An Efficient Local Search for the Minimum Independent Dominating Set Problem

In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses k-swap as the neighborhood operation. Given a feasible solution S, it is the operation of obtaining another feasible solution by dropping exactly k vertices from S and then by adding any number of vertices to it. We show that, when k=2, (resp., k=3 and a given solution is minimal with respect to 2-swap), we can find an improved solution in the neighborhood or conclude that no such solution exists in O(n\Delta) (resp., O(n\Delta^3)) time, where n denotes the number of vertices and \Delta denotes the maximum degree. We develop a metaheuristic algorithm that repeats the proposed local search and the plateau search iteratively. The algorithm is so effective that it updates the best-known upper bound for nine DIMACS graphs.