An exact algorithm for solving the vertex separator problem

Authors:
Mohamed Didi Biha;Marie-Jean Meurs
Affiliations:
Laboratoire d'Analyse Non linéaire et Géométrie (EA 2151), Université d'Avignon et des Pays de Vaucluse, Avignon, France 84018 and LMNO, Université de Caen, Caen Cedex, Fr ...;Laboratoire Informatique d'Avignon (EA 931), Université d'Avignon et des Pays de Vaucluse, Avignon, France 84911
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

Given G = (V, E) a connected undirected graph and a positive integer β(|V|), the vertex separator problem is to find a partition of V into no-empty three classes A, B, C such that there is no edge between A and B, max{|A|, |B|} 驴 β(|V|) and |C| is minimum. In this paper we consider the vertex separator problem from a polyhedral point of view. We introduce new classes of valid inequalities for the associated polyhedron. Using a natural lower bound for the optimal solution, we present successful computational experiments.