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

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 article, we study two structural properties of these graph classes that are of particular importance in this context: 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.