Faster Cut-Equivalent Trees in Simple Graphs

06/07/2021

∙

by   Tianyi Zhang, et al.

∙

0

∙

share

Let G = (V, E) be an undirected connected simple graph on n vertices. A cut-equivalent tree of G is an edge-weighted tree on the same vertex set V, such that for any pair of vertices s, t∈ V, the minimum (s, t)-cut in the tree is also a minimum (s, t)-cut in G, and these two cuts have the same cut value. In a recent paper [Abboud, Krauthgamer and Trabelsi, 2021], the authors propose the first subcubic time algorithm for constructing a cut-equivalent tree. More specifically, their algorithm has O(n^2.5) running time. In this paper, we improve the running time to O(n^2) if almost-linear time max-flow algorithms exist. Also, using the currently fastest max-flow algorithm by [van den Brand , 2021], our algorithm runs in time O(n^17/8).