Minimum Cut in O(m log² n) Time
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.
Minimum cut
Minimum 2-respecting cut
Theory of computation~Design and analysis of algorithms
57:1-57:15
Track A: Algorithms, Complexity and Games
A full version of the paper is available at https://arxiv.org/abs/1911.01145.
We thank Daniel Anderson and Guy Blelloch for drawing our attention to an inaccuracy in a prior version of Section 3.1.
Paweł
Gawrychowski
Paweł Gawrychowski
University of Wrocław, Poland
https://orcid.org/0000-0002-6993-5440
Shay
Mozes
Shay Mozes
The Interdisciplinary Center Herzliya, Israel
https://orcid.org/0000-0001-9262-1821
Supported in part by Israel Science Foundation grant 592/17.
Oren
Weimann
Oren Weimann
University of Haifa, Israel
https://orcid.org/0000-0002-4510-7552
Supported in part by Israel Science Foundation grant 592/17.
10.4230/LIPIcs.ICALP.2020.57
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Paweł Gawrychowski, Shay Mozes, and Oren Weimann
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