Minimum Cuts in Directed Graphs via √(n) Max-Flows

04/16/2021

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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^2) time. This improves on the 30 year old bound of Õ(mn) obtained by Hao and Orlin for this problem.

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Minimum Cuts in Directed Graphs via √(n) Max-Flows

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