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An exact algorithm for solving the vertex separator problem

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  • Mohamed Didi Biha
  • Marie-Jean Meurs

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. Copyright Springer Science+Business Media, LLC. 2011

Suggested Citation

  • Mohamed Didi Biha & Marie-Jean Meurs, 2011. "An exact algorithm for solving the vertex separator problem," Journal of Global Optimization, Springer, vol. 49(3), pages 425-434, March.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:3:p:425-434
    DOI: 10.1007/s10898-010-9568-y
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    Cited by:

    1. Hager, William W. & Hungerford, James T., 2015. "Continuous quadratic programming formulations of optimization problems on graphs," European Journal of Operational Research, Elsevier, vol. 240(2), pages 328-337.
    2. Xiaolong Zheng & Daniel Zeng & Fei-Yue Wang, 2015. "Social balance in signed networks," Information Systems Frontiers, Springer, vol. 17(5), pages 1077-1095, October.
    3. Fanz Rendl & Renata Sotirov, 2018. "The min-cut and vertex separator problem," Computational Optimization and Applications, Springer, vol. 69(1), pages 159-187, January.
    4. Benlic, Una & Epitropakis, Michael G. & Burke, Edmund K., 2017. "A hybrid breakout local search and reinforcement learning approach to the vertex separator problem," European Journal of Operational Research, Elsevier, vol. 261(3), pages 803-818.
    5. Xinxin Li & Ting Kei Pong & Hao Sun & Henry Wolkowicz, 2021. "A strictly contractive Peaceman-Rachford splitting method for the doubly nonnegative relaxation of the minimum cut problem," Computational Optimization and Applications, Springer, vol. 78(3), pages 853-891, April.

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