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arXiv · 2111.08959

Minimum Cuts in Directed Graphs via Partial Sparsification

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

We give an algorithm to find a minimum cut in an edge-weighted directed graph with $n$ vertices and $m$ edges in $\tilde O(n\cdot \max(m^{2/3}, n))$ time. This improves on the 30 year old bound of $\tilde O(nm)$ obtained by Hao and Orlin for this problem. Our main technique is to reduce the directed mincut problem to $\tilde O(\min(n/m^{1/3}, \sqrt{n}))$ calls of {\em any} maxflow subroutine. Using state-of-the-art maxflow algorithms, this yields the above running time. Our techniques also yield fast {\em approximation} algorithms for finding minimum cuts in directed graphs. For both edge and vertex weighted graphs, we give $(1+\epsilon)$-approximation algorithms that run in $\tilde O(n^2 / \epsilon^2)$ time.

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Ruoxu Cen, Jason Li, Danupon Nanongkai, Debmalya Panigrahi, Kent Quanrud, Thatchaphol Saranurak. 2021-11-17. Minimum Cuts in Directed Graphs via Partial Sparsification. https://arxiv.org/abs/2111.08959

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