Dory, M., Efron, Y., Mukhopadhyay, S. orcid.org/0000-0002-3722-4679 et al. (1 more author) (2021) Distributed weighted min-cut in nearly-optimal time. In: Khuller, S., (ed.) STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, 21-25 Jun 2021, Virtual Italy. Association for Computing Machinery (ACM) , pp. 1144-1153. ISBN 9781450380539
Abstract
Minimum-weight cut (min-cut) is a basic measure of a network’s connectivity strength. While the min-cut can be computed efficiently in the sequential setting [Karger STOC’96], there was no efficient way for a distributed network to compute its own min-cut without limiting the input structure or dropping the output quality: In the standard CONGEST model, existing algorithms with nearly-optimal time (e.g. [Ghaffari, Kuhn, DISC’13; Nanongkai, Su, DISC’14]) can guarantee a solution that is (1+є)-approximation at best while the exact Õ(n0.8D0.2 + n0.9)-time algorithm [Ghaffari, Nowicki, Thorup, SODA’20] works only on simple networks (no weights and no parallel edges). Throughout, n and D denote the network’s number of vertices and hop-diameter, respectively. For the weighted case, the best bound was Õ(n) [Daga, Henzinger, Nanongkai, Saranurak, STOC’19]. In this paper, we provide an exact Õ(√n + D)-time algorithm for computing min-cut on weighted networks. Our result improves even the previous algorithm that works only on simple networks. Its time complexity matches the known lower bound up to polylogarithmic factors. At the heart of our algorithm are a routing trick and two structural lemmas regarding the structure of a minimum cut of a graph. These two structural lemmas considerably strengthen and generalize the framework of Mukhopadhyay-Nanongkai [STOC’20] and can be of independent interest.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2021 ACM. This is an author-produced version of a paper subsequently published in STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | CONGEST model; Minimun-cut |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 28 Jun 2023 13:59 |
Last Modified: | 29 Jun 2023 13:25 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Refereed: | Yes |
Identification Number: | 10.1145/3406325.3451020 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200972 |