Experimental evaluation of kernelization algorithms to Dominating Set

TL;DR

This paper experimentally evaluates kernelization algorithms for the Dominating Set problem on sparse graph classes, comparing their effectiveness with previous preprocessing approaches to improve algorithmic efficiency.

Contribution

It provides the first experimental assessment of kernelization techniques for Dominating Set on sparse graphs, highlighting their practical performance and potential advantages.

Findings

Kernelization algorithms show promising results in preprocessing sparse graphs.

Compared to previous methods, kernelization offers more efficient reduction routines.

Experimental results suggest kernelization can significantly improve solving times for Dominating Set.

Abstract

The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the flagship problems are Dominating Set and its generalization r-Dominating Set. They have been precursors for model checking of first order logic on sparse graph classes. On class of graphs of bounded expansions the r-Dominating Set problem admits a constant factor approximation, a fixed-parameter algorithm, and an efficient preprocessing routine: the so-called linear kernel. This should be put in constrast with general graphs where Dominating Set is APX-hard and W[2]-complete. In this paper we provide an experimental evaluation of kernelization algorithm for Dominating Set in sparse graph classes and compare it with previous approaches designed to the preprocessing for Dominating Set.