Journal of Global Optimization

, Volume 49, Issue 3, pp 425–434 | Cite as

An exact algorithm for solving the vertex separator problem

Article

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|} ≤ 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.

Keywords

Graph partitioning Vertex separator Polyhedral approach 

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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Laboratoire d’Analyse Non linéaire et Géométrie (EA 2151)Université d’Avignon et des Pays de VaucluseAvignonFrance
  2. 2.LMNO, Université de CaenCaen CedexFrance
  3. 3.Laboratoire Informatique d’Avignon (EA 931)Université d’Avignon et des Pays de VaucluseAvignonFrance

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