al., STOC 2022] is a fixed-parameter algorithm<br>for the weighted version of \textsc{Directed Feedback Vertex Set}, a landmark<br>problem in parameterized complexity. In this note we explore applicability of<br>flow-augmentation to other weighted graph separation problems parameterized by<br>the size of the cutset. We show the following. -- In weighted undirected graphs<br>\textsc{Multicut} is FPT, both in the edge- and vertex-deletion version. -- The<br>weighted version of \textsc{Group Feedback Vertex Set} is FPT, even with an<br>oracle access to group operations. -- The weighted version of \textsc{Directed<br>Subset Feedback Vertex Set} is FPT. Our study reveals \textsc{Directed<br>Symmetric Multicut} as the next important graph separation problem whose<br>parameterized complexity remains unknown, even in the unweighted setting.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,
[112]
A. Kinali-Dogan, “On Time, Time Synchronization and Noise in Time Measurement Systems,” Universität des Saarlandes, Saarbrücken, 2022.
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@phdthesis{Attilaphd2022, TITLE = {On Time, Time Synchronization and Noise in Time Measurement Systems}, AUTHOR = {Kinali-Dogan, Attila}, LANGUAGE = {eng}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, }
Endnote
%0 Thesis %A Kinali-Dogan, Attila %Y Lenzen, Christoph %A referee: Mehlhorn, Kurt %A referee: Vernotte, Francoise %+ 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 On Time, Time Synchronization and Noise in Time Measurement Systems : %G eng %U http://hdl.handle.net/21.11116/0000-000B-5436-A %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2022 %P 140 p. %V phd %9 phd
[113]
D. Kirkpatrick, H. U. Simon, and S. Zilles, “Optimal Collusion-Free Teaching,” Journal of Machine Learning Research. (arXiv: 1903.04012, Accepted/in press)
Abstract
Formal models of learning from teachers need to respect certain criteria to<br>avoid collusion. The most commonly accepted notion of collusion-freeness was<br>proposed by Goldman and Mathias (1996), and various teaching models obeying<br>their criterion have been studied. For each model $M$ and each concept class<br>$\mathcal{C}$, a parameter $M$-$\mathrm{TD}(\mathcal{C})$ refers to the<br>teaching dimension of concept class $\mathcal{C}$ in model $M$---defined to be<br>the number of examples required for teaching a concept, in the worst case over<br>all concepts in $\mathcal{C}$.<br> This paper introduces a new model of teaching, called no-clash teaching,<br>together with the corresponding parameter $\mathrm{NCTD}(\mathcal{C})$.<br>No-clash teaching is provably optimal in the strong sense that, given any<br>concept class $\mathcal{C}$ and any model $M$ obeying Goldman and Mathias's<br>collusion-freeness criterion, one obtains $\mathrm{NCTD}(\mathcal{C})\le<br>M$-$\mathrm{TD}(\mathcal{C})$. We also study a corresponding notion<br>$\mathrm{NCTD}^+$ for the case of learning from positive data only, establish<br>useful bounds on $\mathrm{NCTD}$ and $\mathrm{NCTD}^+$, and discuss relations<br>of these parameters to the VC-dimension and to sample compression.<br> In addition to formulating an optimal model of collusion-free teaching, our<br>main results are on the computational complexity of deciding whether<br>$\mathrm{NCTD}^+(\mathcal{C})=k$ (or $\mathrm{NCTD}(\mathcal{C})=k$) for given<br>$\mathcal{C}$ and $k$. We show some such decision problems to be equivalent to<br>the existence question for certain constrained matchings in bipartite graphs.<br>Our NP-hardness results for the latter are of independent interest in the study<br>of constrained graph matchings.<br>
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@article{KirkpatrickJMLR, TITLE = {Optimal Collusion-Free Teaching}, AUTHOR = {Kirkpatrick, David and Simon, Hans U. and Zilles, Sandra}, LANGUAGE = {eng}, ISSN = {1532-4435}, EPRINT = {1903.04012}, EPRINTTYPE = {arXiv}, PUBLISHER = {JMLR.org}, YEAR = {2022}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Formal models of learning from teachers need to respect certain criteria to<br>avoid collusion. The most commonly accepted notion of collusion-freeness was<br>proposed by Goldman and Mathias (1996), and various teaching models obeying<br>their criterion have been studied. For each model $M$ and each concept class<br>$\mathcal{C}$, a parameter $M$-$\mathrm{TD}(\mathcal{C})$ refers to the<br>teaching dimension of concept class $\mathcal{C}$ in model $M$---defined to be<br>the number of examples required for teaching a concept, in the worst case over<br>all concepts in $\mathcal{C}$.<br> This paper introduces a new model of teaching, called no-clash teaching,<br>together with the corresponding parameter $\mathrm{NCTD}(\mathcal{C})$.<br>No-clash teaching is provably optimal in the strong sense that, given any<br>concept class $\mathcal{C}$ and any model $M$ obeying Goldman and Mathias's<br>collusion-freeness criterion, one obtains $\mathrm{NCTD}(\mathcal{C})\le<br>M$-$\mathrm{TD}(\mathcal{C})$. We also study a corresponding notion<br>$\mathrm{NCTD}^+$ for the case of learning from positive data only, establish<br>useful bounds on $\mathrm{NCTD}$ and $\mathrm{NCTD}^+$, and discuss relations<br>of these parameters to the VC-dimension and to sample compression.<br> In addition to formulating an optimal model of collusion-free teaching, our<br>main results are on the computational complexity of deciding whether<br>$\mathrm{NCTD}^+(\mathcal{C})=k$ (or $\mathrm{NCTD}(\mathcal{C})=k$) for given<br>$\mathcal{C}$ and $k$. We show some such decision problems to be equivalent to<br>the existence question for certain constrained matchings in bipartite graphs.<br>Our NP-hardness results for the latter are of independent interest in the study<br>of constrained graph matchings.<br>}, JOURNAL = {Journal of Machine Learning Research}, }
Endnote
%0 Journal Article %A Kirkpatrick, David %A Simon, Hans U. %A Zilles, Sandra %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Collusion-Free Teaching : %G eng %U http://hdl.handle.net/21.11116/0000-000C-332F-7 %D 2022 %X Formal models of learning from teachers need to respect certain criteria to<br>avoid collusion. The most commonly accepted notion of collusion-freeness was<br>proposed by Goldman and Mathias (1996), and various teaching models obeying<br>their criterion have been studied. For each model $M$ and each concept class<br>$\mathcal{C}$, a parameter $M$-$\mathrm{TD}(\mathcal{C})$ refers to the<br>teaching dimension of concept class $\mathcal{C}$ in model $M$---defined to be<br>the number of examples required for teaching a concept, in the worst case over<br>all concepts in $\mathcal{C}$.<br> This paper introduces a new model of teaching, called no-clash teaching,<br>together with the corresponding parameter $\mathrm{NCTD}(\mathcal{C})$.<br>No-clash teaching is provably optimal in the strong sense that, given any<br>concept class $\mathcal{C}$ and any model $M$ obeying Goldman and Mathias's<br>collusion-freeness criterion, one obtains $\mathrm{NCTD}(\mathcal{C})\le<br>M$-$\mathrm{TD}(\mathcal{C})$. We also study a corresponding notion<br>$\mathrm{NCTD}^+$ for the case of learning from positive data only, establish<br>useful bounds on $\mathrm{NCTD}$ and $\mathrm{NCTD}^+$, and discuss relations<br>of these parameters to the VC-dimension and to sample compression.<br> In addition to formulating an optimal model of collusion-free teaching, our<br>main results are on the computational complexity of deciding whether<br>$\mathrm{NCTD}^+(\mathcal{C})=k$ (or $\mathrm{NCTD}(\mathcal{C})=k$) for given<br>$\mathcal{C}$ and $k$. We show some such decision problems to be equivalent to<br>the existence question for certain constrained matchings in bipartite graphs.<br>Our NP-hardness results for the latter are of independent interest in the study<br>of constrained graph matchings.<br> %K Computer Science, Learning, cs.LG,Statistics, Machine Learning, stat.ML %J Journal of Machine Learning Research %I JMLR.org %@ false
[114]
S. Kisfaludi-Bak, J. Nederlof, and K. Węgrzycki, “A Gap-ETH-Tight Approximation Scheme for Euclidean TSP,” in FOCS 2021, IEEE 62nd Annual Symposium on Foundations of Computer Science, Denver, CO, USA (Virtual Conference), 2022.
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@inproceedings{Kisfaludi-Bak_FOCS21, TITLE = {A {G}ap-{ETH}-Tight Approximation Scheme for {E}uclidean {TSP}}, AUTHOR = {Kisfaludi-Bak, S{\'a}ndor and Nederlof, Jesper and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, ISBN = {978-1-6654-2055-6}, DOI = {10.1109/FOCS52979.2021.00043}, PUBLISHER = {IEEE}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {FOCS 2021, IEEE 62nd Annual Symposium on Foundations of Computer Science}, PAGES = {351--362}, ADDRESS = {Denver, CO, USA (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %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/21.11116/0000-000A-C557-6 %R 10.1109/FOCS52979.2021.00043 %D 2022 %B IEEE 62nd Annual Symposium on Foundations of Computer Science %Z date of event: 2022-02-07 - 2022-02-10 %C Denver, CO, USA (Virtual Conference) %B FOCS 2021 %P 351 - 362 %I IEEE %@ 978-1-6654-2055-6
[115]
T. Kociumaka, G. Navarro, and F. Olivares, “Near-Optimal Search Time in δ-Optimal Space,” in LATIN 2022: Theoretical Informatics, Guanajuato, Mexico, 2022.
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@inproceedings{Kociumaka_LATIN22, TITLE = {Near-optimal search time in $\delta$-optimal space}, AUTHOR = {Kociumaka, Tomasz and Navarro, Gonzalo and Olivares, Francisco}, LANGUAGE = {eng}, ISBN = {978-3-031-20623-8}, DOI = {10.1007/978-3-031-20624-5_6}, PUBLISHER = {Springer}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {LATIN 2022: Theoretical Informatics}, EDITOR = {Casta{\~n}eda, Armando and Rodr{\'i}guez-Henr{\'i}quez, Francisco}, PAGES = {88--103}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13568}, ADDRESS = {Guanajuato, Mexico}, }
Endnote
%0 Conference Proceedings %A Kociumaka, Tomasz %A Navarro, Gonzalo %A Olivares, Francisco %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Near-Optimal Search Time in &#948;-Optimal Space : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1534-2 %R 10.1007/978-3-031-20624-5_6 %D 2022 %B 5th Latin American Theoretical Informatics Symposium %Z date of event: 2022-11-07 - 2022-11-11 %C Guanajuato, Mexico %B LATIN 2022: Theoretical Informatics %E Casta&#241;eda, Armando; Rodr&#237;guez-Henr&#237;quez, Francisco %P 88 - 103 %I Springer %@ 978-3-031-20623-8 %B Lecture Notes in Computer Science %N 13568 %U https://rdcu.be/c19vn
[116]
T. Kociumaka, G. Navarro, and N. Prezza, “Towards a Definitive Compressibility Measure for Repetitive Sequences,” IEEE Transactions on Information Theory, 2022.
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@article{TIT22, TITLE = {Towards a Definitive Compressibility Measure for Repetitive Sequences}, AUTHOR = {Kociumaka, Tomasz and Navarro, Gonzalo and Prezza, Nicola}, LANGUAGE = {eng}, ISSN = {0018-9448}, DOI = {10.1109/TIT.2022.3224382}, PUBLISHER = {IEEE}, ADDRESS = {Piscataway, NJ}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {IEEE Transactions on Information Theory}, }
Endnote
%0 Journal Article %A Kociumaka, Tomasz %A Navarro, Gonzalo %A Prezza, Nicola %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Towards a Definitive Compressibility Measure for Repetitive Sequences : %G eng %U http://hdl.handle.net/21.11116/0000-000C-150A-2 %R 10.1109/TIT.2022.3224382 %7 2022 %D 2022 %J IEEE Transactions on Information Theory %I IEEE %C Piscataway, NJ %@ false
[117]
R. Krithika, R. Sharma, and P. Tale, “The Complexity of Contracting Bipartite Graphs into Small Cycles,” in Graph-Theoretic Concepts in Computer Science (WG 2022), Tübingen, Germany, 2022.
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@inproceedings{KrithikaWG22, TITLE = {The Complexity of Contracting Bipartite Graphs into Small Cycles}, AUTHOR = {Krithika, R. and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, ISBN = {978-3-031-15913-8}, DOI = {10.1007/978-3-031-15914-5_26}, PUBLISHER = {Springer}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, BOOKTITLE = {Graph-Theoretic Concepts in Computer Science (WG 2022)}, EDITOR = {Bekos, Michael A. and Kaufmann, Michael}, PAGES = {356--369}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {13453}, ADDRESS = {T{\"u}bingen, Germany}, }
Endnote
%0 Conference Proceedings %A Krithika, R. %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T The Complexity of Contracting Bipartite Graphs into Small Cycles : %G eng %U http://hdl.handle.net/21.11116/0000-000B-5928-5 %R 10.1007/978-3-031-15914-5_26 %D 2022 %B 48th International Workshop on Graph-Theoretic Concepts in Computer Science %Z date of event: 2022-06-22 - 2022-06-24 %C T&#252;bingen, Germany %B Graph-Theoretic Concepts in Computer Science %E Bekos, Michael A.; Kaufmann, Michael %P 356 - 369 %I Springer %@ 978-3-031-15913-8 %B Lecture Notes in Computer Science %N 13453
[118]
R. Krithika, R. Sharma, and P. Tale, “The Complexity of Contracting Bipartite Graphs into Small Cycles,” 2022. [Online]. Available: https://arxiv.org/abs/2206.07358. (arXiv: 2206.07358)
Abstract
For a positive integer $\ell \geq 3$, the $C_\ell$-Contractibility problem<br>takes as input an undirected simple graph $G$ and determines whether $G$ can be<br>transformed into a graph isomorphic to $C_\ell$ (the induced cycle on $\ell$<br>vertices) using only edge contractions. Brouwer and Veldman [JGT 1987] showed<br>that $C_4$-Contractibility is NP-complete in general graphs. It is easy to<br>verify that $C_3$-Contractibility is polynomial-time solvable. Dabrowski and<br>Paulusma [IPL 2017] showed that $C_{\ell}$-Contractibility is \NP-complete\ on<br>bipartite graphs for $\ell = 6$ and posed as open problems the status of the<br>problem when $\ell$ is 4 or 5. In this paper, we show that both<br>$C_5$-Contractibility and $C_4$-Contractibility are NP-complete on bipartite<br>graphs.<br>
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@online{Krithika22, TITLE = {The Complexity of Contracting Bipartite Graphs into Small Cycles}, AUTHOR = {Krithika, R. and Sharma, Roohani and Tale, Prafullkumar}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2206.07358}, EPRINT = {2206.07358}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {For a positive integer $\ell \geq 3$, the $C_\ell$-Contractibility problem<br>takes as input an undirected simple graph $G$ and determines whether $G$ can be<br>transformed into a graph isomorphic to $C_\ell$ (the induced cycle on $\ell$<br>vertices) using only edge contractions. Brouwer and Veldman [JGT 1987] showed<br>that $C_4$-Contractibility is NP-complete in general graphs. It is easy to<br>verify that $C_3$-Contractibility is polynomial-time solvable. Dabrowski and<br>Paulusma [IPL 2017] showed that $C_{\ell}$-Contractibility is \NP-complete\ on<br>bipartite graphs for $\ell = 6$ and posed as open problems the status of the<br>problem when $\ell$ is 4 or 5. In this paper, we show that both<br>$C_5$-Contractibility and $C_4$-Contractibility are NP-complete on bipartite<br>graphs.<br>}, }
Endnote
%0 Report %A Krithika, R. %A Sharma, Roohani %A Tale, Prafullkumar %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T The Complexity of Contracting Bipartite Graphs into Small Cycles : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1DCB-0 %U https://arxiv.org/abs/2206.07358 %D 2022 %X For a positive integer $\ell \geq 3$, the $C_\ell$-Contractibility problem<br>takes as input an undirected simple graph $G$ and determines whether $G$ can be<br>transformed into a graph isomorphic to $C_\ell$ (the induced cycle on $\ell$<br>vertices) using only edge contractions. Brouwer and Veldman [JGT 1987] showed<br>that $C_4$-Contractibility is NP-complete in general graphs. It is easy to<br>verify that $C_3$-Contractibility is polynomial-time solvable. Dabrowski and<br>Paulusma [IPL 2017] showed that $C_{\ell}$-Contractibility is \NP-complete\ on<br>bipartite graphs for $\ell = 6$ and posed as open problems the status of the<br>problem when $\ell$ is 4 or 5. In this paper, we show that both<br>$C_5$-Contractibility and $C_4$-Contractibility are NP-complete on bipartite<br>graphs.<br> %K Computer Science, Computational Complexity, cs.CC
[119]
M. Künnemann and A. Nusser, “Polygon Placement Revisited: (Degree of Freedom + 1)-SUM Hardness and an Improvement via Offline Dynamic Rectangle Union,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022), Virtual, 2022.
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@inproceedings{Kuennemann_SODA22b, TITLE = {Polygon Placement Revisited: (Degree of Freedom + 1)-{SUM} Hardness and an Improvement via Offline Dynamic Rectangle Union}, AUTHOR = {K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, ISBN = {978-1-61197-707-3}, DOI = {10.1137/1.9781611977073}, PUBLISHER = {SIAM}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2022)}, EDITOR = {Naor, Seffi and Buchbinder, Niv}, PAGES = {3181--3201}, ADDRESS = {Virtual}, }
Endnote
%0 Conference Proceedings %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Polygon Placement Revisited: (Degree of Freedom + 1)-SUM Hardness and an Improvement via Offline Dynamic Rectangle Union : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F8F-2 %R 10.1137/1.9781611977073 %D 2022 %B Thirty-Third Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2022-01-09 - 2022-01-12 %C Virtual %B Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms %E Naor, Seffi; Buchbinder, Niv %P 3181 - 3201 %I SIAM %@ 978-1-61197-707-3
[120]
F. Mansouri, H. U. Simon, A. Singla, and S. Zilles, “On Batch Teaching with Sample Complexity Bounded by VCD,” in Advances in Neural Information Processing Systems 35 (NeurIPS 2022), New Orleans, LA, USA, 2022.
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@inproceedings{Mansouri_Neurips22, TITLE = {On Batch Teaching with Sample Complexity Bounded by {VCD}}, AUTHOR = {Mansouri, Farnam and Simon, Hans U. and Singla, Adish and Zilles, Sandra}, LANGUAGE = {eng}, PUBLISHER = {Curran Associates, Inc}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 35 (NeurIPS 2022)}, EDITOR = {Koyejo, S. and Mohamed, S. and Agarwal, A. and Belgrave, D. and Cho, K. and Oh, A.}, PAGES = {15732--15742}, ADDRESS = {New Orleans, LA, USA}, }
Endnote
%0 Conference Proceedings %A Mansouri, Farnam %A Simon, Hans U. %A Singla, Adish %A Zilles, Sandra %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T On Batch Teaching with Sample Complexity Bounded by VCD : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1601-A %D 2022 %B 36th Conference on Neural Information Processing Systems %Z date of event: 2022-11-28 - 2022-12-09 %C New Orleans, LA, USA %B Advances in Neural Information Processing Systems 35 %E Koyejo, S.; Mohamed, S.; Agarwal, A.; Belgrave, D.; Cho, K.; Oh, A. %P 15732 - 15742 %I Curran Associates, Inc %U https://openreview.net/pdf?id=wKf5dRSartn
[121]
J. Nederlof, M. Pilipczuk, and K. Węgrzycki, “Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models,” 2022. [Online]. Available: https://arxiv.org/abs/2201.09340. (arXiv: 2201.09340)
Abstract
We study Koebe orderings of planar graphs: vertex orderings obtained by<br>modelling the graph as the intersection graph of pairwise internally-disjoint<br>discs in the plane, and ordering the vertices by non-increasing radii of the<br>associated discs. We prove that for every $d\in \mathbb{N}$, any such ordering<br>has $d$-admissibility bounded by $O(d/\ln d)$ and weak $d$-coloring number<br>bounded by $O(d^4 \ln d)$. This in particular shows that the $d$-admissibility<br>of planar graphs is bounded by $O(d/\ln d)$, which asymptotically matches a<br>known lower bound due to Dvo\v{r}\'ak and Siebertz.<br>
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@online{Nederlof2201.09340, TITLE = {Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models}, AUTHOR = {Nederlof, Jesper and Pilipczuk, Micha{\l} and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2201.09340}, EPRINT = {2201.09340}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study Koebe orderings of planar graphs: vertex orderings obtained by<br>modelling the graph as the intersection graph of pairwise internally-disjoint<br>discs in the plane, and ordering the vertices by non-increasing radii of the<br>associated discs. We prove that for every $d\in \mathbb{N}$, any such ordering<br>has $d$-admissibility bounded by $O(d/\ln d)$ and weak $d$-coloring number<br>bounded by $O(d^4 \ln d)$. This in particular shows that the $d$-admissibility<br>of planar graphs is bounded by $O(d/\ln d)$, which asymptotically matches a<br>known lower bound due to Dvo\v{r}\'ak and Siebertz.<br>}, }
Endnote
%0 Report %A Nederlof, Jesper %A Pilipczuk, Micha&#322; %A W&#281;grzycki, Karol %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1EF3-1 %U https://arxiv.org/abs/2201.09340 %D 2022 %X We study Koebe orderings of planar graphs: vertex orderings obtained by<br>modelling the graph as the intersection graph of pairwise internally-disjoint<br>discs in the plane, and ordering the vertices by non-increasing radii of the<br>associated discs. We prove that for every $d\in \mathbb{N}$, any such ordering<br>has $d$-admissibility bounded by $O(d/\ln d)$ and weak $d$-coloring number<br>bounded by $O(d^4 \ln d)$. This in particular shows that the $d$-admissibility<br>of planar graphs is bounded by $O(d/\ln d)$, which asymptotically matches a<br>known lower bound due to Dvo\v{r}\'ak and Siebertz.<br> %K Mathematics, Combinatorics, math.CO,Computer Science, Discrete Mathematics, cs.DM
[122]
J. Nederlof, M. Pilipczuk, C. M. F. Swennenhuis, and K. Węgrzycki, “Isolation Schemes for Problems on Decomposable Graphs,” in 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022), Marseille, France (Virtual Conference), 2022.
