A Nearly Optimal All-Pairs Min-Cuts Algorithm in Simple Graphs
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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 Õ(n^2.5) by Abboud et al. (FOCS 2021). Our running time is nearly optimal as a function of n.
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