A GRASP approach for solving the 2-connected m-dominating set problem

TL;DR

This paper introduces a GRASP-based heuristic for the 2-connected m-dominating set problem, combining greedy construction, ear extension, correction, and randomization to efficiently solve dense graph instances.

Contribution

It presents a novel GRASP approach with a specialized ear extension and correction procedures for the 2-connected m-dominating set problem, improving solution quality and efficiency.

Findings

Highly competitive performance on dense graphs

Effective extension of greedy heuristics with randomization

Improved solutions through correction procedures

Abstract

In this paper, we present a constructive heuristic algorithm for the $2$-connected $m$-dominating set problem. It is based on a greedy heuristic in which a 2-connected subgraph is iteratively extended with suitable open ears. The growth procedure is an adaptation of the breadth-first-search which efficiently manages to find open ears. Further, a heuristic function is defined for selecting the best ear out of a list of candidates. The performance of the basic approach is improved by adding a correction procedure which removes unnecessary nodes from a generated solution. Finally, randomization is included and the method is extended towards the GRASP metaheuristic. In our computational experiments, we compare the performance of the proposed algorithm to recently published results and show that the method is highly competitive and especially suitable for dense graphs.