A Heuristic for the Stability Number of a Graph Based on Convex Quadratic Programming and Tabu Search
نویسنده
چکیده
Recently a characterization of the Lovász theta number based on convex quadratic programming was established. As a consequence of this formulation, we introduce a new upper bound on the stability number of a graph which slightly improves the theta number. Like this number, the new bound can be characterized as the minimum of a function whose values are the optimum values of convex quadratic programs. This paper is mainly oriented to the following question: how can the new bound be used to approximate the maximum stable set for large graphs? With this in mind we present a two-phase heuristic for the stability problem which begins by computing suboptimal solutions using the new bound de nition. In the second phase a multi-start tabu search heuristic is implemented. The results of applying this heuristic to some DIMACS benchmark graphs are reported.
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