Polynomial Time Data Reduction for Dominating Set

TL;DR

This paper presents simple, effective data reduction rules that produce small problem kernels for the NP-complete Dominating Set problem, especially on planar graphs, with promising practical results.

Contribution

It introduces new linear-size kernelization techniques for Dominating Set on planar graphs, combining theoretical proof and practical implementation.

Findings

Linear problem kernel for Dominating Set on planar graphs

Effective reduction rules are easy to implement

Preliminary experiments show strong practical potential

Abstract

Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy to implement reduction rules. Moreover, having implemented our reduction rules, first experiments indicate the impressive practical potential of these rules. Thus, this work seems to open up a new and prospective way how to cope with one of the most important problems in graph theory and combinatorial optimization.