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@inproceedings{Nederlof_STACS2022, TITLE = {Isolation Schemes for Problems on Decomposable Graphs}, AUTHOR = {Nederlof, Jesper and Pilipczuk, Micha{\l} and Swennenhuis, C{\'e}line M. F. and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-222-8}, URL = {urn:nbn:de:0030-drops-158601}, DOI = {10.4230/LIPIcs.STACS.2022.50}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)}, EDITOR = {Berenbrink, Petra and Monmege, Benjamin}, PAGES = {1--20}, EID = {50}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {219}, ADDRESS = {Marseille, France (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Nederlof, Jesper %A Pilipczuk, Micha&#322; %A Swennenhuis, C&#233;line M. F. %A W&#281;grzycki, Karol %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Isolation Schemes for Problems on Decomposable Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1EEC-A %R 10.4230/LIPIcs.STACS.2022.50 %U urn:nbn:de:0030-drops-158601 %D 2022 %B 39th International Symposium on Theoretical Aspects of Computer Science %Z date of event: 2022-03-15 - 2022-03-18 %C Marseille, France (Virtual Conference) %B 39th International Symposium on Theoretical Aspects of Computer Science %E Berenbrink, Petra; Monmege, Benjamin %P 1 - 20 %Z sequence number: 50 %I Schloss Dagstuhl %@ 978-3-95977-222-8 %B Leibniz International Proceedings in Informatics %N 219 %@ false
[123]
J. Nederlof, C. M. F. Swennenhuis, and K. Węgrzycki, “Makespan Scheduling of Unit Jobs with Precedence Constraints in O(1.995n) time,” 2022. [Online]. Available: https://arxiv.org/abs/2208.02664. (arXiv: 2208.02664)
Abstract
In a classical scheduling problem, we are given a set of $n$ jobs of unit<br>length along with precedence constraints and the goal is to find a schedule of<br>these jobs on $m$ identical machines that minimizes the makespan. This problem<br>is well-known to be NP-hard for an unbounded number of machines. Using standard<br>3-field notation, it is known as $P|\text{prec}, p_j=1|C_{\max}$.<br> We present an algorithm for this problem that runs in $O(1.995^n)$ time.<br>Before our work, even for $m=3$ machines the best known algorithms ran in<br>$O^\ast(2^n)$ time. In contrast, our algorithm works when the number of<br>machines $m$ is unbounded. A crucial ingredient of our approach is an algorithm<br>with a runtime that is only single-exponential in the vertex cover of the<br>comparability graph of the precedence constraint graph. This heavily relies on<br>insights from a classical result by Dolev and Warmuth (Journal of Algorithms<br>1984) for precedence graphs without long chains.<br>
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@online{Nederlof2208.02664, TITLE = {Makespan Scheduling of Unit Jobs with Precedence Constraints in $O(1.995^n)$ time}, AUTHOR = {Nederlof, Jesper and Swennenhuis, C{\'e}line M. F. and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2208.02664}, EPRINT = {2208.02664}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In a classical scheduling problem, we are given a set of $n$ jobs of unit<br>length along with precedence constraints and the goal is to find a schedule of<br>these jobs on $m$ identical machines that minimizes the makespan. This problem<br>is well-known to be NP-hard for an unbounded number of machines. Using standard<br>3-field notation, it is known as $P|\text{prec}, p_j=1|C_{\max}$.<br> We present an algorithm for this problem that runs in $O(1.995^n)$ time.<br>Before our work, even for $m=3$ machines the best known algorithms ran in<br>$O^\ast(2^n)$ time. In contrast, our algorithm works when the number of<br>machines $m$ is unbounded. A crucial ingredient of our approach is an algorithm<br>with a runtime that is only single-exponential in the vertex cover of the<br>comparability graph of the precedence constraint graph. This heavily relies on<br>insights from a classical result by Dolev and Warmuth (Journal of Algorithms<br>1984) for precedence graphs without long chains.<br>}, }
Endnote
%0 Report %A Nederlof, Jesper %A Swennenhuis, C&#233;line M. F. %A W&#281;grzycki, Karol %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Makespan Scheduling of Unit Jobs with Precedence Constraints in O(1.995n) time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F35-7 %U https://arxiv.org/abs/2208.02664 %D 2022 %X In a classical scheduling problem, we are given a set of $n$ jobs of unit<br>length along with precedence constraints and the goal is to find a schedule of<br>these jobs on $m$ identical machines that minimizes the makespan. This problem<br>is well-known to be NP-hard for an unbounded number of machines. Using standard<br>3-field notation, it is known as $P|\text{prec}, p_j=1|C_{\max}$.<br> We present an algorithm for this problem that runs in $O(1.995^n)$ time.<br>Before our work, even for $m=3$ machines the best known algorithms ran in<br>$O^\ast(2^n)$ time. In contrast, our algorithm works when the number of<br>machines $m$ is unbounded. A crucial ingredient of our approach is an algorithm<br>with a runtime that is only single-exponential in the vertex cover of the<br>comparability graph of the precedence constraint graph. This heavily relies on<br>insights from a classical result by Dolev and Warmuth (Journal of Algorithms<br>1984) for precedence graphs without long chains.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[124]
A. Nusser, “Fine-Grained Complexity and Algorithm Engineering of Geometric Similarity Measures,” Universität des Saarlandes, Saarbrücken, 2022.
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@phdthesis{NusserPhD22, TITLE = {Fine-Grained Complexity and Algorithm Engineering of Geometric Similarity Measures}, AUTHOR = {Nusser, Andr{\'e}}, LANGUAGE = {eng}, URL = {urn:nbn:de:bsz:291--ds-370184}, DOI = {10.22028/D291-37018}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, }
Endnote
%0 Thesis %A Nusser, Andr&#233; %Y Bringmann, Karl %A referee: Mehlhorn, Kurt %A referee: Chan, Timothy %A referee: de Ber, Mark %+ 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 External Organizations %T Fine-Grained Complexity and Algorithm Engineering of Geometric Similarity Measures : %G eng %U http://hdl.handle.net/21.11116/0000-000C-2693-3 %R 10.22028/D291-37018 %U urn:nbn:de:bsz:291--ds-370184 %F OTHER: hdl:20.500.11880/33904 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2022 %P XIV, 210 p. %V phd %9 phd %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/33904
[125]
B. Ray Chaudhury, Y. K. Cheung, J. Garg, N. Garg, M. Hoefer, and K. Mehlhorn, “Fair Division of Indivisible Goods for a Class of Concave Valuations,” Journal of Artificial Intelligence Research, vol. 74, 2022.
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@article{RayChaudhury22, TITLE = {Fair Division of Indivisible Goods for a Class of Concave Valuations}, AUTHOR = {Ray Chaudhury, Bhaskar and Cheung, Yun Kuen and Garg, Jugal and Garg, Naveen and Hoefer, Martin and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {1076-9757}, DOI = {10.1613/jair.1.12911}, PUBLISHER = {AI Access Foundation}, ADDRESS = {S.l.}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Artificial Intelligence Research}, VOLUME = {74}, PAGES = {111--142}, }
Endnote
%0 Journal Article %A Ray Chaudhury, Bhaskar %A Cheung, Yun Kuen %A Garg, Jugal %A Garg, Naveen %A Hoefer, Martin %A Mehlhorn, Kurt %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fair Division of Indivisible Goods for a Class of Concave Valuations : %G eng %U http://hdl.handle.net/21.11116/0000-000A-9DB8-6 %R 10.1613/jair.1.12911 %7 2022 %D 2022 %J Journal of Artificial Intelligence Research %V 74 %& 111 %P 111 - 142 %I AI Access Foundation %C S.l. %@ false
[126]
M. Roth, J. Schmitt, and P. Wellnitz, “Counting Small Induced Subgraphs Satisfying Monotone Properties,” SIAM Journal on Computing, 2022.
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@article{Roth22, TITLE = {Counting Small Induced Subgraphs Satisfying Monotone Properties}, AUTHOR = {Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/20M1365624}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, JOURNAL = {SIAM Journal on Computing}, PAGES = {FOCS20-139--FOCS20-174}, }
Endnote
%0 Journal Article %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/21.11116/0000-000C-1EB6-6 %R 10.1137/20M1365624 %7 2022 %D 2022 %J SIAM Journal on Computing %& FOCS20-139 %P FOCS20-139 - FOCS20-174 %I SIAM %C Philadelphia, PA %@ false
[127]
B. Wiederhake, “Pulse Propagation, Graph Cover, and Packet Forwarding,” Universität des Saarlandes, Saarbrücken, 2022.
Abstract
We study distributed systems, with a particular focus on graph problems and fault<br>tolerance.<br>Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using<br>a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal<br>by being a distributed system consisting of very simple nodes. We show that even in<br>the typical mode of operation without faults, TRIX performs significantly better than a<br>regular wire or clock tree: Statistical evaluation of our simulated experiments show that<br>we achieve a skew with standard deviation of O(log log H), where H is the height of the<br>TRIX grid.<br>The distance-r generalization of classic graph problems can give us insights on how<br>distance affects hardness of a problem. For the distance-r dominating set problem, we<br>present both an algorithmic upper and unconditional lower bound for any graph class<br>with certain high-girth and sparseness criteria. In particular, our algorithm achieves a<br>O(r · f(r))-approximation in time O(r), where f is the expansion function, which correlates<br>with density. For constant r, this implies a constant approximation factor, in constant<br>time. We also show that no algorithm can achieve a (2r + 1 − δ)-approximation for any<br>δ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we<br>extend the algorithm to related graph cover problems and even to a different execution<br>model.<br>Furthermore, we investigate the problem of packet forwarding, which addresses the<br>question of how and when best to forward packets in a distributed system. These packets<br>are injected by an adversary. We build on the existing algorithm OED to handle more<br>than a single destination. In particular, we show that buffers of size O(log n) are sufficient<br>for this algorithm, in contrast to O(n) for the naive approach.
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@phdthesis{Wiederhakephd2021, TITLE = {Pulse Propagation, Graph Cover, and Packet Forwarding}, AUTHOR = {Wiederhake, Ben}, LANGUAGE = {eng}, URL = {nbn:de:bsz:291--ds-366085}, DOI = {10.22028/D291-36608}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, DATE = {2022}, ABSTRACT = {We study distributed systems, with a particular focus on graph problems and fault<br>tolerance.<br>Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using<br>a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal<br>by being a distributed system consisting of very simple nodes. We show that even in<br>the typical mode of operation without faults, TRIX performs significantly better than a<br>regular wire or clock tree: Statistical evaluation of our simulated experiments show that<br>we achieve a skew with standard deviation of O(log log H), where H is the height of the<br>TRIX grid.<br>The distance-r generalization of classic graph problems can give us insights on how<br>distance affects hardness of a problem. For the distance-r dominating set problem, we<br>present both an algorithmic upper and unconditional lower bound for any graph class<br>with certain high-girth and sparseness criteria. In particular, our algorithm achieves a<br>O(r &#183; f(r))-approximation in time O(r), where f is the expansion function, which correlates<br>with density. For constant r, this implies a constant approximation factor, in constant<br>time. We also show that no algorithm can achieve a (2r + 1 {\textminus} $\delta$)-approximation for any<br>$\delta$ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we<br>extend the algorithm to related graph cover problems and even to a different execution<br>model.<br>Furthermore, we investigate the problem of packet forwarding, which addresses the<br>question of how and when best to forward packets in a distributed system. These packets<br>are injected by an adversary. We build on the existing algorithm OED to handle more<br>than a single destination. In particular, we show that buffers of size O(log n) are sufficient<br>for this algorithm, in contrast to O(n) for the naive approach.}, }
Endnote
%0 Thesis %A Wiederhake, Ben %Y Lenzen, Christoph %A referee: 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 Pulse Propagation, Graph Cover, and Packet Forwarding : %G eng %U http://hdl.handle.net/21.11116/0000-000A-CEBE-9 %R 10.22028/D291-36608 %U nbn:de:bsz:291--ds-366085 %F OTHER: hdl:20.500.11880/33316 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2022 %P 83 p. %V phd %9 phd %X We study distributed systems, with a particular focus on graph problems and fault<br>tolerance.<br>Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using<br>a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal<br>by being a distributed system consisting of very simple nodes. We show that even in<br>the typical mode of operation without faults, TRIX performs significantly better than a<br>regular wire or clock tree: Statistical evaluation of our simulated experiments show that<br>we achieve a skew with standard deviation of O(log log H), where H is the height of the<br>TRIX grid.<br>The distance-r generalization of classic graph problems can give us insights on how<br>distance affects hardness of a problem. For the distance-r dominating set problem, we<br>present both an algorithmic upper and unconditional lower bound for any graph class<br>with certain high-girth and sparseness criteria. In particular, our algorithm achieves a<br>O(r &#183; f(r))-approximation in time O(r), where f is the expansion function, which correlates<br>with density. For constant r, this implies a constant approximation factor, in constant<br>time. We also show that no algorithm can achieve a (2r + 1 &#8722; &#948;)-approximation for any<br>&#948; > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we<br>extend the algorithm to related graph cover problems and even to a different execution<br>model.<br>Furthermore, we investigate the problem of packet forwarding, which addresses the<br>question of how and when best to forward packets in a distributed system. These packets<br>are injected by an adversary. We build on the existing algorithm OED to handle more<br>than a single destination. In particular, we show that buffers of size O(log n) are sufficient<br>for this algorithm, in contrast to O(n) for the naive approach. %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/33316
[128]
D. Woodruff and A. Zandieh, “Leverage Score Sampling for Tensor Product Matrices in Input Sparsity Time,” in Proceedings of the 39th International Conference on Machine Learning (ICML 2022), Baltimore, MA, USA, 2022.
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BibTeX
@inproceedings{Woodruff_ICML22, TITLE = {Leverage Score Sampling for Tensor Product Matrices in Input Sparsity Time}, AUTHOR = {Woodruff, David and Zandieh, Amir}, LANGUAGE = {eng}, ISSN = {1938-7228}, URL = {https://proceedings.mlr.press/v162/woodruff22a.html}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 39th International Conference on Machine Learning (ICML 2022)}, EDITOR = {Chaudhuri, Kamalika and Jegelka, Stefanie and Le, Song and Csaba, Szepesvari and Gang, Niu and Sabato, Sivan}, PAGES = {23933--23964}, SERIES = {Proceedings of the Machine Learning Research}, VOLUME = {162}, ADDRESS = {Baltimore, MA, USA}, }
Endnote
%0 Conference Proceedings %A Woodruff, David %A Zandieh, Amir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Leverage Score Sampling for Tensor Product Matrices in Input Sparsity Time : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9101-E %U https://proceedings.mlr.press/v162/woodruff22a.html %D 2022 %B 39th International Conference on Machine Learning %Z date of event: 2022-07-17 - 2022-07-23 %C Baltimore, MA, USA %B Proceedings of the 39th International Conference on Machine Learning %E Chaudhuri, Kamalika; Jegelka, Stefanie; Le, Song; Csaba, Szepesvari; Gang, Niu; Sabato, Sivan %P 23933 - 23964 %B Proceedings of the Machine Learning Research %N 162 %@ false
[129]
A. Zandieh, I. Han, and H. Avron, “Near Optimal Reconstruction of Spherical Harmonic Expansions,” 2022. [Online]. Available: https://arxiv.org/abs/2202.12995. (arXiv: 2202.12995)
Abstract
We propose an algorithm for robust recovery of the spherical harmonic<br>expansion of functions defined on the d-dimensional unit sphere<br>$\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show<br>that for any $f \in L^2(\mathbb{S}^{d-1})$, the number of evaluations of $f$<br>needed to recover its degree-$q$ spherical harmonic expansion equals the<br>dimension of the space of spherical harmonics of degree at most $q$ up to a<br>logarithmic factor. Moreover, we develop a simple yet efficient algorithm to<br>recover degree-$q$ expansion of $f$ by only evaluating the function on<br>uniformly sampled points on $\mathbb{S}^{d-1}$. Our algorithm is based on the<br>connections between spherical harmonics and Gegenbauer polynomials and leverage<br>score sampling methods. Unlike the prior results on fast spherical harmonic<br>transform, our proposed algorithm works efficiently using a nearly optimal<br>number of samples in any dimension d. We further illustrate the empirical<br>performance of our algorithm on numerical examples.<br>
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@online{zandieh2202.12995, TITLE = {Near Optimal Reconstruction of Spherical Harmonic Expansions}, AUTHOR = {Zandieh, Amir and Han, Insu and Avron, Haim}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2202.12995}, EPRINT = {2202.12995}, EPRINTTYPE = {arXiv}, YEAR = {2022}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We propose an algorithm for robust recovery of the spherical harmonic<br>expansion of functions defined on the d-dimensional unit sphere<br>$\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show<br>that for any $f \in L^2(\mathbb{S}^{d-1})$, the number of evaluations of $f$<br>needed to recover its degree-$q$ spherical harmonic expansion equals the<br>dimension of the space of spherical harmonics of degree at most $q$ up to a<br>logarithmic factor. Moreover, we develop a simple yet efficient algorithm to<br>recover degree-$q$ expansion of $f$ by only evaluating the function on<br>uniformly sampled points on $\mathbb{S}^{d-1}$. Our algorithm is based on the<br>connections between spherical harmonics and Gegenbauer polynomials and leverage<br>score sampling methods. Unlike the prior results on fast spherical harmonic<br>transform, our proposed algorithm works efficiently using a nearly optimal<br>number of samples in any dimension d. We further illustrate the empirical<br>performance of our algorithm on numerical examples.<br>}, }
Endnote
%0 Report %A Zandieh, Amir %A Han, Insu %A Avron, Haim %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Near Optimal Reconstruction of Spherical Harmonic Expansions : %G eng %U http://hdl.handle.net/21.11116/0000-000C-9105-A %U https://arxiv.org/abs/2202.12995 %D 2022 %X We propose an algorithm for robust recovery of the spherical harmonic<br>expansion of functions defined on the d-dimensional unit sphere<br>$\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show<br>that for any $f \in L^2(\mathbb{S}^{d-1})$, the number of evaluations of $f$<br>needed to recover its degree-$q$ spherical harmonic expansion equals the<br>dimension of the space of spherical harmonics of degree at most $q$ up to a<br>logarithmic factor. Moreover, we develop a simple yet efficient algorithm to<br>recover degree-$q$ expansion of $f$ by only evaluating the function on<br>uniformly sampled points on $\mathbb{S}^{d-1}$. Our algorithm is based on the<br>connections between spherical harmonics and Gegenbauer polynomials and leverage<br>score sampling methods. Unlike the prior results on fast spherical harmonic<br>transform, our proposed algorithm works efficiently using a nearly optimal<br>number of samples in any dimension d. We further illustrate the empirical<br>performance of our algorithm on numerical examples.<br> %K Mathematics, Numerical Analysis, math.NA,Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Learning, cs.LG,Computer Science, Numerical Analysis, cs.NA,eess.SP
2021
[130]
H. Akrami, B. Ray Chaudhury, M. Hoefer, K. Mehlhorn, M. Schmalhofer, G. Shahkarami, G. Varricchio, Q. Vermande, and E. van Wijland, “Maximizing Nash Social Welfare in 2-Value Instances,” 2021. [Online]. Available: https://arxiv.org/abs/2107.08965. (arXiv: 2107.08965)
Abstract
We consider the problem of maximizing the Nash social welfare when allocating<br>a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We<br>study instances, in which all agents have 2-value additive valuations: The<br>value of every agent $i \in \mathcal{N}$ for every good $j \in \mathcal{G}$ is<br>$v_{ij} \in \{p,q\}$, for $p,q \in \mathbb{N}$, $p \le q$. Maybe surprisingly,<br>we design an algorithm to compute an optimal allocation in polynomial time if<br>$p$ divides $q$, i.e., when $p=1$ and $q \in \mathbb{N}$ after appropriate<br>scaling. The problem is \classNP-hard whenever $p$ and $q$ are coprime and $p<br>\ge 3$.<br> In terms of approximation, we present positive and negative results for<br>general $p$ and $q$. We show that our algorithm obtains an approximation ratio<br>of at most 1.0345. Moreover, we prove that the problem is \classAPX-hard, with<br>a lower bound of $1.000015$ achieved at $p/q = 4/5$.<br>
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@online{Akrami2107.08965, TITLE = {Maximizing Nash Social Welfare in 2-Value Instances}, AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Hoefer, Martin and Mehlhorn, Kurt and Schmalhofer, Marco and Shahkarami, Golnoosh and Varricchio, Giovanna and Vermande, Quentin and van Wijland, Ernest}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2107.08965}, EPRINT = {2107.08965}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the problem of maximizing the Nash social welfare when allocating<br>a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We<br>study instances, in which all agents have 2-value additive valuations: The<br>value of every agent $i \in \mathcal{N}$ for every good $j \in \mathcal{G}$ is<br>$v_{ij} \in \{p,q\}$, for $p,q \in \mathbb{N}$, $p \le q$. Maybe surprisingly,<br>we design an algorithm to compute an optimal allocation in polynomial time if<br>$p$ divides $q$, i.e., when $p=1$ and $q \in \mathbb{N}$ after appropriate<br>scaling. The problem is \classNP-hard whenever $p$ and $q$ are coprime and $p<br>\ge 3$.<br> In terms of approximation, we present positive and negative results for<br>general $p$ and $q$. We show that our algorithm obtains an approximation ratio<br>of at most 1.0345. Moreover, we prove that the problem is \classAPX-hard, with<br>a lower bound of $1.000015$ achieved at $p/q = 4/5$.<br>}, }
Endnote
%0 Report %A Akrami, Hannaneh %A Ray Chaudhury, Bhaskar %A Hoefer, Martin %A Mehlhorn, Kurt %A Schmalhofer, Marco %A Shahkarami, Golnoosh %A Varricchio, Giovanna %A Vermande, Quentin %A van Wijland, Ernest %+ 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 Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Maximizing Nash Social Welfare in 2-Value Instances : %G eng %U http://hdl.handle.net/21.11116/0000-000C-2000-F %U https://arxiv.org/abs/2107.08965 %D 2021 %X We consider the problem of maximizing the Nash social welfare when allocating<br>a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We<br>study instances, in which all agents have 2-value additive valuations: The<br>value of every agent $i \in \mathcal{N}$ for every good $j \in \mathcal{G}$ is<br>$v_{ij} \in \{p,q\}$, for $p,q \in \mathbb{N}$, $p \le q$. Maybe surprisingly,<br>we design an algorithm to compute an optimal allocation in polynomial time if<br>$p$ divides $q$, i.e., when $p=1$ and $q \in \mathbb{N}$ after appropriate<br>scaling. The problem is \classNP-hard whenever $p$ and $q$ are coprime and $p<br>\ge 3$.<br> In terms of approximation, we present positive and negative results for<br>general $p$ and $q$. We show that our algorithm obtains an approximation ratio<br>of at most 1.0345. Moreover, we prove that the problem is \classAPX-hard, with<br>a lower bound of $1.000015$ achieved at $p/q = 4/5$.<br> %K Computer Science, Computer Science and Game Theory, cs.GT
[131]
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<br>with 2-value additive valuations. Our goal is to find an allocation with<br>maximum Nash social welfare, i.e., the geometric mean of the valuations of the<br>agents. We give a polynomial-time algorithm to find a Nash social welfare<br>maximizing allocation when the valuation functions are integrally 2-valued,<br>i.e., each agent has a value either $1$ or $p$ for each good, for some positive<br>integer $p$. We then extend our algorithm to find a better approximation factor<br>for general 2-value instances.<br>
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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<br>with 2-value additive valuations. Our goal is to find an allocation with<br>maximum Nash social welfare, i.e., the geometric mean of the valuations of the<br>agents. We give a polynomial-time algorithm to find a Nash social welfare<br>maximizing allocation when the valuation functions are integrally 2-valued,<br>i.e., each agent has a value either $1$ or $p$ for each good, for some positive<br>integer $p$. We then extend our algorithm to find a better approximation factor<br>for general 2-value instances.<br>}, }
