An iterated greedy algorithm for finding the minimum dominating set in graphs

A dominating set in a graph is a set of vertices such that every vertex outside the set is adjacent to a vertex in the set. The domination number is the minimum cardinality of a dominating set in the graph. The problem of finding the minimum dominating set is a combinatorial optimization problem that has been proved to be NP-hard. Given the difficulty of this problem, an Iterated Greedy algorithm is proposed for its solution and it is compared to the solution given by an exact algorithm and by the state-of-art algorithms. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. Specifically, from the set of instances which can be optimally solved, the proposed method presents an average deviation of 0.04%. Regarding the more complex set of instances, where the exact method is not able to reach the optimal value, the proposed method achieves an average deviation of 1.23% with respect to the best-known solution.