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Distributed weighted min-cut in nearly-optimal time.(English)Zbl 07765238

Khuller, Samir (ed.) et al., Proceedings of the 53rd annual ACM SIGACT symposium on theory of computing, STOC ’21, virtual, Italy, June 21–25, 2021. New York, NY: Association for Computing Machinery (ACM). 1144-1153 (2021).

MSC:

68Qxx Theory of computing

Cite

References:

[1]Mohamad Ahmadi, Fabian Kuhn, and Rotem Oshman. Distributed approximate maximum matching in the congest model. In 32nd International Symposium on Distributed Computing (DISC 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. ·Zbl 1497.68558
[2]Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. In DISC, volume 91, pages 7:1-7:16, 2017. ·Zbl 1515.68357
[3]Michal Dory, Yuval Efron, Sagnik Mukhopadhyay, and Danupon Nanongkai. Distributed weighted min-cut in nearly-optimal time. CoRR, abs/2004.09129, 2020.
[4]Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. In STOC, pages 363-372, 2011. ·Zbl 1288.68110
[5]Mohit Daga, Monika Henzinger, Danupon Nanongkai, and Thatchaphol Saranurak. Distributed edge connectivity in sublinear time. In STOC, pages 343-354. ACM, 2019. ·Zbl 1433.68598
[6]Michal Dory. Distributed approximation of minimum k-edge-connected spanning subgraphs. In PODC, pages 149-158. ACM, 2018. ·Zbl 1428.68370
[7]Peter Elias, Amiel Feinstein, and Claude E. Shannon. A note on the maximum flow through a network. IRE Trans. Information Theory, 2(4):117-119, 1956.
[8]Michael Elkin, Hartmut Klauck, Danupon Nanongkai, and Gopal Pandurangan. Can quantum communication speed up distributed computation? In PODC, pages 166-175. ACM, 2014. ·Zbl 1321.68072
[9]Michael Elkin. An unconditional lower bound on the time-approximation trade-off for the distributed minimum spanning tree problem. SIAM J. Comput., 36(2):433-456, 2006. ·Zbl 1116.05077
[10]L. R. Ford and D. R. Fulkerson. Maximal Flow Through a Network, pages 243-248. Birkhäuser Boston, Boston, MA, 1987.
[11]Barbara Geissmann and Lukas Gianinazzi. Parallel minimum cuts in near-linear work and low depth. In SPAA, pages 1-11, 2018.
[12]Mohsen Ghaffari and Bernhard Haeupler. Distributed algorithms for planar networks II: low-congestion shortcuts, mst, and min-cut. In SODA, pages 202-219. SIAM, 2016. ·Zbl 1410.68383
[13]Mohsen Ghaffari and Fabian Kuhn. Distributed minimum cut approximation. In Proceedings of the 27th DISC, pages 1-15, 2013. ·Zbl 1435.68379
[14]Mohsen Ghaffari, Andreas Karrenbauer, Fabian Kuhn, Christoph Lenzen, and Boaz Patt-Shamir. Near-optimal distributed maximum flow: Extended abstract. In PODC, pages 81-90, 2015. ·Zbl 1333.68273
[15]Pawel Gawrychowski, Shay Mozes, and Oren Weimann. Minimum cut in o(m \(log^2\) n) time. In ICALP 2020, pages 57:1-57:15, 2020.
[16]Mohsen Ghaffari and Krzysztof Nowicki. Congested clique algorithms for the minimum cut problem. In PODC, pages 357-366. ACM, 2018. ·Zbl 1428.68380
[17]Mohsen Ghaffari, Krzysztof Nowicki, and Mikkel Thorup. Faster algorithms for edge connectivity via random 2-out contractions. In SODA, pages 1260-1279. SIAM, 2020. ·Zbl 07304100
[18]Mohsen Ghaffari and Merav Parter. Near-optimal distributed algorithms for fault-tolerant tree structures. In SPAA, pages 387-396, 2016.
[19]Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In STOC, pages 489-498, 2016. ·Zbl 1375.68218
[20]David R. Karger. Minimum cuts in near-linear time. J. ACM, 47(1):46-76, 2000. ·Zbl 1094.68613
[21]Liah Kor, Amos Korman, and David Peleg. Tight bounds for distributed minimum-weight spanning tree verification. Theory Comput. Syst., 53(2):318-340, 2013. ·Zbl 1286.68317
[22]Sagnik Mukhopadhyay and Danupon Nanongkai. Weighted min-cut: Sequential, cut-query and streaming algorithms. In STOC, 2020. ·Zbl 07298265
[23]Danupon Nanongkai. Distributed approximation algorithms for weighted shortest paths. In Symposium on Theory of Computing (STOC), pages 565-573, 2014. ·Zbl 1315.05136
[24]Danupon Nanongkai and Hsin-Hao Su. Almost-tight distributed minimum cut algorithms. In DISC, pages 439-453, 2014. ·Zbl 1435.68381
[25]Merav Parter. Small cuts and connectivity certificates: A fault tolerant approach. 2019.
[26]David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed minimum-weight spanning tree construction. SIAM J. Comput., 30(5):1427-1442, 2000. ·Zbl 0973.05074
[27]David Pritchard and Ramakrishna Thurimella. Fast computation of small cuts via cycle space sampling. ACM Trans. Algorithms, 7(4):46:1-46:30, 2011. ·Zbl 1295.68205