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<br>with 2-value additive valuations. Our goal is to find an allocation with<br>maximum Nash social welfare, i.e., the geometric mean of the valuations of the<br>agents. We give a polynomial-time algorithm to find a Nash social welfare<br>maximizing allocation when the valuation functions are integrally 2-valued,<br>i.e., each agent has a value either $1$ or $p$ for each good, for some positive<br>integer $p$. We then extend our algorithm to find a better approximation factor<br>for general 2-value instances.<br> %K Computer Science, Computer Science and Game Theory, cs.GT
[132]
G. Amanatidis and P. Kleer, “Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals,” 2021. [Online]. Available: https://arxiv.org/abs/2110.09068. (arXiv: 2110.09068)
Abstract
The approximate uniform sampling of graphs with a given degree sequence is a<br>well-known, extensively studied problem in theoretical computer science and has<br>significant applications, e.g., in the analysis of social networks. In this<br>work we study an extension of the problem, where degree intervals are specified<br>rather than a single degree sequence. We are interested in sampling and<br>counting graphs whose degree sequences satisfy the degree interval constraints.<br>A natural scenario where this problem arises is in hypothesis testing on social<br>networks that are only partially observed.<br> In this work, we provide the first fully polynomial almost uniform sampler<br>(FPAUS) as well as the first fully polynomial randomized approximation scheme<br>(FPRAS) for sampling and counting, respectively, graphs with near-regular<br>degree intervals, in which every node $i$ has a degree from an interval not too<br>far away from a given $d \in \N$. In order to design our FPAUS, we rely on<br>various state-of-the-art tools from Markov chain theory and combinatorics. In<br>particular, we provide the first non-trivial algorithmic application of a<br>breakthrough result of Liebenau and Wormald (2017) regarding an asymptotic<br>formula for the number of graphs with a given near-regular degree sequence.<br>Furthermore, we also make use of the recent breakthrough of Anari et al. (2019)<br>on sampling a base of a matroid under a strongly log-concave probability<br>distribution.<br> As a more direct approach, we also study a natural Markov chain recently<br>introduced by Rechner, Strowick and M\"uller-Hannemann (2018), based on three<br>simple local operations: Switches, hinge flips, and additions/deletions of a<br>single edge. We obtain the first theoretical results for this Markov chain by<br>showing it is rapidly mixing for the case of near-regular degree intervals of<br>size at most one.<br>
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@online{Amanatidis_2110.09068, TITLE = {Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals}, AUTHOR = {Amanatidis, Georgios and Kleer, Pieter}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2110.09068}, EPRINT = {2110.09068}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The approximate uniform sampling of graphs with a given degree sequence is a<br>well-known, extensively studied problem in theoretical computer science and has<br>significant applications, e.g., in the analysis of social networks. In this<br>work we study an extension of the problem, where degree intervals are specified<br>rather than a single degree sequence. We are interested in sampling and<br>counting graphs whose degree sequences satisfy the degree interval constraints.<br>A natural scenario where this problem arises is in hypothesis testing on social<br>networks that are only partially observed.<br> In this work, we provide the first fully polynomial almost uniform sampler<br>(FPAUS) as well as the first fully polynomial randomized approximation scheme<br>(FPRAS) for sampling and counting, respectively, graphs with near-regular<br>degree intervals, in which every node $i$ has a degree from an interval not too<br>far away from a given $d \in \N$. In order to design our FPAUS, we rely on<br>various state-of-the-art tools from Markov chain theory and combinatorics. In<br>particular, we provide the first non-trivial algorithmic application of a<br>breakthrough result of Liebenau and Wormald (2017) regarding an asymptotic<br>formula for the number of graphs with a given near-regular degree sequence.<br>Furthermore, we also make use of the recent breakthrough of Anari et al. (2019)<br>on sampling a base of a matroid under a strongly log-concave probability<br>distribution.<br> As a more direct approach, we also study a natural Markov chain recently<br>introduced by Rechner, Strowick and M\"uller-Hannemann (2018), based on three<br>simple local operations: Switches, hinge flips, and additions/deletions of a<br>single edge. We obtain the first theoretical results for this Markov chain by<br>showing it is rapidly mixing for the case of near-regular degree intervals of<br>size at most one.<br>}, }
Endnote
%0 Report %A Amanatidis, Georgios %A Kleer, Pieter %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B839-8 %U https://arxiv.org/abs/2110.09068 %D 2021 %X The approximate uniform sampling of graphs with a given degree sequence is a<br>well-known, extensively studied problem in theoretical computer science and has<br>significant applications, e.g., in the analysis of social networks. In this<br>work we study an extension of the problem, where degree intervals are specified<br>rather than a single degree sequence. We are interested in sampling and<br>counting graphs whose degree sequences satisfy the degree interval constraints.<br>A natural scenario where this problem arises is in hypothesis testing on social<br>networks that are only partially observed.<br> In this work, we provide the first fully polynomial almost uniform sampler<br>(FPAUS) as well as the first fully polynomial randomized approximation scheme<br>(FPRAS) for sampling and counting, respectively, graphs with near-regular<br>degree intervals, in which every node $i$ has a degree from an interval not too<br>far away from a given $d \in \N$. In order to design our FPAUS, we rely on<br>various state-of-the-art tools from Markov chain theory and combinatorics. In<br>particular, we provide the first non-trivial algorithmic application of a<br>breakthrough result of Liebenau and Wormald (2017) regarding an asymptotic<br>formula for the number of graphs with a given near-regular degree sequence.<br>Furthermore, we also make use of the recent breakthrough of Anari et al. (2019)<br>on sampling a base of a matroid under a strongly log-concave probability<br>distribution.<br> As a more direct approach, we also study a natural Markov chain recently<br>introduced by Rechner, Strowick and M\"uller-Hannemann (2018), based on three<br>simple local operations: Switches, hinge flips, and additions/deletions of a<br>single edge. We obtain the first theoretical results for this Markov chain by<br>showing it is rapidly mixing for the case of near-regular degree intervals of<br>size at most one.<br> %K Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Combinatorics, math.CO
[133]
I. Anagnostides, T. Gouleakis, and A. Marashian, “Robust Learning under Strong Noise via SQs,” in Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021), Virtual Conference, 2021.
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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}, URL = {https://proceedings.mlr.press/v130/anagnostides21a.html}, PUBLISHER = {PMLR}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021)}, EDITOR = {Banerjee, Arindam and Fukumizu, Kenli}, PAGES = {3808--3816}, SERIES = {Proceedings of the Machine Learning Research}, VOLUME = {130}, 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 %U https://proceedings.mlr.press/v130/anagnostides21a.html %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 24th International Conference on Artificial Intelligence and Statistics %E Banerjee, Arindam; Fukumizu, Kenli %P 3808 - 3816 %I PMLR %B Proceedings of the Machine Learning Research %N 130
[134]
I. Anagnostides and T. Gouleakis, “Deterministic Distributed Algorithms and Lower Bounds in the Hybrid Model,” in 35th International Symposium on Distributed Computing (DISC 2021), Freiburg, Germany (Virtual Conference), 2021.
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@inproceedings{Anagnostides_DISC21, TITLE = {Deterministic Distributed Algorithms and Lower Bounds in the Hybrid Model}, AUTHOR = {Anagnostides, Ioannis and Gouleakis, Themis}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-210-5}, URL = {urn:nbn:de:0030-drops-148077}, DOI = {10.4230/LIPIcs.DISC.2021.5}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {35th International Symposium on Distributed Computing (DISC 2021)}, EDITOR = {Gilbert, Seth}, PAGES = {1--19}, EID = {5}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {209}, ADDRESS = {Freiburg, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Anagnostides, Ioannis %A Gouleakis, Themis %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Deterministic Distributed Algorithms and Lower Bounds in the Hybrid Model : %G eng %U http://hdl.handle.net/21.11116/0000-000C-7306-C %R 10.4230/LIPIcs.DISC.2021.5 %U urn:nbn:de:0030-drops-148077 %D 2021 %B 35th International Symposium on Distributed Computing %Z date of event: 2021-10-04 - 2021-10-08 %C Freiburg, Germany (Virtual Conference) %B 35th International Symposium on Distributed Computing %E Gilbert, Seth %P 1 - 19 %Z sequence number: 5 %I Schloss Dagstuhl %@ 978-3-95977-210-5 %B Leibniz International Proceedings in Informatics %N 209 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2021/14807/https://creativecommons.org/licenses/by/4.0/legalcode
[135]
I. Anagnostides, C. Lenzen, B. Haeupler, G. Zuzic, and T. Gouleakis, “Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts,” 2021. [Online]. Available: https://arxiv.org/abs/2109.05151. (arXiv: 2109.05151)
Abstract
In this work we refine the analysis of the distributed Laplacian solver<br>recently established by Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS '21),<br>via the Ghaffari-Haeupler framework (SODA '16) of low-congestion shortcuts.<br>Specifically, if $\epsilon > 0$ represents the error of the solver, we derive<br>two main results. First, for any $n$-node graph $G$ with hop-diameter $D$ and<br>treewidth bounded by $k$, we show the existence of a Laplacian solver with<br>round complexity $O(n^{o(1)}kD \log(1/\epsilon))$ in the CONGEST model. For<br>graphs with bounded treewidth this circumvents the notorious $\Omega(\sqrt{n})$<br>lower bound for "global" problems in general graphs. Moreover, following a<br>recent line of work in distributed algorithms, we consider a hybrid<br>communication model which enhances CONGEST with very limited global power in<br>the form of the recently introduced node-capacitated clique. In this model, we<br>show the existence of a Laplacian solver with round complexity $O(n^{o(1)}<br>\log(1/\epsilon))$. The unifying thread of these results is an application of<br>accelerated distributed algorithms for a congested variant of the standard<br>part-wise aggregation problem that we introduce. This primitive constitutes the<br>primary building block for simulating "local" operations on low-congestion<br>minors, and we believe that this framework could be more generally applicable.<br>
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@online{Anagnostides_2109.05151, TITLE = {Almost Universally Optimal Distributed {L}aplacian Solvers via Low-Congestion Shortcuts}, AUTHOR = {Anagnostides, Ioannis and Lenzen, Christoph and Haeupler, Bernhard and Zuzic, Goran and Gouleakis, Themis}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2109.05151}, EPRINT = {2109.05151}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In this work we refine the analysis of the distributed Laplacian solver<br>recently established by Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS '21),<br>via the Ghaffari-Haeupler framework (SODA '16) of low-congestion shortcuts.<br>Specifically, if $\epsilon > 0$ represents the error of the solver, we derive<br>two main results. First, for any $n$-node graph $G$ with hop-diameter $D$ and<br>treewidth bounded by $k$, we show the existence of a Laplacian solver with<br>round complexity $O(n^{o(1)}kD \log(1/\epsilon))$ in the CONGEST model. For<br>graphs with bounded treewidth this circumvents the notorious $\Omega(\sqrt{n})$<br>lower bound for "global" problems in general graphs. Moreover, following a<br>recent line of work in distributed algorithms, we consider a hybrid<br>communication model which enhances CONGEST with very limited global power in<br>the form of the recently introduced node-capacitated clique. In this model, we<br>show the existence of a Laplacian solver with round complexity $O(n^{o(1)}<br>\log(1/\epsilon))$. The unifying thread of these results is an application of<br>accelerated distributed algorithms for a congested variant of the standard<br>part-wise aggregation problem that we introduce. This primitive constitutes the<br>primary building block for simulating "local" operations on low-congestion<br>minors, and we believe that this framework could be more generally applicable.<br>}, }
Endnote
%0 Report %A Anagnostides, Ioannis %A Lenzen, Christoph %A Haeupler, Bernhard %A Zuzic, Goran %A Gouleakis, Themis %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B83F-2 %U https://arxiv.org/abs/2109.05151 %D 2021 %X In this work we refine the analysis of the distributed Laplacian solver<br>recently established by Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS '21),<br>via the Ghaffari-Haeupler framework (SODA '16) of low-congestion shortcuts.<br>Specifically, if $\epsilon > 0$ represents the error of the solver, we derive<br>two main results. First, for any $n$-node graph $G$ with hop-diameter $D$ and<br>treewidth bounded by $k$, we show the existence of a Laplacian solver with<br>round complexity $O(n^{o(1)}kD \log(1/\epsilon))$ in the CONGEST model. For<br>graphs with bounded treewidth this circumvents the notorious $\Omega(\sqrt{n})$<br>lower bound for "global" problems in general graphs. Moreover, following a<br>recent line of work in distributed algorithms, we consider a hybrid<br>communication model which enhances CONGEST with very limited global power in<br>the form of the recently introduced node-capacitated clique. In this model, we<br>show the existence of a Laplacian solver with round complexity $O(n^{o(1)}<br>\log(1/\epsilon))$. The unifying thread of these results is an application of<br>accelerated distributed algorithms for a congested variant of the standard<br>part-wise aggregation problem that we introduce. This primitive constitutes the<br>primary building block for simulating "local" operations on low-congestion<br>minors, and we believe that this framework could be more generally applicable.<br> %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[136]
H. An, M. Gurumukhani, R. Impagliazzo, M. Jaber, M. Künnemann, and M. P. Parga Nina, “The Fine-Grained Complexity of Multi-Dimensional Ordering Properties,” in 16th International Symposium on Parameterized and Exact Computation (IPEC 2021), Lisbon, Portugal, 2021.
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@inproceedings{An_IPEC21, TITLE = {The Fine-Grained Complexity of Multi-Dimensional Ordering Properties}, AUTHOR = {An, Haozhe and Gurumukhani, Mohit and Impagliazzo, Russell and Jaber, Michael and K{\"u}nnemann, Marvin and Parga Nina, Maria Paula}, LANGUAGE = {eng}, ISBN = {978-3-95977-216-7}, URL = {urn:nbn:de:0030-drops-153869}, DOI = {10.4230/LIPIcs.IPEC.2021.3}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)}, EDITOR = {Golovach, Petr A. and Zehavi, Meirav}, PAGES = {1--15}, EID = {3}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {214}, ADDRESS = {Lisbon, Portugal}, }
Endnote
%0 Conference Proceedings %A An, Haozhe %A Gurumukhani, Mohit %A Impagliazzo, Russell %A Jaber, Michael %A K&#252;nnemann, Marvin %A Parga Nina, Maria Paula %+ External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T The Fine-Grained Complexity of Multi-Dimensional Ordering Properties : %G eng %U http://hdl.handle.net/21.11116/0000-0009-CBD6-1 %R 10.4230/LIPIcs.IPEC.2021.3 %U urn:nbn:de:0030-drops-153869 %D 2021 %B 16th International Symposium on Parameterized and Exact Computation %Z date of event: 2021-09-08 - 2021-09-10 %C Lisbon, Portugal %B 16th International Symposium on Parameterized and Exact Computation %E Golovach, Petr A.; Zehavi, Meirav %P 1 - 15 %Z sequence number: 3 %I Schloss Dagstuhl %@ 978-3-95977-216-7 %B Leibniz International Proceedings in Informatics %N 214 %U https://drops.dagstuhl.de/opus/volltexte/2021/15386/https://creativecommons.org/licenses/by/4.0/legalcode
[137]
A. Antoniadis, R. Hoeksma, S. Kisfaludi-Bak, and K. Schewior, “Online Search for a Hyperplane in High-Dimensional Euclidean Space,” 2021. [Online]. Available: https://arxiv.org/abs/2109.04340. (arXiv: 2109.04340)
Abstract
We consider the online search problem in which a server starting at the<br>origin of a $d$-dimensional Euclidean space has to find an arbitrary<br>hyperplane. The best-possible competitive ratio and the length of the shortest<br>curve from which each point on the $d$-dimensional unit sphere can be seen are<br>within a constant factor of each other. We show that this length is in<br>$\Omega(d)\cap O(d^{3/2})$.<br>
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@online{Antoniadis_2109.04340, TITLE = {Online Search for a Hyperplane in High-Dimensional Euclidean Space}, AUTHOR = {Antoniadis, Antonios and Hoeksma, Ruben and Kisfaludi-Bak, S{\'a}ndor and Schewior, Kevin}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2109.04340}, EPRINT = {2109.04340}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We consider the online search problem in which a server starting at the<br>origin of a $d$-dimensional Euclidean space has to find an arbitrary<br>hyperplane. The best-possible competitive ratio and the length of the shortest<br>curve from which each point on the $d$-dimensional unit sphere can be seen are<br>within a constant factor of each other. We show that this length is in<br>$\Omega(d)\cap O(d^{3/2})$.<br>}, }
Endnote
%0 Report %A Antoniadis, Antonios %A Hoeksma, Ruben %A Kisfaludi-Bak, S&#225;ndor %A Schewior, Kevin %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Online Search for a Hyperplane in High-Dimensional Euclidean Space : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B814-1 %U https://arxiv.org/abs/2109.04340 %D 2021 %X We consider the online search problem in which a server starting at the<br>origin of a $d$-dimensional Euclidean space has to find an arbitrary<br>hyperplane. The best-possible competitive ratio and the length of the shortest<br>curve from which each point on the $d$-dimensional unit sphere can be seen are<br>within a constant factor of each other. We show that this length is in<br>$\Omega(d)\cap O(d^{3/2})$.<br> %K Computer Science, Computational Geometry, cs.CG,Computer Science, Data Structures and Algorithms, cs.DS
[138]
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
[139]
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
[140]
B. A. Berendsohn, L. Kozma, and D. Marx, “Finding and Counting Permutations via CSPs,” Algorithmica, vol. 83, 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 = {83}, PAGES = {2552--2577}, }
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 83 %& 2552 %P 2552 - 2577 %I Springer %C New York, NY %@ false
[141]
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<br>science. We examine the problem when the pattern graph H is of bounded<br>treewidth, as occurs in a variety of applications. This problem has a<br>well-known algorithm via color-coding that runs in time $O(n^{tw(H)+1})$ [Alon,<br>Yuster, Zwick'95], where $n$ is the number of vertices of the host graph $G$.<br>While there are pattern graphs known for which Subgraph Isomorphism can be<br>solved in an improved running time of $O(n^{tw(H)+1-\varepsilon})$ or even<br>faster (e.g. for $k$-cliques), it is not known whether such improvements are<br>possible for all patterns. The only known lower bound rules out time<br>$n^{o(tw(H) / \log(tw(H)))}$ for any class of patterns of unbounded treewidth<br>assuming the Exponential Time Hypothesis [Marx'07].<br> In this paper, we demonstrate the existence of maximally hard pattern graphs<br>$H$ that require time $n^{tw(H)+1-o(1)}$. Specifically, under the Strong<br>Exponential Time Hypothesis (SETH), a standard assumption from fine-grained<br>complexity theory, we prove the following asymptotic statement for large<br>treewidth $t$: For any $\varepsilon > 0$ there exists $t \ge 3$ and a pattern<br>graph $H$ of treewidth $t$ such that Subgraph Isomorphism on pattern $H$ has no<br>algorithm running in time $O(n^{t+1-\varepsilon})$.<br> Under the more recent 3-uniform Hyperclique hypothesis, we even obtain tight<br>lower bounds for each specific treewidth $t \ge 3$: For any $t \ge 3$ there<br>exists a pattern graph $H$ of treewidth $t$ such that for any $\varepsilon>0$<br>Subgraph Isomorphism on pattern $H$ has no algorithm running in time<br>$O(n^{t+1-\varepsilon})$.<br> In addition to these main results, we explore (1) colored and uncolored<br>problem variants (and why they are equivalent for most cases), (2) Subgraph<br>Isomorphism for $tw < 3$, (3) Subgraph Isomorphism parameterized by pathwidth,<br>and (4) a weighted problem variant.<br>
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@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<br>science. We examine the problem when the pattern graph H is of bounded<br>treewidth, as occurs in a variety of applications. This problem has a<br>well-known algorithm via color-coding that runs in time $O(n^{tw(H)+1})$ [Alon,<br>Yuster, Zwick'95], where $n$ is the number of vertices of the host graph $G$.<br>While there are pattern graphs known for which Subgraph Isomorphism can be<br>solved in an improved running time of $O(n^{tw(H)+1-\varepsilon})$ or even<br>faster (e.g. for $k$-cliques), it is not known whether such improvements are<br>possible for all patterns. The only known lower bound rules out time<br>$n^{o(tw(H) / \log(tw(H)))}$ for any class of patterns of unbounded treewidth<br>assuming the Exponential Time Hypothesis [Marx'07].<br> In this paper, we demonstrate the existence of maximally hard pattern graphs<br>$H$ that require time $n^{tw(H)+1-o(1)}$. Specifically, under the Strong<br>Exponential Time Hypothesis (SETH), a standard assumption from fine-grained<br>complexity theory, we prove the following asymptotic statement for large<br>treewidth $t$: For any $\varepsilon > 0$ there exists $t \ge 3$ and a pattern<br>graph $H$ of treewidth $t$ such that Subgraph Isomorphism on pattern $H$ has no<br>algorithm running in time $O(n^{t+1-\varepsilon})$.<br> Under the more recent 3-uniform Hyperclique hypothesis, we even obtain tight<br>lower bounds for each specific treewidth $t \ge 3$: For any $t \ge 3$ there<br>exists a pattern graph $H$ of treewidth $t$ such that for any $\varepsilon>0$<br>Subgraph Isomorphism on pattern $H$ has no algorithm running in time<br>$O(n^{t+1-\varepsilon})$.<br> In addition to these main results, we explore (1) colored and uncolored<br>problem variants (and why they are equivalent for most cases), (2) Subgraph<br>Isomorphism for $tw < 3$, (3) Subgraph Isomorphism parameterized by pathwidth,<br>and (4) a weighted problem variant.<br>}, }
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<br>science. We examine the problem when the pattern graph H is of bounded<br>treewidth, as occurs in a variety of applications. This problem has a<br>well-known algorithm via color-coding that runs in time $O(n^{tw(H)+1})$ [Alon,<br>Yuster, Zwick'95], where $n$ is the number of vertices of the host graph $G$.<br>While there are pattern graphs known for which Subgraph Isomorphism can be<br>solved in an improved running time of $O(n^{tw(H)+1-\varepsilon})$ or even<br>faster (e.g. for $k$-cliques), it is not known whether such improvements are<br>possible for all patterns. The only known lower bound rules out time<br>$n^{o(tw(H) / \log(tw(H)))}$ for any class of patterns of unbounded treewidth<br>assuming the Exponential Time Hypothesis [Marx'07].<br> In this paper, we demonstrate the existence of maximally hard pattern graphs<br>$H$ that require time $n^{tw(H)+1-o(1)}$. Specifically, under the Strong<br>Exponential Time Hypothesis (SETH), a standard assumption from fine-grained<br>complexity theory, we prove the following asymptotic statement for large<br>treewidth $t$: For any $\varepsilon > 0$ there exists $t \ge 3$ and a pattern<br>graph $H$ of treewidth $t$ such that Subgraph Isomorphism on pattern $H$ has no<br>algorithm running in time $O(n^{t+1-\varepsilon})$.<br> Under the more recent 3-uniform Hyperclique hypothesis, we even obtain tight<br>lower bounds for each specific treewidth $t \ge 3$: For any $t \ge 3$ there<br>exists a pattern graph $H$ of treewidth $t$ such that for any $\varepsilon>0$<br>Subgraph Isomorphism on pattern $H$ has no algorithm running in time<br>$O(n^{t+1-\varepsilon})$.<br> In addition to these main results, we explore (1) colored and uncolored<br>problem variants (and why they are equivalent for most cases), (2) Subgraph<br>Isomorphism for $tw < 3$, (3) Subgraph Isomorphism parameterized by pathwidth,<br>and (4) a weighted problem variant.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,
[142]
K. Bringmann, N. Fischer, and V. Nakos, “Sparse Nonnegative Convolution is Equivalent to Dense Nonnegative Convolution,” in STOC ’21, 53rd Annual ACM SIGACT Symposium on Theory of Computing, 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, 53rd Annual ACM SIGACT Symposium on Theory of Computing}, 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
[143]
K. Bringmann, M. Künnemann, and A. Nusser, “Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance,” Journal of Computational Geometry, vol. 12, no. 1, 2021.
