Efficient algorithms for generalized cut‐trees
Dan Gusfield, Dalit Naor · Networks · 1991
Abstract The Gomory–Hu cut tree is a compact and efficiently computed representation of selected minimum edge cuts in a weighted undirected graph G = (V, E) with n nodes. It represents ( ) minimum cuts, one for each pair of nodes in G, and can be constructed with only n − 1 flow computations. In this article, we generalize the types of cut‐trees that can be efficiently constructed. We solve the open problem, posed by Hu [9], of constructing with n − 1 flows a cut‐tree for minimum node weighted cuts in an undirected graph. We then show how to build cut‐trees that compactly represent the minimum edge cuts in directed graphs, partially solving the open problem of constructing cut‐trees for weighted edge cuts in directed graphs.