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

We give an algorithm to find a mincut in an n-vertex, m-edge weighted directed graph using Õ( √ n) calls to any maxflow subroutine. Using state of the art maxflow algorithms, this yields a directed mincut algorithm that runs in Õ(m √ n+ n) time. This improves on the 30 year old bound of Õ(mn) obtained by Hao and Orlin for this problem. ar X iv :2 10 4. 07 89 8v 1 [ cs .D S] 1 6 A pr 2 02 1

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