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@article{Bringmann21, 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}, DOI = {10.20382/jocg.v12i1a4}, PUBLISHER = {JoCG.org}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Computational Geometry}, VOLUME = {12}, NUMBER = {1}, PAGES = {70--108}, }
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 Walking the Dog Fast in Practice: Algorithm Engineering of the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1F8A-7 %R 10.20382/jocg.v12i1a4 %7 2021 %D 2021 %J Journal of Computational Geometry %V 12 %N 1 %& 70 %P 70 - 108 %I JoCG.org
[144]
K. Bringmann, “Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry,” 2021. [Online]. Available: https://arxiv.org/abs/2110.10283. (arXiv: 2110.10283)
Abstract
Fine-grained complexity theory is the area of theoretical computer science<br>that proves conditional lower bounds based on the Strong Exponential Time<br>Hypothesis and similar conjectures. This area has been thriving in the last<br>decade, leading to conditionally best-possible algorithms for a wide variety of<br>problems on graphs, strings, numbers etc. This article is an introduction to<br>fine-grained lower bounds in computational geometry, with a focus on lower<br>bounds for polynomial-time problems based on the Orthogonal Vectors Hypothesis.<br>Specifically, we discuss conditional lower bounds for nearest neighbor search<br>under the Euclidean distance and Fr\'echet distance.<br>
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@online{Bringmann2110.10283, TITLE = {Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry}, AUTHOR = {Bringmann, Karl}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2110.10283}, EPRINT = {2110.10283}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Fine-grained complexity theory is the area of theoretical computer science<br>that proves conditional lower bounds based on the Strong Exponential Time<br>Hypothesis and similar conjectures. This area has been thriving in the last<br>decade, leading to conditionally best-possible algorithms for a wide variety of<br>problems on graphs, strings, numbers etc. This article is an introduction to<br>fine-grained lower bounds in computational geometry, with a focus on lower<br>bounds for polynomial-time problems based on the Orthogonal Vectors Hypothesis.<br>Specifically, we discuss conditional lower bounds for nearest neighbor search<br>under the Euclidean distance and Fr\'echet distance.<br>}, }
Endnote
%0 Report %A Bringmann, Karl %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B42E-9 %U https://arxiv.org/abs/2110.10283 %D 2021 %X Fine-grained complexity theory is the area of theoretical computer science<br>that proves conditional lower bounds based on the Strong Exponential Time<br>Hypothesis and similar conjectures. This area has been thriving in the last<br>decade, leading to conditionally best-possible algorithms for a wide variety of<br>problems on graphs, strings, numbers etc. This article is an introduction to<br>fine-grained lower bounds in computational geometry, with a focus on lower<br>bounds for polynomial-time problems based on the Orthogonal Vectors Hypothesis.<br>Specifically, we discuss conditional lower bounds for nearest neighbor search<br>under the Euclidean distance and Fr\'echet distance.<br> %K Computer Science, Computational Geometry, cs.CG,Computer Science, Data Structures and Algorithms, cs.DS
[145]
K. Bringmann, “Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry,” in Connecting with Computability (CiE 2021), Ghent, Belgium (Virtual Event), 2021.
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BibTeX
@inproceedings{Bringmann_CiE21, TITLE = {Fine-Grained Complexity Theory: {C}onditional Lower Bounds for Computational Geometry}, AUTHOR = {Bringmann, Karl}, LANGUAGE = {eng}, ISBN = {978-3-030-80048-2}, DOI = {10.1007/978-3-030-80049-9_6}, PUBLISHER = {Springer}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Connecting with Computability (CiE 2021)}, EDITOR = {De Mol, Liesbeth and Weiermann, Andreas and Manea, Florin and Fern{\'a}ndez-Duque, David}, PAGES = {60--70}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {12813}, ADDRESS = {Ghent, Belgium (Virtual Event)}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B428-F %R 10.1007/978-3-030-80049-9_6 %D 2021 %B 17th Conference on Computability in Europe %Z date of event: 2021-07-05 - 2021-07-09 %C Ghent, Belgium (Virtual Event) %B Connecting with Computability %E De Mol, Liesbeth; Weiermann, Andreas; Manea, Florin; Fern&#225;ndez-Duque, David %P 60 - 70 %I Springer %@ 978-3-030-80048-2 %B Lecture Notes in Computer Science %N 12813
[146]
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<br>imaging, geometric shape comparison, trajectory analysis, and many more<br>settings. Arguably the most basic distance measure for this task is the<br>Hausdorff distance, which assigns to each point from one set the closest point<br>in the other set and then evaluates the maximum distance of any assigned pair.<br>A drawback is that this distance measure is not translational invariant, that<br>is, comparing two objects just according to their shape while disregarding<br>their position in space is impossible.<br> Fortunately, there is a canonical translational invariant version, the<br>Hausdorff distance under translation, which minimizes the Hausdorff distance<br>over all translations of one of the point sets. For point sets of size $n$ and<br>$m$, the Hausdorff distance under translation can be computed in time $\tilde<br>O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm<br>(n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93].<br> As these bounds have not been improved for over 25 years, in this paper we<br>approach the Hausdorff distance under translation from the perspective of<br>fine-grained complexity theory. We show (i) a matching lower bound of<br>$(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ assuming the Orthogonal Vectors<br>Hypothesis and (ii) a matching lower bound of $n^{2-o(1)}$ for $L_2$ in the<br>imbalanced case of $m = O(1)$ assuming the 3SUM Hypothesis.<br>
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BibTeX
@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<br>imaging, geometric shape comparison, trajectory analysis, and many more<br>settings. Arguably the most basic distance measure for this task is the<br>Hausdorff distance, which assigns to each point from one set the closest point<br>in the other set and then evaluates the maximum distance of any assigned pair.<br>A drawback is that this distance measure is not translational invariant, that<br>is, comparing two objects just according to their shape while disregarding<br>their position in space is impossible.<br> Fortunately, there is a canonical translational invariant version, the<br>Hausdorff distance under translation, which minimizes the Hausdorff distance<br>over all translations of one of the point sets. For point sets of size $n$ and<br>$m$, the Hausdorff distance under translation can be computed in time $\tilde<br>O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm<br>(n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93].<br> As these bounds have not been improved for over 25 years, in this paper we<br>approach the Hausdorff distance under translation from the perspective of<br>fine-grained complexity theory. We show (i) a matching lower bound of<br>$(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ assuming the Orthogonal Vectors<br>Hypothesis and (ii) a matching lower bound of $n^{2-o(1)}$ for $L_2$ in the<br>imbalanced case of $m = O(1)$ assuming the 3SUM Hypothesis.<br>}, }
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<br>imaging, geometric shape comparison, trajectory analysis, and many more<br>settings. Arguably the most basic distance measure for this task is the<br>Hausdorff distance, which assigns to each point from one set the closest point<br>in the other set and then evaluates the maximum distance of any assigned pair.<br>A drawback is that this distance measure is not translational invariant, that<br>is, comparing two objects just according to their shape while disregarding<br>their position in space is impossible.<br> Fortunately, there is a canonical translational invariant version, the<br>Hausdorff distance under translation, which minimizes the Hausdorff distance<br>over all translations of one of the point sets. For point sets of size $n$ and<br>$m$, the Hausdorff distance under translation can be computed in time $\tilde<br>O(nm)$ for the $L_1$ and $L_\infty$ norm [Chew, Kedem SWAT'92] and $\tilde O(nm<br>(n+m))$ for the $L_2$ norm [Huttenlocher, Kedem, Sharir DCG'93].<br> As these bounds have not been improved for over 25 years, in this paper we<br>approach the Hausdorff distance under translation from the perspective of<br>fine-grained complexity theory. We show (i) a matching lower bound of<br>$(nm)^{1-o(1)}$ for $L_1$ and $L_\infty$ assuming the Orthogonal Vectors<br>Hypothesis and (ii) a matching lower bound of $n^{2-o(1)}$ for $L_2$ in the<br>imbalanced case of $m = O(1)$ assuming the 3SUM Hypothesis.<br> %K Computer Science, Computational Geometry, cs.CG,Computer Science, Computational Complexity, cs.CC
[147]
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
[148]
K. Bringmann and A. Nusser, “Translating Hausdorff is Hard: Fine-Grained Lower Bounds for Hausdorff Distance under Translation,” Journal of Computational Geometry, vol. 13, no. 2, 2021.
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@article{Bringmann22b, TITLE = {Translating {Hausdorff} is hard: {F}ine-grained lower bounds for {H}ausdorff distance under translation}, AUTHOR = {Bringmann, Karl and Nusser, Andr{\'e}}, LANGUAGE = {eng}, DOI = {10.20382/jocg.v13i2a3}, PUBLISHER = {JoCG.org}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Computational Geometry}, VOLUME = {13}, NUMBER = {2}, PAGES = {30--50}, }
Endnote
%0 Journal Article %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/21.11116/0000-000C-2690-6 %R 10.20382/jocg.v13i2a3 %7 2021 %D 2021 %J Journal of Computational Geometry %V 13 %N 2 %& 30 %P 30 - 50 %I JoCG.org
[149]
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<br>wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of<br>computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq<br>\mathbb{Z}_m$. Boolean convolution formalizes the frequent task of combining<br>two subproblems, where the whole problem has a solution of size $k$ if for some<br>$i$ the first subproblem has a solution of size~$i$ and the second subproblem<br>has a solution of size $k-i$. Our problem formalizes a natural generalization,<br>namely combining solutions of $n$ subproblems subject to a modular constraint.<br>This simultaneously generalises Modular Subset Sum and Boolean Convolution<br>(Sumset Computation). Although nearly optimal algorithms are known for special<br>cases of this problem, not even tiny improvements are known for the general<br>case.<br> We almost resolve the computational complexity of this problem, shaving<br>essentially a factor of $n$ from the running time of previous algorithms.<br>Specifically, we present a \emph{deterministic} algorithm running in<br>\emph{almost} linear time with respect to the input plus output size $k$. We<br>also present a \emph{Las Vegas} algorithm running in \emph{nearly} linear<br>expected time with respect to the input plus output size $k$. Previously, no<br>deterministic or randomized $o(nk)$ algorithm was known.<br> At the heart of our approach lies a careful usage of Kneser's theorem from<br>Additive Combinatorics, and a new deterministic almost linear output-sensitive<br>algorithm for non-negative sparse convolution. In total, our work builds a<br>solid toolbox that could be of independent interest.<br>
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@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<br>wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of<br>computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq<br>\mathbb{Z}_m$. Boolean convolution formalizes the frequent task of combining<br>two subproblems, where the whole problem has a solution of size $k$ if for some<br>$i$ the first subproblem has a solution of size~$i$ and the second subproblem<br>has a solution of size $k-i$. Our problem formalizes a natural generalization,<br>namely combining solutions of $n$ subproblems subject to a modular constraint.<br>This simultaneously generalises Modular Subset Sum and Boolean Convolution<br>(Sumset Computation). Although nearly optimal algorithms are known for special<br>cases of this problem, not even tiny improvements are known for the general<br>case.<br> We almost resolve the computational complexity of this problem, shaving<br>essentially a factor of $n$ from the running time of previous algorithms.<br>Specifically, we present a \emph{deterministic} algorithm running in<br>\emph{almost} linear time with respect to the input plus output size $k$. We<br>also present a \emph{Las Vegas} algorithm running in \emph{nearly} linear<br>expected time with respect to the input plus output size $k$. Previously, no<br>deterministic or randomized $o(nk)$ algorithm was known.<br> At the heart of our approach lies a careful usage of Kneser's theorem from<br>Additive Combinatorics, and a new deterministic almost linear output-sensitive<br>algorithm for non-negative sparse convolution. In total, our work builds a<br>solid toolbox that could be of independent interest.<br>}, }
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<br>wraparound) of $n$~vectors of dimension $m$, or, equivalently, the problem of<br>computing the sumset $A_1+A_2+\ldots+A_n$ for $A_1,\ldots,A_n \subseteq<br>\mathbb{Z}_m$. Boolean convolution formalizes the frequent task of combining<br>two subproblems, where the whole problem has a solution of size $k$ if for some<br>$i$ the first subproblem has a solution of size~$i$ and the second subproblem<br>has a solution of size $k-i$. Our problem formalizes a natural generalization,<br>namely combining solutions of $n$ subproblems subject to a modular constraint.<br>This simultaneously generalises Modular Subset Sum and Boolean Convolution<br>(Sumset Computation). Although nearly optimal algorithms are known for special<br>cases of this problem, not even tiny improvements are known for the general<br>case.<br> We almost resolve the computational complexity of this problem, shaving<br>essentially a factor of $n$ from the running time of previous algorithms.<br>Specifically, we present a \emph{deterministic} algorithm running in<br>\emph{almost} linear time with respect to the input plus output size $k$. We<br>also present a \emph{Las Vegas} algorithm running in \emph{nearly} linear<br>expected time with respect to the input plus output size $k$. Previously, no<br>deterministic or randomized $o(nk)$ algorithm was known.<br> At the heart of our approach lies a careful usage of Kneser's theorem from<br>Additive Combinatorics, and a new deterministic almost linear output-sensitive<br>algorithm for non-negative sparse convolution. In total, our work builds a<br>solid toolbox that could be of independent interest.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[150]
K. Bringmann, A. Driemel, A. Nusser, and I. Psarros, “Tight Bounds for Approximate Near Neighbor Searching for Time Series under the Fréchet Distance,” 2021. [Online]. Available: https://arxiv.org/abs/2107.07792. (arXiv: 2107.07792)
Abstract
We study the $c$-approximate near neighbor problem under the continuous<br>Fr\'echet distance: Given a set of $n$ polygonal curves with $m$ vertices, a<br>radius $\delta > 0$, and a parameter $k \leq m$, we want to preprocess the<br>curves into a data structure that, given a query curve $q$ with $k$ vertices,<br>either returns an input curve with Fr\'echet distance at most $c\cdot \delta$<br>to $q$, or returns that there exists no input curve with Fr\'echet distance at<br>most $\delta$ to $q$. We focus on the case where the input and the queries are<br>one-dimensional polygonal curves -- also called time series -- and we give a<br>comprehensive analysis for this case. We obtain new upper bounds that provide<br>different tradeoffs between approximation factor, preprocessing time, and query<br>time.<br> Our data structures improve upon the state of the art in several ways. We<br>show that for any $0 < \varepsilon \leq 1$ an approximation factor of<br>$(1+\varepsilon)$ can be achieved within the same asymptotic time bounds as the<br>previously best result for $(2+\varepsilon)$. Moreover, we show that an<br>approximation factor of $(2+\varepsilon)$ can be obtained by using<br>preprocessing time and space $O(nm)$, which is linear in the input size, and<br>query time in $O(\frac{1}{\varepsilon})^{k+2}$, where the previously best<br>result used preprocessing time in $n \cdot O(\frac{m}{\varepsilon k})^k$ and<br>query time in $O(1)^k$. We complement our upper bounds with matching<br>conditional lower bounds based on the Orthogonal Vectors Hypothesis.<br>Interestingly, some of our lower bounds already hold for any super-constant<br>value of $k$. This is achieved by proving hardness of a one-sided sparse<br>version of the Orthogonal Vectors problem as an intermediate problem, which we<br>believe to be of independent interest.<br>
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@online{Bringmann_2107.07792, TITLE = {Tight Bounds for Approximate Near Neighbor Searching for Time Series under the {F}r\'{e}chet Distance}, AUTHOR = {Bringmann, Karl and Driemel, Anne and Nusser, Andr{\'e} and Psarros, Ioannis}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2107.07792}, EPRINT = {2107.07792}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the $c$-approximate near neighbor problem under the continuous<br>Fr\'echet distance: Given a set of $n$ polygonal curves with $m$ vertices, a<br>radius $\delta > 0$, and a parameter $k \leq m$, we want to preprocess the<br>curves into a data structure that, given a query curve $q$ with $k$ vertices,<br>either returns an input curve with Fr\'echet distance at most $c\cdot \delta$<br>to $q$, or returns that there exists no input curve with Fr\'echet distance at<br>most $\delta$ to $q$. We focus on the case where the input and the queries are<br>one-dimensional polygonal curves -- also called time series -- and we give a<br>comprehensive analysis for this case. We obtain new upper bounds that provide<br>different tradeoffs between approximation factor, preprocessing time, and query<br>time.<br> Our data structures improve upon the state of the art in several ways. We<br>show that for any $0 < \varepsilon \leq 1$ an approximation factor of<br>$(1+\varepsilon)$ can be achieved within the same asymptotic time bounds as the<br>previously best result for $(2+\varepsilon)$. Moreover, we show that an<br>approximation factor of $(2+\varepsilon)$ can be obtained by using<br>preprocessing time and space $O(nm)$, which is linear in the input size, and<br>query time in $O(\frac{1}{\varepsilon})^{k+2}$, where the previously best<br>result used preprocessing time in $n \cdot O(\frac{m}{\varepsilon k})^k$ and<br>query time in $O(1)^k$. We complement our upper bounds with matching<br>conditional lower bounds based on the Orthogonal Vectors Hypothesis.<br>Interestingly, some of our lower bounds already hold for any super-constant<br>value of $k$. This is achieved by proving hardness of a one-sided sparse<br>version of the Orthogonal Vectors problem as an intermediate problem, which we<br>believe to be of independent interest.<br>}, }
Endnote
%0 Report %A Bringmann, Karl %A Driemel, Anne %A Nusser, Andr&#233; %A Psarros, Ioannis %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Tight Bounds for Approximate Near Neighbor Searching for Time Series under the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B43F-6 %U https://arxiv.org/abs/2107.07792 %D 2021 %X We study the $c$-approximate near neighbor problem under the continuous<br>Fr\'echet distance: Given a set of $n$ polygonal curves with $m$ vertices, a<br>radius $\delta > 0$, and a parameter $k \leq m$, we want to preprocess the<br>curves into a data structure that, given a query curve $q$ with $k$ vertices,<br>either returns an input curve with Fr\'echet distance at most $c\cdot \delta$<br>to $q$, or returns that there exists no input curve with Fr\'echet distance at<br>most $\delta$ to $q$. We focus on the case where the input and the queries are<br>one-dimensional polygonal curves -- also called time series -- and we give a<br>comprehensive analysis for this case. We obtain new upper bounds that provide<br>different tradeoffs between approximation factor, preprocessing time, and query<br>time.<br> Our data structures improve upon the state of the art in several ways. We<br>show that for any $0 < \varepsilon \leq 1$ an approximation factor of<br>$(1+\varepsilon)$ can be achieved within the same asymptotic time bounds as the<br>previously best result for $(2+\varepsilon)$. Moreover, we show that an<br>approximation factor of $(2+\varepsilon)$ can be obtained by using<br>preprocessing time and space $O(nm)$, which is linear in the input size, and<br>query time in $O(\frac{1}{\varepsilon})^{k+2}$, where the previously best<br>result used preprocessing time in $n \cdot O(\frac{m}{\varepsilon k})^k$ and<br>query time in $O(1)^k$. We complement our upper bounds with matching<br>conditional lower bounds based on the Orthogonal Vectors Hypothesis.<br>Interestingly, some of our lower bounds already hold for any super-constant<br>value of $k$. This is achieved by proving hardness of a one-sided sparse<br>version of the Orthogonal Vectors problem as an intermediate problem, which we<br>believe to be of independent interest.<br> %K Computer Science, Computational Geometry, cs.CG,Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[151]
