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arXiv · 1911.01145

Minimum Cut in $O(m\log^2 n)$ Time

Paweł Gawrychowski·Shay Mozes·Oren Weimann
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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 $O(m \log^2 n)$ time. This is the first improvement to Karger's celebrated $O(m \log^3 n)$ 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) $T$.

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Paweł Gawrychowski, Shay Mozes, Oren Weimann. 2019-11-04. Minimum Cut in $O(m\log^2 n)$ Time. https://arxiv.org/abs/1911.01145

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