License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.57
URN: urn:nbn:de:0030-drops-124646
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Gawrychowski, Paweł ; Mozes, Shay ; Weimann, Oren

Minimum Cut in O(m log² n) Time

LIPIcs-ICALP-2020-57.pdf (0.6 MB)


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(m log² n) time. This is the first improvement to Karger’s celebrated O(m log³ n) time algorithm from 1996. Our main technical contribution is a deterministic O(m log 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.

BibTeX - Entry

  author =	{Paweł Gawrychowski and Shay Mozes and Oren Weimann},
  title =	{{Minimum Cut in O(m log² n) Time}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-124646},
  doi =		{10.4230/LIPIcs.ICALP.2020.57},
  annote =	{Keywords: Minimum cut, Minimum 2-respecting cut}

Keywords: Minimum cut, Minimum 2-respecting cut
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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