Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-Wideness

TL;DR

This paper empirically evaluates approximation algorithms for generalized graph coloring and uniform quasi-wideness, focusing on their performance on real-world graphs and theoretical bounds within certain graph classes.

Contribution

It introduces a new polynomial-size algorithm for uniform quasi-wideness in bounded expansion graph classes and provides empirical analysis of approximation algorithms on real-world data.

Findings

Approximation algorithms perform well on real-world graphs.

The new algorithm for uniform quasi-wideness has near-optimal guarantees.

Experimental results support theoretical bounds in specific graph classes.

Abstract

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we study two structural properties of these graph classes that are of particular importance in this context, namely the property of having bounded generalized coloring numbers and the property of being uniformly quasi-wide. We provide experimental evaluations of several algorithms that approximate these parameters on real-world graphs. On the theoretical side, we provide a new algorithm for uniform quasi-wideness with polynomial size guarantees in graph classes of bounded expansion and show a lower bound indicating that the guarantees of this algorithm are close to optimal in graph classes with fixed excluded minor.