Solving the 2-connected m-dominating set problem using a GRASP approach for applications in power systems

TLDR: This paper presents a constructive heuristic algorithm based on a greedy heuristic in which a 2-connected subgraph is iteratively extended with suitable open ears and extended towards the GRASP metaheuristic.

Abstract: The dominating set problem and its variations are growing in importance in the context of power distributions systems in both the communication and monitoring systems of smart grids. One important aspect of such systems is fault tolerance which is well modeled by including the 2-connectivity constraint to the standard dominating set problem. 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.