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

We give an n2+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 Õ(n2.5) by Abboud et al. (STOC 2021). Our running time is nearly optimal as a function of n. ar X iv :2 10 6. 02 23 3v 2 [ cs .D S] 3 N ov 2 02 1

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