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arXiv · 2104.07898

Minimum Cuts in Directed Graphs via $\sqrt{n}$ Max-Flows

Ruoxu Cen·Jason Li·Danupon Nanongkai·Debmalya Panigrahi·Thatchaphol Saranurak
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Abstract

We give an algorithm to find a mincut in an $n$-vertex, $m$-edge weighted directed graph using $\tilde O(\sqrt{n})$ calls to any maxflow subroutine. Using state of the art maxflow algorithms, this yields a directed mincut algorithm that runs in $\tilde O(m\sqrt{n} + n^2)$ time. This improves on the 30 year old bound of $\tilde O(mn)$ obtained by Hao and Orlin for this problem.

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Ruoxu Cen, Jason Li, Danupon Nanongkai, Debmalya Panigrahi, Thatchaphol Saranurak. 2021-04-16. Minimum Cuts in Directed Graphs via $\sqrt{n}$ Max-Flows. https://arxiv.org/abs/2104.07898

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