Reactive Local Search for Maximum Clique

A heuristic algorithm is proposed for the solution of the Maximum-Clique problem in graphs. The algorithm is based on local search complemented by a \reactive" (history{sensitive) scheme to determine the amount of diversiication (Reactive Local Search, or RLS). The reaction acts on a parameter that determines the length of the temporary prohibition of selected moves in the neighborhood. The worst-case complexity per iteration of the algorithm is O(maxfn; mg) where n and m are the number of nodes and edges of the graph. The performance obtained in computational tests, when one considers both the quality of the heuristic solutions and the computational cost, appears to dominate all alternative heuristics for the problem.