Minimum Cut in O(mlog2n) Time

Paweł Gawrychowski; Shay Mozes; Oren Weimann

doi:10.1007/s00224-024-10179-7

Minimum Cut in O(mlog2n) Time

Paweł Gawrychowski
, Shay Mozes
, Oren Weimann

Department of Computer Science

Research output: Contribution to journal › Article › 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(mlog²n) time. This is the first improvement to Karger’s celebrated O(mlog³n) time algorithm from 1996. Our main technical contribution is a deterministic O(mlogn) 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
Pages (from-to)	814-834
Number of pages	21
Journal	Theory of Computing Systems
Volume	68
Issue number	4
DOIs	https://doi.org/10.1007/s00224-024-10179-7
State	Published - Aug 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

Karger’s algorithm
Minimum 2-respecting cut
Minimum cut

ASJC Scopus subject areas

Theoretical Computer Science
Computational Theory and Mathematics

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10.1007/s00224-024-10179-7

Cite this

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keywords = "Karger{\textquoteright}s algorithm, Minimum 2-respecting cut, Minimum cut",

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AU - Weimann, Oren

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Y1 - 2024/8

N2 - 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(mlog2n) time. This is the first improvement to Karger’s celebrated O(mlog3n) time algorithm from 1996. Our main technical contribution is a deterministic O(mlogn) time algorithm that, given a spanning tree T of G, finds a minimum cut of G that 2-respects (cuts two edges of) T.

AB - 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(mlog2n) time. This is the first improvement to Karger’s celebrated O(mlog3n) time algorithm from 1996. Our main technical contribution is a deterministic O(mlogn) time algorithm that, given a spanning tree T of G, finds a minimum cut of G that 2-respects (cuts two edges of) T.

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KW - Minimum 2-respecting cut

KW - Minimum cut

UR - https://www.scopus.com/pages/publications/85195701660

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ER -

Minimum Cut in O(mlog2n) Time

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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