Minimum cut in O(m log2 n) time

Paweł Gawrychowski; Shay Mozes; Oren Weimann

doi:10.4230/LIPIcs.ICALP.2020.57

Minimum cut in O(m log² n) time

Paweł Gawrychowski, Shay Mozes, Oren Weimann

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Editors	Artur Czumaj, Anuj Dawar, Emanuela Merelli
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771382
DOIs	https://doi.org/10.4230/LIPIcs.ICALP.2020.57
State	Published - 1 Jun 2020
Event	47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany Duration: 8 Jul 2020 → 11 Jul 2020

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	168
ISSN (Print)	1868-8969

Conference

Conference	47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Country/Territory	Germany
City	Virtual, Online
Period	8/07/20 → 11/07/20

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

Access to Document

10.4230/LIPIcs.ICALP.2020.57

Cite this

Gawrychowski, P., Mozes, S., & Weimann, O. (2020). Minimum cut in O(m log² n) time. In A. Czumaj, A. Dawar, & E. Merelli (Eds.), 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 Article 57 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 168). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2020.57

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Gawrychowski, P, Mozes, S & Weimann, O 2020, Minimum cut in O(m log² n) time. in A Czumaj, A Dawar & E Merelli (eds), 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020., 57, Leibniz International Proceedings in Informatics, LIPIcs, vol. 168, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, Virtual, Online, Germany, 8/07/20. https://doi.org/10.4230/LIPIcs.ICALP.2020.57

Minimum cut in O(m log² n) time. / Gawrychowski, Paweł; Mozes, Shay; Weimann, Oren.
47th International Colloquium on Automata, Languages, and Programming, ICALP 2020. ed. / Artur Czumaj; Anuj Dawar; Emanuela Merelli. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2020. 57 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 168).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Gawrychowski P, Mozes S, Weimann O. Minimum cut in O(m log² n) time. In Czumaj A, Dawar A, Merelli E, editors, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2020. 57. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.ICALP.2020.57