A heuristic for the stability number of a graph based on convex quadratic progr...

• Author(s): Cavique, Luís ; Luz, Carlos J.
• Date: 2009
• Persistent ID: http://hdl.handle.net/10400.2/1901
• Origin: Repositório Aberto da Universidade Aberta
• Subject(s): Stability number ofa graph; Convex quadratic programming; Tabu search
• Document Type: Article
• Language: English

Description

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.