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
Journal	Theory of Computing Systems
DOIs	https://doi.org/10.1007/s00224-024-10179-7
State	Accepted/In press - 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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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{\textquoteright}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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AU - Mozes, Shay

AU - Weimann, Oren

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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.

KW - Karger’s algorithm

KW - Minimum 2-respecting cut

KW - Minimum cut

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M3 - Article

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JF - Theory of Computing Systems

ER -

Minimum Cut in O(mlog2n) Time

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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