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
[152]
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
[153]
K. Bringmann, M. Kapralov, M. Makarov, V. Nakos, A. Yagudin, and A. Zandieh, “Sparse Fourier Transform by Traversing Cooley-Tukey FFT Computation Graphs,” 2021. [Online]. Available: https://arxiv.org/abs/2107.07347. (arXiv: 2107.07347)
Abstract
Computing the dominant Fourier coefficients of a vector is a common task in<br>many fields, such as signal processing, learning theory, and computational<br>complexity. In the Sparse Fast Fourier Transform (Sparse FFT) problem, one is<br>given oracle access to a $d$-dimensional vector $x$ of size $N$, and is asked<br>to compute the best $k$-term approximation of its Discrete Fourier Transform,<br>quickly and using few samples of the input vector $x$. While the sample<br>complexity of this problem is quite well understood, all previous approaches<br>either suffer from an exponential dependence of runtime on the dimension $d$ or<br>can only tolerate a trivial amount of noise. This is in sharp contrast with the<br>classical FFT algorithm of Cooley and Tukey, which is stable and completely<br>insensitive to the dimension of the input vector: its runtime is $O(N\log N)$<br>in any dimension $d$.<br> In this work, we introduce a new high-dimensional Sparse FFT toolkit and use<br>it to obtain new algorithms, both on the exact, as well as in the case of<br>bounded $\ell_2$ noise. This toolkit includes i) a new strategy for exploring a<br>pruned FFT computation tree that reduces the cost of filtering, ii) new<br>structural properties of adaptive aliasing filters recently introduced by<br>Kapralov, Velingker and Zandieh'SODA'19, and iii) a novel lazy estimation<br>argument, suited to reducing the cost of estimation in FFT tree-traversal<br>approaches. Our robust algorithm can be viewed as a highly optimized sparse,<br>stable extension of the Cooley-Tukey FFT algorithm.<br> Finally, we explain the barriers we have faced by proving a conditional<br>quadratic lower bound on the running time of the well-studied non-equispaced<br>Fourier transform problem. This resolves a natural and frequently asked<br>question in computational Fourier transforms. Lastly, we provide a preliminary<br>experimental evaluation comparing the runtime of our algorithm to FFTW and SFFT<br>2.0.<br>
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@online{Bringmann_2107.07347, TITLE = {Sparse {Fourier Transform} by Traversing {Cooley-Tukey FFT} Computation Graphs}, AUTHOR = {Bringmann, Karl and Kapralov, Michael and Makarov, Mikhail and Nakos, Vasileios and Yagudin, Amir and Zandieh, Amir}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2107.07347}, EPRINT = {2107.07347}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Computing the dominant Fourier coefficients of a vector is a common task in<br>many fields, such as signal processing, learning theory, and computational<br>complexity. In the Sparse Fast Fourier Transform (Sparse FFT) problem, one is<br>given oracle access to a $d$-dimensional vector $x$ of size $N$, and is asked<br>to compute the best $k$-term approximation of its Discrete Fourier Transform,<br>quickly and using few samples of the input vector $x$. While the sample<br>complexity of this problem is quite well understood, all previous approaches<br>either suffer from an exponential dependence of runtime on the dimension $d$ or<br>can only tolerate a trivial amount of noise. This is in sharp contrast with the<br>classical FFT algorithm of Cooley and Tukey, which is stable and completely<br>insensitive to the dimension of the input vector: its runtime is $O(N\log N)$<br>in any dimension $d$.<br> In this work, we introduce a new high-dimensional Sparse FFT toolkit and use<br>it to obtain new algorithms, both on the exact, as well as in the case of<br>bounded $\ell_2$ noise. This toolkit includes i) a new strategy for exploring a<br>pruned FFT computation tree that reduces the cost of filtering, ii) new<br>structural properties of adaptive aliasing filters recently introduced by<br>Kapralov, Velingker and Zandieh'SODA'19, and iii) a novel lazy estimation<br>argument, suited to reducing the cost of estimation in FFT tree-traversal<br>approaches. Our robust algorithm can be viewed as a highly optimized sparse,<br>stable extension of the Cooley-Tukey FFT algorithm.<br> Finally, we explain the barriers we have faced by proving a conditional<br>quadratic lower bound on the running time of the well-studied non-equispaced<br>Fourier transform problem. This resolves a natural and frequently asked<br>question in computational Fourier transforms. Lastly, we provide a preliminary<br>experimental evaluation comparing the runtime of our algorithm to FFTW and SFFT<br>2.0.<br>}, }
Endnote
%0 Report %A Bringmann, Karl %A Kapralov, Michael %A Makarov, Mikhail %A Nakos, Vasileios %A Yagudin, Amir %A Zandieh, Amir %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society 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 Sparse Fourier Transform by Traversing Cooley-Tukey FFT Computation Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B459-8 %U https://arxiv.org/abs/2107.07347 %D 2021 %X Computing the dominant Fourier coefficients of a vector is a common task in<br>many fields, such as signal processing, learning theory, and computational<br>complexity. In the Sparse Fast Fourier Transform (Sparse FFT) problem, one is<br>given oracle access to a $d$-dimensional vector $x$ of size $N$, and is asked<br>to compute the best $k$-term approximation of its Discrete Fourier Transform,<br>quickly and using few samples of the input vector $x$. While the sample<br>complexity of this problem is quite well understood, all previous approaches<br>either suffer from an exponential dependence of runtime on the dimension $d$ or<br>can only tolerate a trivial amount of noise. This is in sharp contrast with the<br>classical FFT algorithm of Cooley and Tukey, which is stable and completely<br>insensitive to the dimension of the input vector: its runtime is $O(N\log N)$<br>in any dimension $d$.<br> In this work, we introduce a new high-dimensional Sparse FFT toolkit and use<br>it to obtain new algorithms, both on the exact, as well as in the case of<br>bounded $\ell_2$ noise. This toolkit includes i) a new strategy for exploring a<br>pruned FFT computation tree that reduces the cost of filtering, ii) new<br>structural properties of adaptive aliasing filters recently introduced by<br>Kapralov, Velingker and Zandieh'SODA'19, and iii) a novel lazy estimation<br>argument, suited to reducing the cost of estimation in FFT tree-traversal<br>approaches. Our robust algorithm can be viewed as a highly optimized sparse,<br>stable extension of the Cooley-Tukey FFT algorithm.<br> Finally, we explain the barriers we have faced by proving a conditional<br>quadratic lower bound on the running time of the well-studied non-equispaced<br>Fourier transform problem. This resolves a natural and frequently asked<br>question in computational Fourier transforms. Lastly, we provide a preliminary<br>experimental evaluation comparing the runtime of our algorithm to FFTW and SFFT<br>2.0.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[154]
K. Bringmann and A. Nusser, “Translating Hausdorff Is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation,” in 37th International Symposium on Computational 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 on Computational 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 on Computational 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
[155]
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
[156]
K. Bringmann, N. Fischer, and V. Nakos, “Deterministic and Las Vegas Algorithms for Sparse Nonnegative Convolution,” 2021. [Online]. Available: https://arxiv.org/abs/2107.07625. (arXiv: 2107.07625)
Abstract
Computing the convolution $A\star B$ of two length-$n$ integer vectors $A,B$<br>is a core problem in several disciplines. It frequently comes up in algorithms<br>for Knapsack, $k$-SUM, All-Pairs Shortest Paths, and string pattern matching<br>problems. For these applications it typically suffices to compute convolutions<br>of nonnegative vectors. This problem can be classically solved in time $O(n\log<br>n)$ using the Fast Fourier Transform.<br> However, often the involved vectors are sparse and hence one could hope for<br>output-sensitive algorithms to compute nonnegative convolutions. This question<br>was raised by Muthukrishnan and solved by Cole and Hariharan (STOC '02) by a<br>randomized algorithm running in near-linear time in the (unknown) output-size<br>$t$. Chan and Lewenstein (STOC '15) presented a deterministic algorithm with a<br>$2^{O(\sqrt{\log t\cdot\log\log n})}$ overhead in running time and the<br>additional assumption that a small superset of the output is given; this<br>assumption was later removed by Bringmann and Nakos (ICALP '21).<br> In this paper we present the first deterministic near-linear-time algorithm<br>for computing sparse nonnegative convolutions. This immediately gives improved<br>deterministic algorithms for the state-of-the-art of output-sensitive Subset<br>Sum, block-mass pattern matching, $N$-fold Boolean convolution, and others,<br>matching up to log-factors the fastest known randomized algorithms for these<br>problems. Our algorithm is a blend of algebraic and combinatorial ideas and<br>techniques.<br> Additionally, we provide two fast Las Vegas algorithms for computing sparse<br>nonnegative convolutions. In particular, we present a simple $O(t\log^2t)$ time<br>algorithm, which is an accessible alternative to Cole and Hariharan's<br>algorithm. We further refine this new algorithm to run in Las Vegas time<br>$O(t\log t\cdot\log\log t)$, matching the running time of the dense case apart<br>from the $\log\log t$ factor.<br>
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BibTeX
@online{Bringmann_2107.07625, TITLE = {Deterministic and {Las Vegas} Algorithms for Sparse Nonnegative Convolution}, AUTHOR = {Bringmann, Karl and Fischer, Nick and Nakos, Vasileios}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2107.07625}, EPRINT = {2107.07625}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Computing the convolution $A\star B$ of two length-$n$ integer vectors $A,B$<br>is a core problem in several disciplines. It frequently comes up in algorithms<br>for Knapsack, $k$-SUM, All-Pairs Shortest Paths, and string pattern matching<br>problems. For these applications it typically suffices to compute convolutions<br>of nonnegative vectors. This problem can be classically solved in time $O(n\log<br>n)$ using the Fast Fourier Transform.<br> However, often the involved vectors are sparse and hence one could hope for<br>output-sensitive algorithms to compute nonnegative convolutions. This question<br>was raised by Muthukrishnan and solved by Cole and Hariharan (STOC '02) by a<br>randomized algorithm running in near-linear time in the (unknown) output-size<br>$t$. Chan and Lewenstein (STOC '15) presented a deterministic algorithm with a<br>$2^{O(\sqrt{\log t\cdot\log\log n})}$ overhead in running time and the<br>additional assumption that a small superset of the output is given; this<br>assumption was later removed by Bringmann and Nakos (ICALP '21).<br> In this paper we present the first deterministic near-linear-time algorithm<br>for computing sparse nonnegative convolutions. This immediately gives improved<br>deterministic algorithms for the state-of-the-art of output-sensitive Subset<br>Sum, block-mass pattern matching, $N$-fold Boolean convolution, and others,<br>matching up to log-factors the fastest known randomized algorithms for these<br>problems. Our algorithm is a blend of algebraic and combinatorial ideas and<br>techniques.<br> Additionally, we provide two fast Las Vegas algorithms for computing sparse<br>nonnegative convolutions. In particular, we present a simple $O(t\log^2t)$ time<br>algorithm, which is an accessible alternative to Cole and Hariharan's<br>algorithm. We further refine this new algorithm to run in Las Vegas time<br>$O(t\log t\cdot\log\log t)$, matching the running time of the dense case apart<br>from the $\log\log t$ factor.<br>}, }
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 Deterministic and Las Vegas Algorithms for Sparse Nonnegative Convolution : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B454-D %U https://arxiv.org/abs/2107.07625 %D 2021 %X Computing the convolution $A\star B$ of two length-$n$ integer vectors $A,B$<br>is a core problem in several disciplines. It frequently comes up in algorithms<br>for Knapsack, $k$-SUM, All-Pairs Shortest Paths, and string pattern matching<br>problems. For these applications it typically suffices to compute convolutions<br>of nonnegative vectors. This problem can be classically solved in time $O(n\log<br>n)$ using the Fast Fourier Transform.<br> However, often the involved vectors are sparse and hence one could hope for<br>output-sensitive algorithms to compute nonnegative convolutions. This question<br>was raised by Muthukrishnan and solved by Cole and Hariharan (STOC '02) by a<br>randomized algorithm running in near-linear time in the (unknown) output-size<br>$t$. Chan and Lewenstein (STOC '15) presented a deterministic algorithm with a<br>$2^{O(\sqrt{\log t\cdot\log\log n})}$ overhead in running time and the<br>additional assumption that a small superset of the output is given; this<br>assumption was later removed by Bringmann and Nakos (ICALP '21).<br> In this paper we present the first deterministic near-linear-time algorithm<br>for computing sparse nonnegative convolutions. This immediately gives improved<br>deterministic algorithms for the state-of-the-art of output-sensitive Subset<br>Sum, block-mass pattern matching, $N$-fold Boolean convolution, and others,<br>matching up to log-factors the fastest known randomized algorithms for these<br>problems. Our algorithm is a blend of algebraic and combinatorial ideas and<br>techniques.<br> Additionally, we provide two fast Las Vegas algorithms for computing sparse<br>nonnegative convolutions. In particular, we present a simple $O(t\log^2t)$ time<br>algorithm, which is an accessible alternative to Cole and Hariharan's<br>algorithm. We further refine this new algorithm to run in Las Vegas time<br>$O(t\log t\cdot\log\log t)$, matching the running time of the dense case apart<br>from the $\log\log t$ factor.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[157]
K. Bringmann and V. Nakos, “Top-k-Convolution and the Quest for Near-Linear Output-Sensitive Subset Sum,” 2021. [Online]. Available: https://arxiv.org/abs/2107.13206. (arXiv: 2107.13206)
Abstract
In the classical Subset Sum problem we are given a set $X$ and a target $t$,<br>and the task is to decide whether there exists a subset of $X$ which sums to<br>$t$. A recent line of research has resulted in $\tilde{O}(t)$-time algorithms,<br>which are (near-)optimal under popular complexity-theoretic assumptions. On the<br>other hand, the standard dynamic programming algorithm runs in time $O(n \cdot<br>|\mathcal{S}(X,t)|)$, where $\mathcal{S}(X,t)$ is the set of all subset sums of<br>$X$ that are smaller than $t$. Furthermore, all known pseudopolynomial<br>algorithms actually solve a stronger task, since they actually compute the<br>whole set $\mathcal{S}(X,t)$.<br> As the aforementioned two running times are incomparable, in this paper we<br>ask whether one can achieve the best of both worlds: running time<br>$\tilde{O}(|\mathcal{S}(X,t)|)$. In particular, we ask whether<br>$\mathcal{S}(X,t)$ can be computed in near-linear time in the output-size.<br>Using a diverse toolkit containing techniques such as color coding, sparse<br>recovery, and sumset estimates, we make considerable progress towards this<br>question and design an algorithm running in time<br>$\tilde{O}(|\mathcal{S}(X,t)|^{4/3})$.<br> Central to our approach is the study of top-$k$-convolution, a natural<br>problem of independent interest: given sparse polynomials with non-negative<br>coefficients, compute the lowest $k$ non-zero monomials of their product. We<br>design an algorithm running in time $\tilde{O}(k^{4/3})$, by a combination of<br>sparse convolution and sumset estimates considered in Additive Combinatorics.<br>Moreover, we provide evidence that going beyond some of the barriers we have<br>faced requires either an algorithmic breakthrough or possibly new techniques<br>from Additive Combinatorics on how to pass from information on restricted<br>sumsets to information on unrestricted sumsets.<br>
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@online{Bringmann_2107.13206, TITLE = {Top-k-Convolution and the Quest for Near-Linear Output-Sensitive Subset Sum}, AUTHOR = {Bringmann, Karl and Nakos, Vasileios}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2107.13206}, EPRINT = {2107.13206}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In the classical Subset Sum problem we are given a set $X$ and a target $t$,<br>and the task is to decide whether there exists a subset of $X$ which sums to<br>$t$. A recent line of research has resulted in $\tilde{O}(t)$-time algorithms,<br>which are (near-)optimal under popular complexity-theoretic assumptions. On the<br>other hand, the standard dynamic programming algorithm runs in time $O(n \cdot<br>|\mathcal{S}(X,t)|)$, where $\mathcal{S}(X,t)$ is the set of all subset sums of<br>$X$ that are smaller than $t$. Furthermore, all known pseudopolynomial<br>algorithms actually solve a stronger task, since they actually compute the<br>whole set $\mathcal{S}(X,t)$.<br> As the aforementioned two running times are incomparable, in this paper we<br>ask whether one can achieve the best of both worlds: running time<br>$\tilde{O}(|\mathcal{S}(X,t)|)$. In particular, we ask whether<br>$\mathcal{S}(X,t)$ can be computed in near-linear time in the output-size.<br>Using a diverse toolkit containing techniques such as color coding, sparse<br>recovery, and sumset estimates, we make considerable progress towards this<br>question and design an algorithm running in time<br>$\tilde{O}(|\mathcal{S}(X,t)|^{4/3})$.<br> Central to our approach is the study of top-$k$-convolution, a natural<br>problem of independent interest: given sparse polynomials with non-negative<br>coefficients, compute the lowest $k$ non-zero monomials of their product. We<br>design an algorithm running in time $\tilde{O}(k^{4/3})$, by a combination of<br>sparse convolution and sumset estimates considered in Additive Combinatorics.<br>Moreover, we provide evidence that going beyond some of the barriers we have<br>faced requires either an algorithmic breakthrough or possibly new techniques<br>from Additive Combinatorics on how to pass from information on restricted<br>sumsets to information on unrestricted sumsets.<br>}, }
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 Top-k-Convolution and the Quest for Near-Linear Output-Sensitive Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B434-1 %U https://arxiv.org/abs/2107.13206 %D 2021 %X In the classical Subset Sum problem we are given a set $X$ and a target $t$,<br>and the task is to decide whether there exists a subset of $X$ which sums to<br>$t$. A recent line of research has resulted in $\tilde{O}(t)$-time algorithms,<br>which are (near-)optimal under popular complexity-theoretic assumptions. On the<br>other hand, the standard dynamic programming algorithm runs in time $O(n \cdot<br>|\mathcal{S}(X,t)|)$, where $\mathcal{S}(X,t)$ is the set of all subset sums of<br>$X$ that are smaller than $t$. Furthermore, all known pseudopolynomial<br>algorithms actually solve a stronger task, since they actually compute the<br>whole set $\mathcal{S}(X,t)$.<br> As the aforementioned two running times are incomparable, in this paper we<br>ask whether one can achieve the best of both worlds: running time<br>$\tilde{O}(|\mathcal{S}(X,t)|)$. In particular, we ask whether<br>$\mathcal{S}(X,t)$ can be computed in near-linear time in the output-size.<br>Using a diverse toolkit containing techniques such as color coding, sparse<br>recovery, and sumset estimates, we make considerable progress towards this<br>question and design an algorithm running in time<br>$\tilde{O}(|\mathcal{S}(X,t)|^{4/3})$.<br> Central to our approach is the study of top-$k$-convolution, a natural<br>problem of independent interest: given sparse polynomials with non-negative<br>coefficients, compute the lowest $k$ non-zero monomials of their product. We<br>design an algorithm running in time $\tilde{O}(k^{4/3})$, by a combination of<br>sparse convolution and sumset estimates considered in Additive Combinatorics.<br>Moreover, we provide evidence that going beyond some of the barriers we have<br>faced requires either an algorithmic breakthrough or possibly new techniques<br>from Additive Combinatorics on how to pass from information on restricted<br>sumsets to information on unrestricted sumsets.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Discrete Mathematics, cs.DM
[158]
K. Bringmann, A. Cassis, N. Fischer, and M. Künnemann, “Fine-Grained Completeness for Optimization in P,” in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021), Seattle, WA, USA, 2021.
