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An exact approach for the multi-constraint graph partitioning problem

Author

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  • Diego Recalde

    (Escuela Politécnica Nacional
    Escuela Politécnica Nacional)

  • Ramiro Torres

    (Escuela Politécnica Nacional)

  • Polo Vaca

    (Escuela Politécnica Nacional)

Abstract

In this work, a multi-constraint graph partitioning problem is introduced. The input is an undirected graph with costs on the edges and multiple weights on the nodes. The problem calls for a partition of the node set into a fixed number of clusters, such that each cluster satisfies a collection of node weight constraints, and the total cost of the edges whose end nodes are in the same cluster is minimized. It arises as a sub-problem of an integrated vehicle and pollster problem from a real-world application. Two integer programming formulations are provided, and several families of valid inequalities associated with the respective polyhedra are proved. An exact algorithm based on Branch & Bound and cutting planes is proposed, and it is tested on real-world instances.

Suggested Citation

  • Diego Recalde & Ramiro Torres & Polo Vaca, 2020. "An exact approach for the multi-constraint graph partitioning problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 289-308, October.
    • Handle: RePEc:spr:eurjco:v:8:y:2020:i:3:d:10.1007_s13675-020-00126-9
    DOI: 10.1007/s13675-020-00126-9
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    References listed on IDEAS

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    1. Neng Fan & Panos Pardalos, 2010. "Linear and quadratic programming approaches for the general graph partitioning problem," Journal of Global Optimization, Springer, vol. 48(1), pages 57-71, September.
    2. Diego Recalde & Daniel Severín & Ramiro Torres & Polo Vaca, 2018. "An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 916-936, October.
    3. 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).
    4. John E. Mitchell, 2003. "Realignment in the National Football League: Did they do it right?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 683-701, October.
    5. 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.
    6. R. C. Carlson & G. L. Nemhauser, 1966. "Scheduling to Minimize Interaction Cost," Operations Research, INFORMS, vol. 14(1), pages 52-58, February.
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    Cited by:

    1. Arie M. C. A. Koster & Clemens Thielen, 2020. "Special issue on: Computational discrete optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 201-203, October.

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