A Cross-Entropy Approach to the Domination Problem and Its Variants

Abstract

The domination problem and three of its variants (total domination, 2-domination, and secure domination) are considered. These problems have various real-world applications, including error correction codes, ad hoc routing for wireless networks, and social network analysis, among others. However, each of them is NP-hard to solve to provable optimality, making fast heuristics for these problems desirable. There are 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 gap in the literature by proposing a novel implementation of the cross-entropy method that can be applied to any sensible variant of domination. We present results from experiments that 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.

Keywords

• domination
• total domination
• 2-domination
• secure domination
• cross-entropy
• variants