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@inproceedings{Bringmann_APPROXRANDOM21, TITLE = {Fine-Grained Completeness for Optimization in {P}}, AUTHOR = {Bringmann, Karl and Cassis, Alejandro and Fischer, Nick and K{\"u}nnemann, Marvin}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-207-5}, URL = {urn:nbn:de:0030-drops-147024}, DOI = {10.4230/LIPIcs.APPROX/RANDOM.2021.9}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)}, EDITOR = {Wootters, Mary and Sanit{\a}, Laura}, PAGES = {1--22}, EID = {9}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {207}, ADDRESS = {Seattle, WA, USA}, }
Endnote
%0 Conference Proceedings %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/21.11116/0000-0009-B411-8 %R 10.4230/LIPIcs.APPROX/RANDOM.2021.9 %U urn:nbn:de:0030-drops-147024 %D 2021 %B 24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 25th International Conference on Randomization and Computation %Z date of event: 2021-08-16 - 2021-08-18 %C Seattle, WA, USA %B Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques %E Wootters, Mary; Sanit&#224;, Laura %P 1 - 22 %Z sequence number: 9 %I Schloss Dagstuhl %@ 978-3-95977-207-5 %B Leibniz International Proceedings in Informatics %N 207 %@ false
[159]
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<br>approximate optimization in the polynomial-time regime. Inspired by the first<br>completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova,<br>Williams, TALG 2019) as well as the classic class MaxSNP and<br>MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis,<br>JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain<br>a number of natural optimization problems in P, including Maximum Inner<br>Product, general forms of nearest neighbor search and optimization variants of<br>the $k$-XOR problem. Specifically, we define MaxSP as the class of problems<br>definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) :<br>\phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free<br>first-order property over a given relational structure (with MinSP defined<br>analogously). On $m$-sized structures, we can solve each such problem in time<br>$O(m^{k+\ell-1})$. Our results are:<br> - We determine (a sparse variant of) the Maximum/Minimum Inner Product<br>problem as complete under *deterministic* fine-grained reductions: A strongly<br>subquadratic algorithm for Maximum/Minimum Inner Product would beat the<br>baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by<br>a polynomial factor.<br> - This completeness transfers to approximation: Maximum/Minimum Inner Product<br>is also complete in the sense that a strongly subquadratic $c$-approximation<br>would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in<br>time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen<br>arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019),<br>we obtain the perhaps surprising consequence that refuting the OV Hypothesis is<br>*equivalent* to giving a $O(1)$-approximation for all MinSP problems in<br>faster-than-$O(m^{k+\ell-1})$ time.<br>
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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<br>approximate optimization in the polynomial-time regime. Inspired by the first<br>completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova,<br>Williams, TALG 2019) as well as the classic class MaxSNP and<br>MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis,<br>JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain<br>a number of natural optimization problems in P, including Maximum Inner<br>Product, general forms of nearest neighbor search and optimization variants of<br>the $k$-XOR problem. Specifically, we define MaxSP as the class of problems<br>definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) :<br>\phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free<br>first-order property over a given relational structure (with MinSP defined<br>analogously). On $m$-sized structures, we can solve each such problem in time<br>$O(m^{k+\ell-1})$. Our results are:<br> -- We determine (a sparse variant of) the Maximum/Minimum Inner Product<br>problem as complete under *deterministic* fine-grained reductions: A strongly<br>subquadratic algorithm for Maximum/Minimum Inner Product would beat the<br>baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by<br>a polynomial factor.<br> -- This completeness transfers to approximation: Maximum/Minimum Inner Product<br>is also complete in the sense that a strongly subquadratic $c$-approximation<br>would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in<br>time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen<br>arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019),<br>we obtain the perhaps surprising consequence that refuting the OV Hypothesis is<br>*equivalent* to giving a $O(1)$-approximation for all MinSP problems in<br>faster-than-$O(m^{k+\ell-1})$ time.<br>}, }
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<br>approximate optimization in the polynomial-time regime. Inspired by the first<br>completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova,<br>Williams, TALG 2019) as well as the classic class MaxSNP and<br>MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis,<br>JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain<br>a number of natural optimization problems in P, including Maximum Inner<br>Product, general forms of nearest neighbor search and optimization variants of<br>the $k$-XOR problem. Specifically, we define MaxSP as the class of problems<br>definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) :<br>\phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free<br>first-order property over a given relational structure (with MinSP defined<br>analogously). On $m$-sized structures, we can solve each such problem in time<br>$O(m^{k+\ell-1})$. Our results are:<br> - We determine (a sparse variant of) the Maximum/Minimum Inner Product<br>problem as complete under *deterministic* fine-grained reductions: A strongly<br>subquadratic algorithm for Maximum/Minimum Inner Product would beat the<br>baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by<br>a polynomial factor.<br> - This completeness transfers to approximation: Maximum/Minimum Inner Product<br>is also complete in the sense that a strongly subquadratic $c$-approximation<br>would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in<br>time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen<br>arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019),<br>we obtain the perhaps surprising consequence that refuting the OV Hypothesis is<br>*equivalent* to giving a $O(1)$-approximation for all MinSP problems in<br>faster-than-$O(m^{k+\ell-1})$ time.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[160]
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
[161]
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
[162]
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<br>ubiquitous computational primitive. Applications range from string problems to<br>Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These<br>applications often come in the form of nonnegative convolution, where the<br>entries of $A,B$ are nonnegative integers. The classical algorithm to compute<br>$A\star B$ uses the Fast Fourier Transform and runs in time $O(n\log n)$.<br> However, often $A$ and $B$ satisfy sparsity conditions, and hence one could<br>hope for significant improvements. The ideal goal is an $O(k\log k)$-time<br>algorithm, where $k$ is the number of non-zero elements in the output, i.e.,<br>the size of the support of $A\star B$. This problem is referred to as sparse<br>nonnegative convolution, and has received considerable attention in the<br>literature; the fastest algorithms to date run in time $O(k\log^2 n)$.<br> The main result of this paper is the first $O(k\log k)$-time algorithm for<br>sparse nonnegative convolution. Our algorithm is randomized and assumes that<br>the length $n$ and the largest entry of $A$ and $B$ are subexponential in $k$.<br>Surprisingly, we can phrase our algorithm as a reduction from the sparse case<br>to the dense case of nonnegative convolution, showing that, under some mild<br>assumptions, sparse nonnegative convolution is equivalent to dense nonnegative<br>convolution for constant-error randomized algorithms. Specifically, if $D(n)$<br>is the time to convolve two nonnegative length-$n$ vectors with success<br>probability $2/3$, and $S(k)$ is the time to convolve two nonnegative vectors<br>with output size $k$ with success probability $2/3$, then<br>$S(k)=O(D(k)+k(\log\log k)^2)$.<br> Our approach uses a variety of new techniques in combination with some old<br>machinery from linear sketching and structured linear algebra, as well as new<br>insights on linear hashing, the most classical hash function.<br>
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@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<br>ubiquitous computational primitive. Applications range from string problems to<br>Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These<br>applications often come in the form of nonnegative convolution, where the<br>entries of $A,B$ are nonnegative integers. The classical algorithm to compute<br>$A\star B$ uses the Fast Fourier Transform and runs in time $O(n\log n)$.<br> However, often $A$ and $B$ satisfy sparsity conditions, and hence one could<br>hope for significant improvements. The ideal goal is an $O(k\log k)$-time<br>algorithm, where $k$ is the number of non-zero elements in the output, i.e.,<br>the size of the support of $A\star B$. This problem is referred to as sparse<br>nonnegative convolution, and has received considerable attention in the<br>literature; the fastest algorithms to date run in time $O(k\log^2 n)$.<br> The main result of this paper is the first $O(k\log k)$-time algorithm for<br>sparse nonnegative convolution. Our algorithm is randomized and assumes that<br>the length $n$ and the largest entry of $A$ and $B$ are subexponential in $k$.<br>Surprisingly, we can phrase our algorithm as a reduction from the sparse case<br>to the dense case of nonnegative convolution, showing that, under some mild<br>assumptions, sparse nonnegative convolution is equivalent to dense nonnegative<br>convolution for constant-error randomized algorithms. Specifically, if $D(n)$<br>is the time to convolve two nonnegative length-$n$ vectors with success<br>probability $2/3$, and $S(k)$ is the time to convolve two nonnegative vectors<br>with output size $k$ with success probability $2/3$, then<br>$S(k)=O(D(k)+k(\log\log k)^2)$.<br> Our approach uses a variety of new techniques in combination with some old<br>machinery from linear sketching and structured linear algebra, as well as new<br>insights on linear hashing, the most classical hash function.<br>}, }
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<br>ubiquitous computational primitive. Applications range from string problems to<br>Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These<br>applications often come in the form of nonnegative convolution, where the<br>entries of $A,B$ are nonnegative integers. The classical algorithm to compute<br>$A\star B$ uses the Fast Fourier Transform and runs in time $O(n\log n)$.<br> However, often $A$ and $B$ satisfy sparsity conditions, and hence one could<br>hope for significant improvements. The ideal goal is an $O(k\log k)$-time<br>algorithm, where $k$ is the number of non-zero elements in the output, i.e.,<br>the size of the support of $A\star B$. This problem is referred to as sparse<br>nonnegative convolution, and has received considerable attention in the<br>literature; the fastest algorithms to date run in time $O(k\log^2 n)$.<br> The main result of this paper is the first $O(k\log k)$-time algorithm for<br>sparse nonnegative convolution. Our algorithm is randomized and assumes that<br>the length $n$ and the largest entry of $A$ and $B$ are subexponential in $k$.<br>Surprisingly, we can phrase our algorithm as a reduction from the sparse case<br>to the dense case of nonnegative convolution, showing that, under some mild<br>assumptions, sparse nonnegative convolution is equivalent to dense nonnegative<br>convolution for constant-error randomized algorithms. Specifically, if $D(n)$<br>is the time to convolve two nonnegative length-$n$ vectors with success<br>probability $2/3$, and $S(k)$ is the time to convolve two nonnegative vectors<br>with output size $k$ with success probability $2/3$, then<br>$S(k)=O(D(k)+k(\log\log k)^2)$.<br> Our approach uses a variety of new techniques in combination with some old<br>machinery from linear sketching and structured linear algebra, as well as new<br>insights on linear hashing, the most classical hash function.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[163]
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<br>(LCS) of two strings of length $n$. While a simple quadratic algorithm has been<br>known for the problem for more than 40 years, no faster algorithm has been<br>found despite an extensive effort. The lack of progress on the problem has<br>recently been explained by Abboud, Backurs, and Vassilevska Williams [FOCS'15]<br>and Bringmann and K\"unnemann [FOCS'15] who proved that there is no<br>subquadratic algorithm unless the Strong Exponential Time Hypothesis fails.<br>This has led the community to look for subquadratic approximation algorithms<br>for the problem.<br> Yet, unlike the edit distance problem for which a constant-factor<br>approximation in almost-linear time is known, very little progress has been<br>made on LCS, making it a notoriously difficult problem also in the realm of<br>approximation. For the general setting, only a naive<br>$O(n^{\varepsilon/2})$-approximation algorithm with running time<br>$\tilde{O}(n^{2-\varepsilon})$ has been known, for any constant $0 <<br>\varepsilon \le 1$. Recently, a breakthrough result by Hajiaghayi, Seddighin,<br>Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a<br>$O(n^{0.497956})$-approximation in expectation; improving upon the naive<br>$O(\sqrt{n})$-approximation for the first time.<br> In this paper, we provide an algorithm that in time $O(n^{2-\varepsilon})$<br>computes an $\tilde{O}(n^{2\varepsilon/5})$-approximation with high<br>probability, for any $0 < \varepsilon \le 1$. Our result (1) gives an<br>$\tilde{O}(n^{0.4})$-approximation in linear time, improving upon the bound of<br>Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose<br>approximation scales with any subquadratic running time $O(n^{2-\varepsilon})$,<br>improving upon the naive bound of $O(n^{\varepsilon/2})$ for any $\varepsilon$,<br>and (3) instead of only in expectation, succeeds with high probability.<br>
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@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<br>(LCS) of two strings of length $n$. While a simple quadratic algorithm has been<br>known for the problem for more than 40 years, no faster algorithm has been<br>found despite an extensive effort. The lack of progress on the problem has<br>recently been explained by Abboud, Backurs, and Vassilevska Williams [FOCS'15]<br>and Bringmann and K\"unnemann [FOCS'15] who proved that there is no<br>subquadratic algorithm unless the Strong Exponential Time Hypothesis fails.<br>This has led the community to look for subquadratic approximation algorithms<br>for the problem.<br> Yet, unlike the edit distance problem for which a constant-factor<br>approximation in almost-linear time is known, very little progress has been<br>made on LCS, making it a notoriously difficult problem also in the realm of<br>approximation. For the general setting, only a naive<br>$O(n^{\varepsilon/2})$-approximation algorithm with running time<br>$\tilde{O}(n^{2-\varepsilon})$ has been known, for any constant $0 <<br>\varepsilon \le 1$. Recently, a breakthrough result by Hajiaghayi, Seddighin,<br>Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a<br>$O(n^{0.497956})$-approximation in expectation; improving upon the naive<br>$O(\sqrt{n})$-approximation for the first time.<br> In this paper, we provide an algorithm that in time $O(n^{2-\varepsilon})$<br>computes an $\tilde{O}(n^{2\varepsilon/5})$-approximation with high<br>probability, for any $0 < \varepsilon \le 1$. Our result (1) gives an<br>$\tilde{O}(n^{0.4})$-approximation in linear time, improving upon the bound of<br>Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose<br>approximation scales with any subquadratic running time $O(n^{2-\varepsilon})$,<br>improving upon the naive bound of $O(n^{\varepsilon/2})$ for any $\varepsilon$,<br>and (3) instead of only in expectation, succeeds with high probability.<br>}, }
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<br>(LCS) of two strings of length $n$. While a simple quadratic algorithm has been<br>known for the problem for more than 40 years, no faster algorithm has been<br>found despite an extensive effort. The lack of progress on the problem has<br>recently been explained by Abboud, Backurs, and Vassilevska Williams [FOCS'15]<br>and Bringmann and K\"unnemann [FOCS'15] who proved that there is no<br>subquadratic algorithm unless the Strong Exponential Time Hypothesis fails.<br>This has led the community to look for subquadratic approximation algorithms<br>for the problem.<br> Yet, unlike the edit distance problem for which a constant-factor<br>approximation in almost-linear time is known, very little progress has been<br>made on LCS, making it a notoriously difficult problem also in the realm of<br>approximation. For the general setting, only a naive<br>$O(n^{\varepsilon/2})$-approximation algorithm with running time<br>$\tilde{O}(n^{2-\varepsilon})$ has been known, for any constant $0 <<br>\varepsilon \le 1$. Recently, a breakthrough result by Hajiaghayi, Seddighin,<br>Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a<br>$O(n^{0.497956})$-approximation in expectation; improving upon the naive<br>$O(\sqrt{n})$-approximation for the first time.<br> In this paper, we provide an algorithm that in time $O(n^{2-\varepsilon})$<br>computes an $\tilde{O}(n^{2\varepsilon/5})$-approximation with high<br>probability, for any $0 < \varepsilon \le 1$. Our result (1) gives an<br>$\tilde{O}(n^{0.4})$-approximation in linear time, improving upon the bound of<br>Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose<br>approximation scales with any subquadratic running time $O(n^{2-\varepsilon})$,<br>improving upon the naive bound of $O(n^{\varepsilon/2})$ for any $\varepsilon$,<br>and (3) instead of only in expectation, succeeds with high probability.<br> %K Computer Science, Data Structures and Algorithms, cs.DS,
[164]
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
[165]
B. R. Chaudhury, “Finding Fair and Efficient Allocations,” Universität des Saarlandes, Saarbrücken, 2021.
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@phdthesis{Chaudphd2021, TITLE = {Finding Fair and Efficient Allocations}, AUTHOR = {Chaudhury, Bhaskar Ray}, LANGUAGE = {eng}, URL = {nbn:de:bsz:291--ds-345370}, DOI = {10.22028/D291-34537}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, }
Endnote
%0 Thesis %A Chaudhury, Bhaskar Ray %Y Mehlhorn, Kurt %A referee: Bringmann, Karl %A referee: Roughgarden, Tim %A referee: Moulin, Herve %+ 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 External Organizations %T Finding Fair and Efficient Allocations : %G eng %U http://hdl.handle.net/21.11116/0000-0009-9CC9-5 %R 10.22028/D291-34537 %U nbn:de:bsz:291--ds-345370 %F OTHER: hdl:20.500.11880/31737 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2021 %P 173 p. %V phd %9 phd %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/31737
[166]
B. R. Chaudhury, J. Garg, K. Mehlhorn, R. Mehta, and P. Misra, “Improving EFX Guarantees through Rainbow Cycle Number,” in EC ’21, 22nd ACM Conference on Economics and Computation, Budapest, Hungary (Virtual), 2021.
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@inproceedings{Chaudhury_EC2021, TITLE = {Improving {EFX} Guarantees through Rainbow Cycle Number}, AUTHOR = {Chaudhury, Bhaskar Ray and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta and Misra, Pranabendu}, LANGUAGE = {eng}, ISBN = {978-1-4503-8554-1}, DOI = {10.1145/3465456.3467605}, PUBLISHER = {ACM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {EC '21, 22nd ACM Conference on Economics and Computation}, EDITOR = {Bir{\'o}, P{\'e}ter and Chawla, Shuchi and Echenique, Federico and Sodomka, Eric}, PAGES = {310--311}, ADDRESS = {Budapest, Hungary (Virtual)}, }
Endnote
%0 Conference Proceedings %A Chaudhury, Bhaskar Ray %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/21.11116/0000-0009-B3F6-7 %R 10.1145/3465456.3467605 %D 2021 %B 22nd ACM Conference on Economics and Computation %Z date of event: 2021-07-18 - 2021-07-23 %C Budapest, Hungary (Virtual) %B EC '21 %E Bir&#243;, P&#233;ter; Chawla, Shuchi; Echenique, Federico; Sodomka, Eric %P 310 - 311 %I ACM %@ 978-1-4503-8554-1
[167]
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
[168]
C. Coupette, J. Singh, and H. Spamann, “Simplify Your Law: Using Information Theory to Deduplicate Legal Documents,” in 21st IEEE International Conference on Data Mining Workshops (ICDMW 2021), Virtual Conference, 2021.
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@inproceedings{CoupetteICDMW21, TITLE = {Simplify Your Law: Using Information Theory to Deduplicate Legal Documents}, AUTHOR = {Coupette, Corinna and Singh, Jyotsna and Spamann, Holger}, LANGUAGE = {eng}, ISBN = {978-1-6654-2428-8}, DOI = {10.1109/ICDMW53433.2021.00083}, PUBLISHER = {IEEE}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, BOOKTITLE = {21st IEEE International Conference on Data Mining Workshops (ICDMW 2021)}, EDITOR = {Xue, Bing and Pechenizkiy, Mykola and Koh, Yun Sing}, PAGES = {631--638}, ADDRESS = {Virtual Conference}, }
Endnote
%0 Conference Proceedings %A Coupette, Corinna %A Singh, Jyotsna %A Spamann, Holger %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Simplify Your Law: Using Information Theory to Deduplicate Legal Documents : %G eng %U http://hdl.handle.net/21.11116/0000-000A-5E10-B %R 10.1109/ICDMW53433.2021.00083 %D 2021 %B 21st IEEE International Conference on Data Mining Workshops %Z date of event: 2021-12-07 - 2021-12-10 %C Virtual Conference %B 21st IEEE International Conference on Data Mining Workshops %E Xue, Bing; Pechenizkiy, Mykola; Koh, Yun Sing %P 631 - 638 %I IEEE %@ 978-1-6654-2428-8
[169]
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
[170]
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
[171]
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
[172]
E. Cruciani, E. Natale, A. Nusser, and G. Scornavacca, “Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks,” Distributed Computing, vol. 34, 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 = {34}, PAGES = {207--225}, }
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 34 %& 207 %P 207 - 225 %I Springer International %C Berlin %@ false
[173]
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
[174]
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
[175]
M. de Berg, S. Kisfaludi-Bak, M. Monemizadeh, and L. Theocharous, “Clique-Based Separators for Geometric Intersection Graphs,” in 32nd International Symposium on Algorithms and Computation (ISAAC 2021), Fukuoka, Japan, 2021.
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@inproceedings{deBerg_ISAAC21, TITLE = {Clique-Based Separators for Geometric Intersection Graphs}, AUTHOR = {de Berg, Mark and Kisfaludi-Bak, S{\'a}ndor and Monemizadeh, Morteza and Theocharous, Leonidas}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-214-3}, URL = {urn:nbn:de:0030-drops-154556}, DOI = {10.4230/LIPIcs.ISAAC.2021.22}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)}, EDITOR = {Ahn, Hee-Kap and Sadakane, Kunihiko}, PAGES = {1--15}, EID = {22}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {212}, ADDRESS = {Fukuoka, Japan}, }
Endnote
%0 Conference Proceedings %A de Berg, Mark %A Kisfaludi-Bak, S&#225;ndor %A Monemizadeh, Morteza %A Theocharous, Leonidas %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Clique-Based Separators for Geometric Intersection Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B811-4 %R 10.4230/LIPIcs.ISAAC.2021.22 %U urn:nbn:de:0030-drops-154556 %D 2021 %B 32nd International Symposium on Algorithms and Computation %Z date of event: 2021-12-06 - 2021-12-08 %C Fukuoka, Japan %B 32nd International Symposium on Algorithms and Computation %E Ahn, Hee-Kap; Sadakane, Kunihiko %P 1 - 15 %Z sequence number: 22 %I Schloss Dagstuhl %@ 978-3-95977-214-3 %B Leibniz International Proceedings in Informatics %N 212 %@ false
[176]
I. Diakonikolas, T. Gouleakis, D. M. Kane, J. Peebles, and E. Price, “Optimal Testing of Discrete Distributions with High Probability,” in STOC ’21, 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual, Italy, 2021.
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@inproceedings{Diakonikolas_STOC2021, 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}, ISBN = {9781450380539}, DOI = {10.1145/3406325.3450997}, PUBLISHER = {ACM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '21, 53rd Annual ACM SIGACT Symposium on Theory of Computing}, EDITOR = {Khuller, Samir and Vassilevska Williams, Virginia}, PAGES = {542--555}, ADDRESS = {Virtual, Italy}, }
Endnote
%0 Conference Proceedings %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/21.11116/0000-000A-CD4F-8 %R 10.1145/3406325.3450997 %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 542 - 555 %I ACM %@ 9781450380539
[177]
J. Dörfler, M. Roth, J. Schmitt, and P. Wellnitz, “Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness,” Algorithmica, 2021.
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@article{Doerfler2021, TITLE = {Counting Induced Subgraphs: {A}n Algebraic Approach to \#{W}[1]-hardness}, AUTHOR = {D{\"o}rfler, Julian and Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-021-00894-9}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, }
Endnote
%0 Journal Article %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/21.11116/0000-0009-A583-8 %R 10.1007/s00453-021-00894-9 %7 2021 %D 2021 %J Algorithmica %I Springer-Verlag %C New York %@ false
[178]
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
[179]
M. Dyer, C. Greenhill, P. Kleer, J. Ross, and L. Stougie, “Sampling Hypergraphs with Given Degrees,” Discrete Mathematics, vol. 344, no. 11, 2021.
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@article{Dyer2021, TITLE = {Sampling Hypergraphs with Given Degrees}, AUTHOR = {Dyer, Martin and Greenhill, Catherine and Kleer, Pieter and Ross, James and Stougie, Leen}, LANGUAGE = {eng}, ISSN = {0012-365X}, DOI = {10.1016/j.disc.2021.112566}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, JOURNAL = {Discrete Mathematics}, VOLUME = {344}, NUMBER = {11}, EID = {112566}, }
Endnote
%0 Journal Article %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/21.11116/0000-0009-B820-3 %R 10.1016/j.disc.2021.112566 %7 2021 %D 2021 %J Discrete Mathematics %V 344 %N 11 %Z sequence number: 112566 %I Elsevier %C Amsterdam %@ false
[180]
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
[181]
F. Folz, K. Mehlhorn, and G. Morigi, “Interplay of Periodic Dynamics and Noise: Insights from a Simple Adaptive System,” Physical Review E, vol. 104, no. 5, 2021.
