Efficient Local Search for Minimum Dominating Sets in Large Graphs

The Minimum Dominating Set (MinDS) problem is an NP-hard problem of great importance in both theories and applications. In this paper, we propose a new local search algorithm ScBppw (Score Checking and Best-picking with Probabilistic Walk) to solve the MinDS problem in large graphs. For diversifying the search, our algorithm exploits a tabu strategy, called Score Checking (SC), which forbids a vertex to be added into the current candidate solution if the vertex’s score has not been changed since the last time it was removed out of the candidate solution. Also, to keep a good balance between intensification and diversification during the search, we propose a strategy that combines, in a novel way, best-picking with probabilistic walk at removing stages. At this stage, the algorithm selects a vertex with the minimum loss, or other vertices in the candidate solution with a probability proportional to the their degrees, depending on how repeatedly the area has been visited. Experimental results show that our solver significantly outperforms state-of-the-art MinDS solvers. Also we conducted several experiments to show the individual impacts of our novelties.