[28]Mikkel Thorup. Fully-dynamic min-cut. Combinatorica, 27(1):91-127, 2007. Announced at STOC’01. ·Zbl 1135.68024
[29]Mohamad Ahmadi, Fabian Kuhn, and Rotem Oshman. Distributed approximate maximum matching in the congest model. In 32nd International Symposium on Distributed Computing (DISC 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. ·Zbl 1497.68558
[30]Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. In DISC, volume 91, pages 7:1-7:16, 2017. ·Zbl 1515.68357
[31]Michal Dory, Yuval Efron, Sagnik Mukhopadhyay, and Danupon Nanongkai. Distributed weighted min-cut in nearly-optimal time. CoRR, abs/2004.09129, 2020.
[32]Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. In STOC, pages 363-372, 2011. ·Zbl 1288.68110
[33]Mohit Daga, Monika Henzinger, Danupon Nanongkai, and Thatchaphol Saranurak. Distributed edge connectivity in sublinear time. In STOC, pages 343-354. ACM, 2019. ·Zbl 1433.68598
[34]Michal Dory. Distributed approximation of minimum k-edge-connected spanning subgraphs. In PODC, pages 149-158. ACM, 2018. ·Zbl 1428.68370
[35]Peter Elias, Amiel Feinstein, and Claude E. Shannon. A note on the maximum flow through a network. IRE Trans. Information Theory, 2(4):117-119, 1956.
[36]Michael Elkin, Hartmut Klauck, Danupon Nanongkai, and Gopal Pandurangan. Can quantum communication speed up distributed computation? In PODC, pages 166-175. ACM, 2014. ·Zbl 1321.68072
[37]Michael Elkin. An unconditional lower bound on the time-approximation trade-off for the distributed minimum spanning tree problem. SIAM J. Comput., 36(2):433-456, 2006. ·Zbl 1116.05077
[38]L. R. Ford and D. R. Fulkerson. Maximal Flow Through a Network, pages 243-248. Birkhäuser Boston, Boston, MA, 1987.
[39]Barbara Geissmann and Lukas Gianinazzi. Parallel minimum cuts in near-linear work and low depth. In SPAA, pages 1-11, 2018.
[40]Mohsen Ghaffari and Bernhard Haeupler. Distributed algorithms for planar networks II: low-congestion shortcuts, mst, and min-cut. In SODA, pages 202-219. SIAM, 2016. ·Zbl 1410.68383
[41]Mohsen Ghaffari and Fabian Kuhn. Distributed minimum cut approximation. In Proceedings of the 27th DISC, pages 1-15, 2013. ·Zbl 1435.68379
[42]Mohsen Ghaffari, Andreas Karrenbauer, Fabian Kuhn, Christoph Lenzen, and Boaz Patt-Shamir. Near-optimal distributed maximum flow: Extended abstract. In PODC, pages 81-90, 2015. ·Zbl 1333.68273
[43]Pawel Gawrychowski, Shay Mozes, and Oren Weimann. Minimum cut in o(m \(log^2\) n) time. In ICALP 2020, pages 57:1-57:15, 2020.
[44]Mohsen Ghaffari and Krzysztof Nowicki. Congested clique algorithms for the minimum cut problem. In PODC, pages 357-366. ACM, 2018. ·Zbl 1428.68380
[45]Mohsen Ghaffari, Krzysztof Nowicki, and Mikkel Thorup. Faster algorithms for edge connectivity via random 2-out contractions. In SODA, pages 1260-1279. SIAM, 2020. ·Zbl 07304100
[46]Mohsen Ghaffari and Merav Parter. Near-optimal distributed algorithms for fault-tolerant tree structures. In SPAA, pages 387-396, 2016.
[47]Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In STOC, pages 489-498, 2016. ·Zbl 1375.68218
[48]David R. Karger. Minimum cuts in near-linear time. J. ACM, 47(1):46-76, 2000. ·Zbl 1094.68613
[49]Liah Kor, Amos Korman, and David Peleg. Tight bounds for distributed minimum-weight spanning tree verification. Theory Comput. Syst., 53(2):318-340, 2013. ·Zbl 1286.68317
[50]Sagnik Mukhopadhyay and Danupon Nanongkai. Weighted min-cut: Sequential, cut-query and streaming algorithms. In STOC, 2020. ·Zbl 07298265
[51]Danupon Nanongkai. Distributed approximation algorithms for weighted shortest paths. In Symposium on Theory of Computing (STOC), pages 565-573, 2014. ·Zbl 1315.05136
[52]Danupon Nanongkai and Hsin-Hao Su. Almost-tight distributed minimum cut algorithms. In DISC, pages 439-453, 2014. ·Zbl 1435.68381
[53]Merav Parter. Small cuts and connectivity certificates: A fault tolerant approach. 2019.
[54]David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed minimum-weight spanning tree construction. SIAM J. Comput., 30(5):1427-1442, 2000. ·Zbl 0973.05074
[55]David Pritchard and Ramakrishna Thurimella. Fast computation of small cuts via cycle space sampling. ACM Trans. Algorithms, 7(4):46:1-46:30, 2011. ·Zbl 1295.68205
[56]Mikkel Thorup. Fully-dynamic min-cut. Combinatorica, 27(1):91-127, 2007. Announced at STOC’01. ·Zbl 1135.68024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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