A computational study of Gomory-Hu construction tree algorithms

TL;DR

This study compares different algorithms for constructing Gomory-Hu trees, highlighting the robustness and efficiency of the OrderedCuts-based method through experimental analysis.

Contribution

It introduces practical implementations of Gomory-Hu tree algorithms and experimentally compares their performance, emphasizing the advantages of the OrderedCuts approach.

Findings

OrderedCuts-based method is the most robust.

OrderedCuts often outperforms other algorithms significantly.

Experimental results validate the efficiency of the proposed implementation.

Abstract

This paper studies algorithms for computing a Gomory-Hu tree, which is a classical data structure that compactly stores all minimum $s$-$t$ cuts of an undirected weighted graph. We consider two classes of algorithms: the original method by Gomory and Hu and the method based on "OrderedCuts" that we recently proposed. We describe practical implementations of these methods, and compare them experimentally with the algorithms from the previous experimental studies by Goldberg and Tsioutsiouliklis (2001) and by Akibo et al. (2016) (designed for unweighted simple graphs). Results indicate that the method based on OrderedCuts is the most robust, and often outperforms other implementations by a large factor.