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arXiv · 2106.02233

A Nearly Optimal All-Pairs Min-Cuts Algorithm in Simple Graphs

Jason Li·Debmalya Panigrahi·Thatchaphol Saranurak
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Abstract

We give an $n^{2+o(1)}$-time algorithm for finding $s$-$t$ min-cuts for all pairs of vertices $s$ and $t$ in a simple, undirected graph on $n$ vertices. We do so by constructing a Gomory-Hu tree (or cut equivalent tree) in the same running time, thereby improving on the recent bound of $\tilde{O}(n^{2.5})$ by Abboud et al. (STOC 2021). Our running time is nearly optimal as a function of $n$.

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Jason Li, Debmalya Panigrahi, Thatchaphol Saranurak. 2021-06-04. A Nearly Optimal All-Pairs Min-Cuts Algorithm in Simple Graphs. https://arxiv.org/abs/2106.02233

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