Distributed weighted min-cut in nearly-optimal time

Michal Dory, Yuval Efron, Sagnik Mukhopadhyay, Danupon Nanongkai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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+?)-approximation at best while the exact O(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 O(n) [Daga, Henzinger, Nanongkai, Saranurak, STOC'19]. In this paper, we provide an exact O(?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.

Original languageEnglish
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
PublisherAssociation for Computing Machinery
Pages1144-1153
Number of pages10
ISBN (Electronic)9781450380539
DOIs
StatePublished - 15 Jun 2021
Externally publishedYes
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: 21 Jun 202125 Jun 2021

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period21/06/2125/06/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

  • CONGEST model
  • Minimun-cut

ASJC Scopus subject areas

  • Software

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