Minimum cut in O(m log2 n) time

Paweł Gawrychowski, Shay Mozes, Oren Weimann

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

Abstract

We give a randomized algorithm that finds a minimum cut in an undirected weighted m-edge n-vertex graph G with high probability in O(mlog2 n) time. This is the first improvement to Karger's celebrated O(mlog3 n) time algorithm from 1996. Our main technical contribution is a deterministic O(mlog n) time algorithm that, given a spanning tree T of G, finds a minimum cut of G that 2-respects (cuts two edges of) T.

Original languageEnglish
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
DOIs
StatePublished - 1 Jun 2020
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: 8 Jul 202011 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume168
ISSN (Print)1868-8969

Conference

Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Country/TerritoryGermany
CityVirtual, Online
Period8/07/2011/07/20

Bibliographical note

Funding Information:
Funding Shay Mozes: Supported in part by Israel Science Foundation grant 592/17. Oren Weimann: Supported in part by Israel Science Foundation grant 592/17.

Publisher Copyright:
© Paweł Gawrychowski, Shay Mozes, and Oren Weimann; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).

Keywords

  • Minimum 2-respecting cut
  • Minimum cut

ASJC Scopus subject areas

  • Software

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