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@article{Folz2021, TITLE = {Interplay of Periodic Dynamics and Noise: {I}nsights from a Simple Adaptive System}, AUTHOR = {Folz, Frederic and Mehlhorn, Kurt and Morigi, Giovanna}, LANGUAGE = {eng}, ISSN = {1539-3755}, DOI = {10.1103/PhysRevE.104.054215}, PUBLISHER = {American Physical Society}, ADDRESS = {Melville, NY}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, JOURNAL = {Physical Review E}, VOLUME = {104}, NUMBER = {5}, EID = {054215}, }
Endnote
%0 Journal Article %A Folz, Frederic %A Mehlhorn, Kurt %A Morigi, Giovanna %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Interplay of Periodic Dynamics and Noise: Insights from a Simple Adaptive System : %G eng %U http://hdl.handle.net/21.11116/0000-0009-9D3F-1 %R 10.1103/PhysRevE.104.054215 %7 2021 %D 2021 %J Physical Review E %O Phys. Rev. E %V 104 %N 5 %Z sequence number: 054215 %I American Physical Society %C Melville, NY %@ false
[182]
J. Giliberti and A. Karrenbauer, “Improved Online Algorithm for Fractional Knapsack in the Random Order Model,” 2021. [Online]. Available: https://arxiv.org/abs/2109.04428. (arXiv: 2109.04428)
Abstract
The fractional knapsack problem is one of the classical problems in<br>combinatorial optimization, which is well understood in the offline setting.<br>However, the corresponding online setting has been handled only briefly in the<br>theoretical computer science literature so far, although it appears in several<br>applications. Even the previously best known guarantee for the competitive<br>ratio was worse than the best known for the integral problem in the popular<br>random order model. We show that there is an algorithm for the online<br>fractional knapsack problem that admits a competitive ratio of 4.39. Our result<br>significantly improves over the previously best known competitive ratio of 9.37<br>and surpasses the current best 6.65-competitive algorithm for the integral<br>case. Moreover, our algorithm is deterministic in contrast to the randomized<br>algorithms achieving the results mentioned above.<br>
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@online{Gilberti2109.04428, TITLE = {Improved Online Algorithm for Fractional Knapsack in the Random Order Model}, AUTHOR = {Giliberti, Jeff and Karrenbauer, Andreas}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2109.04428}, EPRINT = {2109.04428}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The fractional knapsack problem is one of the classical problems in<br>combinatorial optimization, which is well understood in the offline setting.<br>However, the corresponding online setting has been handled only briefly in the<br>theoretical computer science literature so far, although it appears in several<br>applications. Even the previously best known guarantee for the competitive<br>ratio was worse than the best known for the integral problem in the popular<br>random order model. We show that there is an algorithm for the online<br>fractional knapsack problem that admits a competitive ratio of 4.39. Our result<br>significantly improves over the previously best known competitive ratio of 9.37<br>and surpasses the current best 6.65-competitive algorithm for the integral<br>case. Moreover, our algorithm is deterministic in contrast to the randomized<br>algorithms achieving the results mentioned above.<br>}, }
Endnote
%0 Report %A Giliberti, Jeff %A Karrenbauer, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Improved Online Algorithm for Fractional Knapsack in the Random Order Model : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B637-C %U https://arxiv.org/abs/2109.04428 %D 2021 %X The fractional knapsack problem is one of the classical problems in<br>combinatorial optimization, which is well understood in the offline setting.<br>However, the corresponding online setting has been handled only briefly in the<br>theoretical computer science literature so far, although it appears in several<br>applications. Even the previously best known guarantee for the competitive<br>ratio was worse than the best known for the integral problem in the popular<br>random order model. We show that there is an algorithm for the online<br>fractional knapsack problem that admits a competitive ratio of 4.39. Our result<br>significantly improves over the previously best known competitive ratio of 9.37<br>and surpasses the current best 6.65-competitive algorithm for the integral<br>case. Moreover, our algorithm is deterministic in contrast to the randomized<br>algorithms achieving the results mentioned above.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[183]
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
[184]
P. Kleer and H. U. Simon, “Primal and Dual Combinatorial Dimensions,” 2021. [Online]. Available: https://arxiv.org/abs/2108.10037. (arXiv: 2108.10037)
Abstract
We give tight bounds on the relation between the primal and dual of various<br>combinatorial dimensions, such as the pseudo-dimension and fat-shattering<br>dimension, for multi-valued function classes. These dimensional notions play an<br>important role in the area of learning theory. We first review some (folklore)<br>results that bound the dual dimension of a function class in terms of its<br>primal, and after that give (almost) matching lower bounds. In particular, we<br>give an appropriate generalization to multi-valued function classes of a<br>well-known bound due to Assouad (1983), that relates the primal and dual<br>VC-dimension of a binary function class.<br>
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@online{Kleer_2108.10037, TITLE = {Primal and Dual Combinatorial Dimensions}, AUTHOR = {Kleer, Pieter and Simon, Hans Ulrich}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2108.10037}, EPRINT = {2108.10037}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We give tight bounds on the relation between the primal and dual of various<br>combinatorial dimensions, such as the pseudo-dimension and fat-shattering<br>dimension, for multi-valued function classes. These dimensional notions play an<br>important role in the area of learning theory. We first review some (folklore)<br>results that bound the dual dimension of a function class in terms of its<br>primal, and after that give (almost) matching lower bounds. In particular, we<br>give an appropriate generalization to multi-valued function classes of a<br>well-known bound due to Assouad (1983), that relates the primal and dual<br>VC-dimension of a binary function class.<br>}, }
Endnote
%0 Report %A Kleer, Pieter %A Simon, Hans Ulrich %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Primal and Dual Combinatorial Dimensions : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B834-D %U https://arxiv.org/abs/2108.10037 %D 2021 %X We give tight bounds on the relation between the primal and dual of various<br>combinatorial dimensions, such as the pseudo-dimension and fat-shattering<br>dimension, for multi-valued function classes. These dimensional notions play an<br>important role in the area of learning theory. We first review some (folklore)<br>results that bound the dual dimension of a function class in terms of its<br>primal, and after that give (almost) matching lower bounds. In particular, we<br>give an appropriate generalization to multi-valued function classes of a<br>well-known bound due to Assouad (1983), that relates the primal and dual<br>VC-dimension of a binary function class.<br> %K Mathematics, Combinatorics, math.CO,Computer Science, Discrete Mathematics, cs.DM,Computer Science, Learning, cs.LG
[185]
P. Kleer, “Sampling from the Gibbs Distribution in Congestion Games,” in EC ’21, 22nd ACM Conference on Economics and Computation, Budapest, Hungary (Virtual), 2021.
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@inproceedings{Kleer_EC2021, TITLE = {Sampling from the {G}ibbs Distribution in Congestion Games}, AUTHOR = {Kleer, Pieter}, LANGUAGE = {eng}, ISBN = {978-1-4503-8554-1}, DOI = {10.1145/3465456.3467597}, PUBLISHER = {ACM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {EC '21, 22nd ACM Conference on Economics and Computation}, EDITOR = {Bir{\'o}, P{\'e}ter and Chawla, Shuchi and Echenique, Federico and Sodomka, Eric}, PAGES = {679--680}, ADDRESS = {Budapest, Hungary (Virtual)}, }
Endnote
%0 Conference Proceedings %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/21.11116/0000-0009-B3F8-5 %R 10.1145/3465456.3467597 %D 2021 %B 22nd ACM Conference on Economics and Computation %Z date of event: 2021-07-18 - 2021-07-23 %C Budapest, Hungary (Virtual) %B EC '21 %E Bir&#243;, P&#233;ter; Chawla, Shuchi; Echenique, Federico; Sodomka, Eric %P 679 - 680 %I ACM %@ 978-1-4503-8554-1
[186]
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<br>bias towards strategic deviations that give a higher improvement in cost. It is<br>used extensively in practice. In congestion (or potential) games, the dynamics<br>converges to the so-called Gibbs distribution over the set of all strategy<br>profiles, when interpreted as a Markov chain. In general, logit dynamics might<br>converge slowly to the Gibbs distribution, but beyond that, not much is known<br>about their algorithmic aspects, nor that of the Gibbs distribution. In this<br>work, we are interested in the following two questions for congestion games: i)<br>Is there an efficient algorithm for sampling from the Gibbs distribution? ii)<br>If yes, do there also exist natural randomized dynamics that converges quickly<br>to the Gibbs distribution?<br> We first study these questions in extension parallel congestion games, a<br>well-studied special case of symmetric network congestion games. As our main<br>result, we show that there is a simple variation on the logit dynamics (in<br>which we in addition are allowed to randomly interchange the strategies of two<br>players) that converges quickly to the Gibbs distribution in such games. This<br>answers both questions above affirmatively. We also address the first question<br>for the class of so-called capacitated $k$-uniform congestion games.<br> To prove our results, we rely on the recent breakthrough work of Anari, Liu,<br>Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base<br>of a matroid according to strongly log-concave probability distribution.<br>
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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<br>bias towards strategic deviations that give a higher improvement in cost. It is<br>used extensively in practice. In congestion (or potential) games, the dynamics<br>converges to the so-called Gibbs distribution over the set of all strategy<br>profiles, when interpreted as a Markov chain. In general, logit dynamics might<br>converge slowly to the Gibbs distribution, but beyond that, not much is known<br>about their algorithmic aspects, nor that of the Gibbs distribution. In this<br>work, we are interested in the following two questions for congestion games: i)<br>Is there an efficient algorithm for sampling from the Gibbs distribution? ii)<br>If yes, do there also exist natural randomized dynamics that converges quickly<br>to the Gibbs distribution?<br> We first study these questions in extension parallel congestion games, a<br>well-studied special case of symmetric network congestion games. As our main<br>result, we show that there is a simple variation on the logit dynamics (in<br>which we in addition are allowed to randomly interchange the strategies of two<br>players) that converges quickly to the Gibbs distribution in such games. This<br>answers both questions above affirmatively. We also address the first question<br>for the class of so-called capacitated $k$-uniform congestion games.<br> To prove our results, we rely on the recent breakthrough work of Anari, Liu,<br>Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base<br>of a matroid according to strongly log-concave probability distribution.<br>}, }
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<br>bias towards strategic deviations that give a higher improvement in cost. It is<br>used extensively in practice. In congestion (or potential) games, the dynamics<br>converges to the so-called Gibbs distribution over the set of all strategy<br>profiles, when interpreted as a Markov chain. In general, logit dynamics might<br>converge slowly to the Gibbs distribution, but beyond that, not much is known<br>about their algorithmic aspects, nor that of the Gibbs distribution. In this<br>work, we are interested in the following two questions for congestion games: i)<br>Is there an efficient algorithm for sampling from the Gibbs distribution? ii)<br>If yes, do there also exist natural randomized dynamics that converges quickly<br>to the Gibbs distribution?<br> We first study these questions in extension parallel congestion games, a<br>well-studied special case of symmetric network congestion games. As our main<br>result, we show that there is a simple variation on the logit dynamics (in<br>which we in addition are allowed to randomly interchange the strategies of two<br>players) that converges quickly to the Gibbs distribution in such games. This<br>answers both questions above affirmatively. We also address the first question<br>for the class of so-called capacitated $k$-uniform congestion games.<br> To prove our results, we rely on the recent breakthrough work of Anari, Liu,<br>Oveis-Gharan and Vinzant (2019) concerning the approximate sampling of the base<br>of a matroid according to strongly log-concave probability distribution.<br> %K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS
[187]
P. Kleer and G. Schäfer, “Computation and Efficiency of Potential Function Minimizers of Combinatorial Congestion Games,” Mathematical Programming, vol. 190, no. 1, 2021.
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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 = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, JOURNAL = {Mathematical Programming}, VOLUME = {190}, NUMBER = {1}, PAGES = {523--560}, }
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 2021 %J Mathematical Programming %V 190 %N 1 %& 523 %P 523 - 560 %I Springer %C New York, NY
[188]
M. Künnemann and A. Nusser, “Polygon Placement Revisited: (Degree of Freedom + 1)-SUM Hardness and an Improvement via Offline Dynamic Rectangle Union,” 2021. [Online]. Available: https://arxiv.org/abs/2111.02544. (arXiv: 2111.02544)
Abstract
We revisit the classical problem of determining the largest copy of a simple<br>polygon $P$ that can be placed into a simple polygon $Q$. Despite significant<br>effort, known algorithms require high polynomial running times. (Barequet and<br>Har-Peled, 2001) give a lower bound of $n^{2-o(1)}$ under the 3SUM conjecture<br>when $P$ and $Q$ are (convex) polygons with $\Theta(n)$ vertices each. This<br>leaves open whether we can establish (1) hardness beyond quadratic time and (2)<br>any superlinear bound for constant-sized $P$ or $Q$.<br> In this paper, we affirmatively answer these questions under the $k$SUM<br>conjecture, proving natural hardness results that increase with each degree of<br>freedom (scaling, $x$-translation, $y$-translation, rotation): (1) Finding the<br>largest copy of $P$ that can be $x$-translated into $Q$ requires time<br>$n^{2-o(1)}$ under the 3SUM conjecture. (2) Finding the largest copy of $P$<br>that can be arbitrarily translated into $Q$ requires time $n^{2-o(1)}$ under<br>the 4SUM conjecture. (3) The above lower bounds are almost tight when one of<br>the polygons is of constant size: we obtain an $\tilde O((pq)^{2.5})$-time<br>algorithm for orthogonal polygons $P,Q$ with $p$ and $q$ vertices,<br>respectively. (4) Finding the largest copy of $P$ that can be arbitrarily<br>rotated and translated into $Q$ requires time $n^{3-o(1)}$ under the 5SUM<br>conjecture.<br> We are not aware of any other such natural $($degree of freedom $+ 1)$-SUM<br>hardness for a geometric optimization problem.<br>
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@online{Kuennemann_2111.02544, TITLE = {Polygon Placement Revisited: (Degree of Freedom + 1)-{SUM} Hardness and an Improvement via Offline Dynamic Rectangle Union}, AUTHOR = {K{\"u}nnemann, Marvin and Nusser, Andr{\'e}}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2111.02544}, EPRINT = {2111.02544}, EPRINTTYPE = {arXiv}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We revisit the classical problem of determining the largest copy of a simple<br>polygon $P$ that can be placed into a simple polygon $Q$. Despite significant<br>effort, known algorithms require high polynomial running times. (Barequet and<br>Har-Peled, 2001) give a lower bound of $n^{2-o(1)}$ under the 3SUM conjecture<br>when $P$ and $Q$ are (convex) polygons with $\Theta(n)$ vertices each. This<br>leaves open whether we can establish (1) hardness beyond quadratic time and (2)<br>any superlinear bound for constant-sized $P$ or $Q$.<br> In this paper, we affirmatively answer these questions under the $k$SUM<br>conjecture, proving natural hardness results that increase with each degree of<br>freedom (scaling, $x$-translation, $y$-translation, rotation): (1) Finding the<br>largest copy of $P$ that can be $x$-translated into $Q$ requires time<br>$n^{2-o(1)}$ under the 3SUM conjecture. (2) Finding the largest copy of $P$<br>that can be arbitrarily translated into $Q$ requires time $n^{2-o(1)}$ under<br>the 4SUM conjecture. (3) The above lower bounds are almost tight when one of<br>the polygons is of constant size: we obtain an $\tilde O((pq)^{2.5})$-time<br>algorithm for orthogonal polygons $P,Q$ with $p$ and $q$ vertices,<br>respectively. (4) Finding the largest copy of $P$ that can be arbitrarily<br>rotated and translated into $Q$ requires time $n^{3-o(1)}$ under the 5SUM<br>conjecture.<br> We are not aware of any other such natural $($degree of freedom $+ 1)$-SUM<br>hardness for a geometric optimization problem.<br>}, }
Endnote
%0 Report %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Polygon Placement Revisited: (Degree of Freedom + 1)-SUM Hardness and an Improvement via Offline Dynamic Rectangle Union : %G eng %U http://hdl.handle.net/21.11116/0000-0009-B462-D %U https://arxiv.org/abs/2111.02544 %D 2021 %X We revisit the classical problem of determining the largest copy of a simple<br>polygon $P$ that can be placed into a simple polygon $Q$. Despite significant<br>effort, known algorithms require high polynomial running times. (Barequet and<br>Har-Peled, 2001) give a lower bound of $n^{2-o(1)}$ under the 3SUM conjecture<br>when $P$ and $Q$ are (convex) polygons with $\Theta(n)$ vertices each. This<br>leaves open whether we can establish (1) hardness beyond quadratic time and (2)<br>any superlinear bound for constant-sized $P$ or $Q$.<br> In this paper, we affirmatively answer these questions under the $k$SUM<br>conjecture, proving natural hardness results that increase with each degree of<br>freedom (scaling, $x$-translation, $y$-translation, rotation): (1) Finding the<br>largest copy of $P$ that can be $x$-translated into $Q$ requires time<br>$n^{2-o(1)}$ under the 3SUM conjecture. (2) Finding the largest copy of $P$<br>that can be arbitrarily translated into $Q$ requires time $n^{2-o(1)}$ under<br>the 4SUM conjecture. (3) The above lower bounds are almost tight when one of<br>the polygons is of constant size: we obtain an $\tilde O((pq)^{2.5})$-time<br>algorithm for orthogonal polygons $P,Q$ with $p$ and $q$ vertices,<br>respectively. (4) Finding the largest copy of $P$ that can be arbitrarily<br>rotated and translated into $Q$ requires time $n^{3-o(1)}$ under the 5SUM<br>conjecture.<br> We are not aware of any other such natural $($degree of freedom $+ 1)$-SUM<br>hardness for a geometric optimization problem.<br> %K Computer Science, Computational Geometry, cs.CG,Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS
[189]
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
[190]
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
[191]
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
[192]
J. Madathil, R. Sharma, and M. Zehavi, “A Sub-exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs,” Algorithmica, vol. 83, 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}, VOLUME = {83}, PAGES = {1861--1884}, }
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 %V 83 %& 1861 %P 1861 - 1884 %I Springer %C New York, NY %@ false
[193]
J. Nederlof and K. Węgrzycki, “Improving Schroeppel and Shamir’s Algorithm for Subset Sum via Orthogonal Vectors,” in STOC ’21, 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual, Italy, 2021.
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@inproceedings{Nederlof_STOC2021, TITLE = {Improving {S}chroeppel and {S}hamir's Algorithm for Subset Sum via Orthogonal Vectors}, AUTHOR = {Nederlof, Jesper and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, ISBN = {9781450380539}, DOI = {10.1145/3406325.3451024}, PUBLISHER = {ACM}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {STOC '21, 53rd Annual ACM SIGACT Symposium on Theory of Computing}, EDITOR = {Khuller, Samir and Vassilevska Williams, Virginia}, PAGES = {1670--1683}, ADDRESS = {Virtual, Italy}, }
Endnote
%0 Conference Proceedings %A Nederlof, Jesper %A W&#281;grzycki, Karol %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Improving Schroeppel and Shamir's Algorithm for Subset Sum via Orthogonal Vectors : %G eng %U http://hdl.handle.net/21.11116/0000-000A-CD68-B %R 10.1145/3406325.3451024 %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 1670 - 1683 %I ACM %@ 9781450380539
[194]
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
[195]
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}, URL = {urn:nbn:de:bsz:291--ds-342440}, 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 %F OTHER: hdl:20.500.11880/31479 %U urn:nbn:de:bsz:291--ds-342440 %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
[196]
A. Polak, L. Rohwedder, and K. Węgrzycki, “Knapsack and Subset Sum with Small Items,” in 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Glasgow, UK (Virtual Conference), 2021.
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@inproceedings{Polak_ICALP2021, TITLE = {Knapsack and Subset Sum with Small Items}, AUTHOR = {Polak, Adam and Rohwedder, Lars and W{\c e}grzycki, Karol}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-195-5}, URL = {urn:nbn:de:0030-drops-141752; https://drops.dagstuhl.de/opus/volltexte/2021/14175/}, DOI = {10.4230/LIPIcs.ICALP.2021.106}, 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--19}, EID = {106}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {198}, ADDRESS = {Glasgow, UK (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Polak, Adam %A Rohwedder, Lars %A W&#281;grzycki, Karol %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Knapsack and Subset Sum with Small Items : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1EEF-7 %R 10.4230/LIPIcs.ICALP.2021.106 %U urn:nbn:de:0030-drops-141752 %U https://drops.dagstuhl.de/opus/volltexte/2021/14175/ %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 - 19 %Z sequence number: 106 %I Schloss Dagstuhl %@ 978-3-95977-195-5 %B Leibniz International Proceedings in Informatics %N 198 %@ false
[197]
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
[198]
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<br>$n$ agents with additive valuations. Envy-freeness up to any good (EFX) is<br>arguably the most compelling fairness notion in this context. However, the<br>existence of EFX allocations has not been settled and is one of the most<br>important problems in fair division. Towards resolving this problem, many<br>impressive results show the existence of its relaxations, e.g., the existence<br>of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated<br>goods. The latter result was recently improved for three agents, in which the<br>two unallocated goods are allocated through an involved procedure. Reducing the<br>number of unallocated goods for arbitrary number of agents is a systematic way<br>to settle the big question. In this paper, we develop a new approach, and show<br>that for every $\varepsilon \in (0,1/2]$, there always exists a<br>$(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and<br>high Nash welfare.<br> For this, we reduce the EFX problem to a novel problem in extremal graph<br>theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d<br>\in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite<br>digraph $G =(\cup_{i \in [k]} V_i, E)$, in which<br> 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for<br>all $i \in [k]$,<br> 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming<br>edge from some vertex in $V_j$ and vice-versa, and<br> 3) there exists no cycle in $G$ that contains at most one vertex from each<br>part.<br> We show that any upper bound on $R(d)$ directly translates to a sublinear<br>bound on the number of unallocated goods. We establish a polynomial upper bound<br>on $R(d)$, yielding our main result. Furthermore, our approach is constructive,<br>which also gives a polynomial-time algorithm for finding such an allocation.<br>
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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<br>$n$ agents with additive valuations. Envy-freeness up to any good (EFX) is<br>arguably the most compelling fairness notion in this context. However, the<br>existence of EFX allocations has not been settled and is one of the most<br>important problems in fair division. Towards resolving this problem, many<br>impressive results show the existence of its relaxations, e.g., the existence<br>of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated<br>goods. The latter result was recently improved for three agents, in which the<br>two unallocated goods are allocated through an involved procedure. Reducing the<br>number of unallocated goods for arbitrary number of agents is a systematic way<br>to settle the big question. In this paper, we develop a new approach, and show<br>that for every $\varepsilon \in (0,1/2]$, there always exists a<br>$(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and<br>high Nash welfare.<br> For this, we reduce the EFX problem to a novel problem in extremal graph<br>theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d<br>\in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite<br>digraph $G =(\cup_{i \in [k]} V_i, E)$, in which<br> 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for<br>all $i \in [k]$,<br> 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming<br>edge from some vertex in $V_j$ and vice-versa, and<br> 3) there exists no cycle in $G$ that contains at most one vertex from each<br>part.<br> We show that any upper bound on $R(d)$ directly translates to a sublinear<br>bound on the number of unallocated goods. We establish a polynomial upper bound<br>on $R(d)$, yielding our main result. Furthermore, our approach is constructive,<br>which also gives a polynomial-time algorithm for finding such an allocation.<br>}, }
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<br>$n$ agents with additive valuations. Envy-freeness up to any good (EFX) is<br>arguably the most compelling fairness notion in this context. However, the<br>existence of EFX allocations has not been settled and is one of the most<br>important problems in fair division. Towards resolving this problem, many<br>impressive results show the existence of its relaxations, e.g., the existence<br>of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated<br>goods. The latter result was recently improved for three agents, in which the<br>two unallocated goods are allocated through an involved procedure. Reducing the<br>number of unallocated goods for arbitrary number of agents is a systematic way<br>to settle the big question. In this paper, we develop a new approach, and show<br>that for every $\varepsilon \in (0,1/2]$, there always exists a<br>$(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and<br>high Nash welfare.<br> For this, we reduce the EFX problem to a novel problem in extremal graph<br>theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d<br>\in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite<br>digraph $G =(\cup_{i \in [k]} V_i, E)$, in which<br> 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for<br>all $i \in [k]$,<br> 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming<br>edge from some vertex in $V_j$ and vice-versa, and<br> 3) there exists no cycle in $G$ that contains at most one vertex from each<br>part.<br> We show that any upper bound on $R(d)$ directly translates to a sublinear<br>bound on the number of unallocated goods. We establish a polynomial upper bound<br>on $R(d)$, yielding our main result. Furthermore, our approach is constructive,<br>which also gives a polynomial-time algorithm for finding such an allocation.<br> %K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Data Structures and Algorithms, cs.DS
[199]
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
[200]
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
[201]
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,” in 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Glasgow, UK (Virtual Conference), 2021.
