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Graph bisection revisited

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  • Renata Sotirov

    (Tilburg University)

Abstract

The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of order n—the number of vertices of the graph—that is equivalent to the currently strongest semidefinite programming relaxation obtained by using vector lifting. The reduction in the size of the matrix variable enables us to impose additional valid inequalities to the relaxation in order to further strengthen it. The numerical results confirm that our simplified and strengthened semidefinite relaxation provides the currently strongest bound for the graph bisection problem in reasonable time.

Suggested Citation

  • Renata Sotirov, 2018. "Graph bisection revisited," Annals of Operations Research, Springer, vol. 265(1), pages 143-154, June.
    • Handle: RePEc:spr:annopr:v:265:y:2018:i:1:d:10.1007_s10479-017-2575-3
    DOI: 10.1007/s10479-017-2575-3
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    References listed on IDEAS

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    1. DE SOUZA, Cid C. & KEUNINGS, Roland & WOLSEY, Laurence A. & ZONE, Olivier, 1994. "A new approach to minimising the frontwidth in finite element calculations," LIDAM Reprints CORE 1076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Renata Sotirov, 2014. "An Efficient Semidefinite Programming Relaxation for the Graph Partition Problem," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 16-30, February.
    3. Stefan E. Karisch & Franz Rendl & Jens Clausen, 2000. "Solving Graph Bisection Problems with Semidefinite Programming," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 177-191, August.
    4. FERREIRA, Carlos E. & MARTIN, Alexander & de SOUZA, Cid C. & WEISMANTEL, Robert, 1998. "The node capacitated graph partitioning problem: A computational study," LIDAM Reprints CORE 1335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Hu, Hao & Sotirov, Renata & Wolkowicz, Henry, 2023. "Facial reduction for symmetry reduced semidefinite and doubly nonnegative programs," Other publications TiSEM 8dd3dbae-58fd-4238-b786-e, Tilburg University, School of Economics and Management.

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