A heuristic for the stability number of a graph based on convex quadratic programming and tabu search

• Autor(a) principal: Cavique, Luís
• Data de Publicação: 2009
• Outros Autores: Luz, Carlos J.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.2/1901
• topic: Stability number ofa graph; Convex quadratic programming; Tabu search

Recently, a characterization of the Lov´asz 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 that 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 oriented mainly 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 that begins by computing suboptimal solutions using the new bound definition. 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.