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@inproceedings{Roth_ICALP2021, TITLE = {Detecting and Counting Small Subgraphs, and Evaluating a Parameterized {Tutte} Polynomial: {L}ower Bounds via {Toroidal} Grids and {Cayley} Graph Expanders}, AUTHOR = {Roth, Marc and Schmitt, Johannes and Wellnitz, Philip}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-195-5}, URL = {urn:nbn:de:0030-drops-141778}, DOI = {10.4230/LIPIcs.ICALP.2021.108}, 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 = {108}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {198}, ADDRESS = {Glasgow, UK (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 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/21.11116/0000-0009-AFBF-C %R 10.4230/LIPIcs.ICALP.2021.108 %U urn:nbn:de:0030-drops-141778 %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: 108 %I Schloss Dagstuhl %@ 978-3-95977-195-5 %B Leibniz International Proceedings in Informatics %N 198 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2021/14177/
[202]
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
[203]
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
[204]
P. Wellnitz, “Counting Patterns in Strings and Graphs,” Universität des Saarlandes, Saarbrücken, 2021.
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@phdthesis{WellnitzPhD21, TITLE = {Counting Patterns in Strings and Graphs}, AUTHOR = {Wellnitz, Philip}, LANGUAGE = {eng}, URL = {urn:nbn:de:bsz:291--ds-350981}, DOI = {10.22028/D291-35098}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, DATE = {2021}, }
Endnote
%0 Thesis %A Wellnitz, Philip %Y Mehlhorn, Kurt %A referee: Landau, Gad M. %A referee: Grohe, Martin %A referee: Bringmann, Karl %+ 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 External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Patterns in Strings and Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-000C-1ED8-0 %R 10.22028/D291-35098 %U urn:nbn:de:bsz:291--ds-350981 %F OTHER: hdl:20.500.11880/32103 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2021 %P 253 p. %V phd %9 phd %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/32103
[205]
A. Zandieh, I. Han, H. Avron, N. Shoham, C. Kim, and J. Shin, “Scaling Neural Tangent Kernels via Sketching and Random Features,” in Advances in Neural Information Processing Systems 34 (NeurIPS 2021), Virtual, 2021.
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@inproceedings{zandieh_NeurIPS21, TITLE = {Scaling Neural Tangent Kernels via Sketching and Random Features}, AUTHOR = {Zandieh, Amir and Han, Insu and Avron, Haim and Shoham, Neta and Kim, Chaewon and Shin, Jinwoo}, LANGUAGE = {eng}, PUBLISHER = {Curran Assoicates, Inc.}, YEAR = {2021}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {Advances in Neural Information Processing Systems 34 (NeurIPS 2021)}, EDITOR = {Ranzato, M. and Beygelzimer, A. and Dauphin, Y. and Liang, P. S. and Wortman Vaughan, J.}, PAGES = {1062--1073}, ADDRESS = {Virtual}, }
Endnote
%0 Conference Proceedings %A Zandieh, Amir %A Han, Insu %A Avron, Haim %A Shoham, Neta %A Kim, Chaewon %A Shin, Jinwoo %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Scaling Neural Tangent Kernels via Sketching and Random Features : %G eng %U http://hdl.handle.net/21.11116/0000-000C-90E3-0 %D 2021 %B 35th Conference on Neural Information Processing Systems %Z date of event: 2021-12-06 - 2021-12-14 %C Virtual %B Advances in Neural Information Processing Systems 34 %E Ranzato, M.; Beygelzimer, A.; Dauphin, Y.; Liang, P. S.; Wortman Vaughan, J. %P 1062 - 1073 %I Curran Assoicates, Inc.
2020
[206]
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}, ISBN = {9781713829546}, PUBLISHER = {Curran Associates, Inc.}, YEAR = {2020}, 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.}, PAGES = {8810--8823}, 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. %P 8810 - 8823 %I Curran Associates, Inc. %@ 9781713829546 %U https://proceedings.neurips.cc/paper/2020/hash/645e6bfdd05d1a69c5e47b20f0a91d46-Abstract.html
[207]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “Scheduling Lower Bounds via AND Subset Sum,” in 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Saarbrücken, Germany (Virtual Conference), 2020.
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@inproceedings{Abboud_ICALP2020, TITLE = {Scheduling Lower Bounds via {AND} Subset Sum}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-138-2}, URL = {urn:nbn:de:0030-drops-124119}, DOI = {10.4230/LIPIcs.ICALP.2020.4}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2020}, BOOKTITLE = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, EDITOR = {Czumaj, Artur and Dawa, Anuj and Merelli, Emanuela}, EID = {4}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {168}, ADDRESS = {Saarbr{\"u}cken, Germany (Virtual Conference)}, }
Endnote
%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Scheduling Lower Bounds via AND Subset Sum : %G eng %U http://hdl.handle.net/21.11116/0000-0007-2826-2 %R 10.4230/LIPIcs.ICALP.2020.4 %U urn:nbn:de:0030-drops-124119 %D 2020 %B 47th International Colloquium on Automata, Languages, and Programming %Z date of event: 2020-07-08 - 2020-07-11 %C Saarbr&#252;cken, Germany (Virtual Conference) %B 47th International Colloquium on Automata, Languages, and Programming %E Czumaj, Artur; Dawa, Anuj; Merelli, Emanuela %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-138-2 %B Leibniz International Proceedings in Informatics %N 168 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/12411/https://creativecommons.org/licenses/by/3.0/legalcode
[208]
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}, 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
[209]
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<br>Subset Sum problem asks to determine whether all of these instances are<br>yes-instances; that is, whether each set of integers $X_i$ has a subset that<br>sums up to the target integer $t_i$. We prove that this problem cannot be<br>solved in time $\tilde{O}((N \cdot t_{max})^{1-\epsilon})$, for $t_{max}=\max_i<br>t_i$ and any $\epsilon > 0$, assuming the $\forall \exists$ Strong Exponential<br>Time Hypothesis ($\forall \exists$-SETH). We then use this result to exclude<br>$\tilde{O}(n+P_{max} \cdot n^{1-\epsilon})$-time algorithms for several<br>scheduling problems on $n$ jobs with maximum processing time $P_{max}$, based<br>on $\forall \exists$-SETH. These include classical problems such as $1||\sum<br>w_jU_j$, the problem of minimizing the total weight of tardy jobs on a single<br>machine, and $P_2||\sum U_j$, the problem of minimizing the number of tardy<br>jobs on two identical parallel machines.<br>
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@online{Abboud_arXIv2003.07113, TITLE = {Scheduling Lower Bounds via {AND} Subset Sum}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, URL = {https://arxiv.org/abs/2003.07113}, EPRINT = {2003.07113}, EPRINTTYPE = {arXiv}, YEAR = {2020}, ABSTRACT = {Given $N$ instances $(X_1,t_1),\ldots,(X_N,t_N)$ of Subset Sum, the AND<br>Subset Sum problem asks to determine whether all of these instances are<br>yes-instances; that is, whether each set of integers $X_i$ has a subset that<br>sums up to the target integer $t_i$. We prove that this problem cannot be<br>solved in time $\tilde{O}((N \cdot t_{max})^{1-\epsilon})$, for $t_{max}=\max_i<br>t_i$ and any $\epsilon > 0$, assuming the $\forall \exists$ Strong Exponential<br>Time Hypothesis ($\forall \exists$-SETH). We then use this result to exclude<br>$\tilde{O}(n+P_{max} \cdot n^{1-\epsilon})$-time algorithms for several<br>scheduling problems on $n$ jobs with maximum processing time $P_{max}$, based<br>on $\forall \exists$-SETH. These include classical problems such as $1||\sum<br>w_jU_j$, the problem of minimizing the total weight of tardy jobs on a single<br>machine, and $P_2||\sum U_j$, the problem of minimizing the number of tardy<br>jobs on two identical parallel machines.<br>}, }
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<br>Subset Sum problem asks to determine whether all of these instances are<br>yes-instances; that is, whether each set of integers $X_i$ has a subset that<br>sums up to the target integer $t_i$. We prove that this problem cannot be<br>solved in time $\tilde{O}((N \cdot t_{max})^{1-\epsilon})$, for $t_{max}=\max_i<br>t_i$ and any $\epsilon > 0$, assuming the $\forall \exists$ Strong Exponential<br>Time Hypothesis ($\forall \exists$-SETH). We then use this result to exclude<br>$\tilde{O}(n+P_{max} \cdot n^{1-\epsilon})$-time algorithms for several<br>scheduling problems on $n$ jobs with maximum processing time $P_{max}$, based<br>on $\forall \exists$-SETH. These include classical problems such as $1||\sum<br>w_jU_j$, the problem of minimizing the total weight of tardy jobs on a single<br>machine, and $P_2||\sum U_j$, the problem of minimizing the number of tardy<br>jobs on two identical parallel machines.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[210]
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}, 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
[211]
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}, 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
[212]
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}, 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
[213]
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}, 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
[214]
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<br>the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width<br>$\delta$. We obtain two main results. First, for the case where the points have<br>distinct integer $x$-coordinates, we prove that a shortest bitonic tour (which<br>can be computed in $O(n\log^2 n)$ time using an existing algorithm) is<br>guaranteed to be a shortest tour overall when $\delta\leq 2\sqrt{2}$, a bound<br>which is best possible. Second, we present an algorithm that is fixed-parameter<br>tractable with respect to $\delta$. More precisely, our algorithm has running<br>time $2^{O(\sqrt{\delta})} n^2$ for sparse point sets, where each<br>$1\times\delta$ rectangle inside the strip contains $O(1)$ points. For random<br>point sets, where the points are chosen uniformly at random from the<br>rectangle~$[0,n]\times [0,\delta]$, it has an expected running time of<br>$2^{O(\sqrt{\delta})} n^2 + O(n^3)$.<br>
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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}, ABSTRACT = {We investigate how the complexity of Euclidean TSP for point sets $P$ inside<br>the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width<br>$\delta$. We obtain two main results. First, for the case where the points have<br>distinct integer $x$-coordinates, we prove that a shortest bitonic tour (which<br>can be computed in $O(n\log^2 n)$ time using an existing algorithm) is<br>guaranteed to be a shortest tour overall when $\delta\leq 2\sqrt{2}$, a bound<br>which is best possible. Second, we present an algorithm that is fixed-parameter<br>tractable with respect to $\delta$. More precisely, our algorithm has running<br>time $2^{O(\sqrt{\delta})} n^2$ for sparse point sets, where each<br>$1\times\delta$ rectangle inside the strip contains $O(1)$ points. For random<br>point sets, where the points are chosen uniformly at random from the<br>rectangle~$[0,n]\times [0,\delta]$, it has an expected running time of<br>$2^{O(\sqrt{\delta})} n^2 + O(n^3)$.<br>}, }
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<br>the strip $(-\infty,+\infty)\times [0,\delta]$ depends on the strip width<br>$\delta$. We obtain two main results. First, for the case where the points have<br>distinct integer $x$-coordinates, we prove that a shortest bitonic tour (which<br>can be computed in $O(n\log^2 n)$ time using an existing algorithm) is<br>guaranteed to be a shortest tour overall when $\delta\leq 2\sqrt{2}$, a bound<br>which is best possible. Second, we present an algorithm that is fixed-parameter<br>tractable with respect to $\delta$. More precisely, our algorithm has running<br>time $2^{O(\sqrt{\delta})} n^2$ for sparse point sets, where each<br>$1\times\delta$ rectangle inside the strip contains $O(1)$ points. For random<br>point sets, where the points are chosen uniformly at random from the<br>rectangle~$[0,n]\times [0,\delta]$, it has an expected running time of<br>$2^{O(\sqrt{\delta})} n^2 + O(n^3)$.<br> %K Computer Science, Computational Geometry, cs.CG
[215]
G. Amanatidis and P. Kleer, “Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences,” Random Structures and Algorithms, vol. 57, no. 3, 2020.
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@article{Amanatidis2020, TITLE = {Rapid mixing of the switch {M}arkov chain for strongly stable degree sequences}, AUTHOR = {Amanatidis, Georgios and Kleer, Pieter}, LANGUAGE = {eng}, ISSN = {1042-9832}, DOI = {10.1002/rsa.20949}, PUBLISHER = {Wiley}, ADDRESS = {New York, N.Y.}, YEAR = {2020}, DATE = {2020}, JOURNAL = {Random Structures and Algorithms}, VOLUME = {57}, NUMBER = {3}, PAGES = {637--657}, }
Endnote
%0 Journal Article %A Amanatidis, Georgios %A Kleer, Pieter %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Rapid Mixing of the Switch Markov Chain for Strongly Stable Degree Sequences : %G eng %U http://hdl.handle.net/21.11116/0000-0006-DC7A-A %R 10.1002/rsa.20949 %7 2020 %D 2020 %J Random Structures and Algorithms %V 57 %N 3 %& 637 %P 637 - 657 %I Wiley %C New York, N.Y. %@ false
[216]
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}, 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
[217]
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-$r$<br>dominating set problem, are among the well-studied problems in the sequential<br>settings. In distributed models of computation, unlike for domination, not much<br>is known about distance-r domination. This is actually the case for other<br>important closely-related covering problem, namely, the distance-$r$<br>independent set problem. By result of Kuhn et al. we know the distributed<br>domination problem is hard on high girth graphs; we study the problem on a<br>slightly restricted subclass of these graphs: graphs of bounded expansion with<br>high girth, i.e. their girth should be at least $4r + 3$. We show that in such<br>graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a<br>constant-factor approximation of the minimum distance-$r$ dominating set<br>problem, in a constant number of rounds. More precisely, our constants are<br>dependent to $r$, not to the size of the graph. This is the first algorithm<br>that shows there are non-trivial constant factor approximations in constant<br>number of rounds for any distance $r$-covering problem in distributed settings.<br>To show the dependency on r is inevitable, we provide an unconditional lower<br>bound showing the same problem is hard already on rings. We also show that our<br>analysis of the algorithm is relatively tight, that is any significant<br>improvement to the approximation factor requires new algorithmic ideas.<br>
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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}, ABSTRACT = {The dominating set problem and its generalization, the distance-$r$<br>dominating set problem, are among the well-studied problems in the sequential<br>settings. In distributed models of computation, unlike for domination, not much<br>is known about distance-r domination. This is actually the case for other<br>important closely-related covering problem, namely, the distance-$r$<br>independent set problem. By result of Kuhn et al. we know the distributed<br>domination problem is hard on high girth graphs; we study the problem on a<br>slightly restricted subclass of these graphs: graphs of bounded expansion with<br>high girth, i.e. their girth should be at least $4r + 3$. We show that in such<br>graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a<br>constant-factor approximation of the minimum distance-$r$ dominating set<br>problem, in a constant number of rounds. More precisely, our constants are<br>dependent to $r$, not to the size of the graph. This is the first algorithm<br>that shows there are non-trivial constant factor approximations in constant<br>number of rounds for any distance $r$-covering problem in distributed settings.<br>To show the dependency on r is inevitable, we provide an unconditional lower<br>bound showing the same problem is hard already on rings. We also show that our<br>analysis of the algorithm is relatively tight, that is any significant<br>improvement to the approximation factor requires new algorithmic ideas.<br>}, }
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-$r$<br>dominating set problem, are among the well-studied problems in the sequential<br>settings. In distributed models of computation, unlike for domination, not much<br>is known about distance-r domination. This is actually the case for other<br>important closely-related covering problem, namely, the distance-$r$<br>independent set problem. By result of Kuhn et al. we know the distributed<br>domination problem is hard on high girth graphs; we study the problem on a<br>slightly restricted subclass of these graphs: graphs of bounded expansion with<br>high girth, i.e. their girth should be at least $4r + 3$. We show that in such<br>graphs, for every constant $r$, a simple greedy CONGEST algorithm provides a<br>constant-factor approximation of the minimum distance-$r$ dominating set<br>problem, in a constant number of rounds. More precisely, our constants are<br>dependent to $r$, not to the size of the graph. This is the first algorithm<br>that shows there are non-trivial constant factor approximations in constant<br>number of rounds for any distance $r$-covering problem in distributed settings.<br>To show the dependency on r is inevitable, we provide an unconditional lower<br>bound showing the same problem is hard already on rings. We also show that our<br>analysis of the algorithm is relatively tight, that is any significant<br>improvement to the approximation factor requires new algorithmic ideas.<br> %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Discrete Mathematics, cs.DM,Mathematics, Combinatorics, math.CO
[218]
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}, 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
[219]
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'<br>statistical query framework against challenging label-noise models. First, we<br>build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that<br>showed noise tolerance of distribution-independently evolvable concept classes<br>under Massart noise. Specifically, we extend their characterization to more<br>general noise models, including the Tsybakov model which considerably<br>generalizes the Massart condition by allowing the flipping probability to be<br>arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary,<br>we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to<br>obtain the first polynomial time algorithm with arbitrarily small excess error<br>for learning linear threshold functions over any spherically symmetric<br>distribution in the presence of spherically symmetric Tsybakov noise. Moreover,<br>we posit access to a stronger oracle, in which for every labeled example we<br>additionally obtain its flipping probability. In this model, we show that every<br>SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$<br>misclassification error for a broad class of noise models. This setting<br>substantially generalizes the widely-studied problem of classification under<br>RCN with known noise rate, and corresponds to a non-convex optimization problem<br>even when the noise function -- i.e. the flipping probabilities of all points<br>-- is known in advance.<br>
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BibTeX
@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}, ABSTRACT = {This work provides several new insights on the robustness of Kearns'<br>statistical query framework against challenging label-noise models. First, we<br>build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that<br>showed noise tolerance of distribution-independently evolvable concept classes<br>under Massart noise. Specifically, we extend their characterization to more<br>general noise models, including the Tsybakov model which considerably<br>generalizes the Massart condition by allowing the flipping probability to be<br>arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary,<br>we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to<br>obtain the first polynomial time algorithm with arbitrarily small excess error<br>for learning linear threshold functions over any spherically symmetric<br>distribution in the presence of spherically symmetric Tsybakov noise. Moreover,<br>we posit access to a stronger oracle, in which for every labeled example we<br>additionally obtain its flipping probability. In this model, we show that every<br>SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$<br>misclassification error for a broad class of noise models. This setting<br>substantially generalizes the widely-studied problem of classification under<br>RCN with known noise rate, and corresponds to a non-convex optimization problem<br>even when the noise function -- i.e. the flipping probabilities of all points<br>-- is known in advance.<br>}, }
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'<br>statistical query framework against challenging label-noise models. First, we<br>build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that<br>showed noise tolerance of distribution-independently evolvable concept classes<br>under Massart noise. Specifically, we extend their characterization to more<br>general noise models, including the Tsybakov model which considerably<br>generalizes the Massart condition by allowing the flipping probability to be<br>arbitrarily close to $\frac{1}{2}$ for a subset of the domain. As a corollary,<br>we employ an evolutionary algorithm by \cite{DBLP:conf/colt/KanadeVV10} to<br>obtain the first polynomial time algorithm with arbitrarily small excess error<br>for learning linear threshold functions over any spherically symmetric<br>distribution in the presence of spherically symmetric Tsybakov noise. Moreover,<br>we posit access to a stronger oracle, in which for every labeled example we<br>additionally obtain its flipping probability. In this model, we show that every<br>SQ learnable class admits an efficient learning algorithm with OPT + $\epsilon$<br>misclassification error for a broad class of noise models. This setting<br>substantially generalizes the widely-studied problem of classification under<br>RCN with known noise rate, and corresponds to a non-convex optimization problem<br>even when the noise function -- i.e. the flipping probabilities of all points<br>-- is known in advance.<br> %K Statistics, Machine Learning, stat.ML,Computer Science, Learning, cs.LG
[220]
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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BibTeX
@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}, ISBN = {9781713829546}, PUBLISHER = {Curran Associates, Inc.}, YEAR = {2020}, 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.}, PAGES = {7933--7944}, 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. %P 7933 - 7944 %I Curran Associates, Inc. %@ 9781713829546
[221]
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<br>instead of a set of points, we are given a set of lines as input, and the goal<br>is to find the shortest tour that visits each line. The best known upper and<br>lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are<br>$\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is<br>based on a reduction to the group Steiner tree problem.<br> We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge 3$.<br>More generally, this implies that TSP with $k$-dimensional flats does not admit<br>a PTAS for any $1\le k \leq d-2$ unless $\mathrm{P}=\mathrm{NP}$, which gives a<br>complete classification of the approximability of these problems, as there are<br>known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to<br>give a stronger inapproximability factor for $d=O(\log n)$ by showing that TSP<br>with lines does not admit a $(2-\epsilon)$-approximation in $d$ dimensions<br>under the unique games conjecture. On the positive side, we leverage recent<br>results on restricted variants of the group Steiner tree problem in order to<br>give an $O(\log^2 n)$-approximation algorithm for the problem, albeit with a<br>running time of $n^{O(\log\log n)}$.<br>
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BibTeX
@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}, ABSTRACT = {We study the variant of the Euclidean Traveling Salesman problem where<br>instead of a set of points, we are given a set of lines as input, and the goal<br>is to find the shortest tour that visits each line. The best known upper and<br>lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are<br>$\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is<br>based on a reduction to the group Steiner tree problem.<br> We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge 3$.<br>More generally, this implies that TSP with $k$-dimensional flats does not admit<br>a PTAS for any $1\le k \leq d-2$ unless $\mathrm{P}=\mathrm{NP}$, which gives a<br>complete classification of the approximability of these problems, as there are<br>known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to<br>give a stronger inapproximability factor for $d=O(\log n)$ by showing that TSP<br>with lines does not admit a $(2-\epsilon)$-approximation in $d$ dimensions<br>under the unique games conjecture. On the positive side, we leverage recent<br>results on restricted variants of the group Steiner tree problem in order to<br>give an $O(\log^2 n)$-approximation algorithm for the problem, albeit with a<br>running time of $n^{O(\log\log n)}$.<br>}, }
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<br>instead of a set of points, we are given a set of lines as input, and the goal<br>is to find the shortest tour that visits each line. The best known upper and<br>lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are<br>$\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is<br>based on a reduction to the group Steiner tree problem.<br> We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge 3$.<br>More generally, this implies that TSP with $k$-dimensional flats does not admit<br>a PTAS for any $1\le k \leq d-2$ unless $\mathrm{P}=\mathrm{NP}$, which gives a<br>complete classification of the approximability of these problems, as there are<br>known PTASes for $k=0$ (i.e., points) and $k=d-1$ (hyperplanes). We are able to<br>give a stronger inapproximability factor for $d=O(\log n)$ by showing that TSP<br>with lines does not admit a $(2-\epsilon)$-approximation in $d$ dimensions<br>under the unique games conjecture. On the positive side, we leverage recent<br>results on restricted variants of the group Steiner tree problem in order to<br>give an $O(\log^2 n)$-approximation algorithm for the problem, albeit with a<br>running time of $n^{O(\log\log n)}$.<br> %K Computer Science, Data Structures and Algorithms, cs.DS
[222]
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}, 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
[223]
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.