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An exact algorithm for solving the vertex separator problem

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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|} ≤ 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.

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Authors and Affiliations

  1. Laboratoire d’Analyse Non linéaire et Géométrie (EA 2151), Université d’Avignon et des Pays de Vaucluse, 84018, Avignon, France

    Mohamed Didi Biha

  2. LMNO, Université de Caen, BP 5186, 14032, Caen Cedex, France

    Mohamed Didi Biha

  3. Laboratoire Informatique d’Avignon (EA 931), Université d’Avignon et des Pays de Vaucluse, 84911, Avignon, France

    Marie-Jean Meurs

Authors
  1. Mohamed Didi Biha
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  2. Marie-Jean Meurs
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Correspondence to Mohamed Didi Biha.

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Didi Biha, M., Meurs, MJ. An exact algorithm for solving the vertex separator problem. J Glob Optim 49, 425–434 (2011). https://doi.org/10.1007/s10898-010-9568-y

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  • DOI: https://doi.org/10.1007/s10898-010-9568-y

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