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The Minimum Weight Dominating Set (MWDS) problem is an importantgeneralization of the Minimum Dominating Set (MDS) problem with extensiveapplications. This paper proposes a new local search algorithm for the MWDSproblem, which is based on two new ideas. The first idea is a heuristic calledtwo-level configuration checking (CC2), which is a new variant of a recentpowerful configuration checking strategy (CC) for effectively avoiding therecent search paths. The second idea is a novel scoring function based on thefrequency of being uncovered of vertices. Our algorithm is called CC2FS,according to the names of the two ideas. The experimental results show that,CC2FS performs much better than some state-of-the-art algorithms in terms ofsolution quality on a broad range of MWDS benchmarks.

Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function