A Cross Entropy Approach to the Domination Problem and its Variants

TL;DR

This paper introduces a cross entropy-based method to efficiently approximate solutions for various domination problem variants, which are NP-hard, demonstrating good performance on large graphs.

Contribution

It presents a versatile cross entropy approach applicable to multiple domination variants, filling a gap in heuristic methods for these NP-hard problems.

Findings

Effective on large graphs

Performs consistently across variants

Produces high-quality solutions efficiently

Abstract

The domination problem and several of its variants (total domination, 2-domination and secure domination) are considered. These problems have various real-world applications, but are NP-hard to solve to provable optimality, making fast heuristics for these problems desirable. There is a wealth of highly-developed heuristics and approximation algorithms for the domination problem, however such heuristics are much less common for variants of the domination problem. We redress this by proposing an implementation of the cross entropy method that can be applied to any sensible variant of domination. We present results from experiments which demonstrate that this approach can produce good results in an efficient manner even for larger graphs, and that it works roughly as well for any of the domination variants considered.