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A two-level graph partitioning problem arising in mobile wireless communications

Author

Listed:
  • Jamie Fairbrother

    (Lancaster University)

  • Adam N. Letchford

    (Lancaster University)

  • Keith Briggs

    (BT Technology, Service & Operations)

Abstract

In the k -partition problem (k-PP), one is given an edge-weighted undirected graph, and one must partition the node set into at most k subsets, in order to minimise (or maximise) the total weight of the edges that have their end-nodes in the same subset. Various hierarchical variants of this problem have been studied in the context of data mining. We consider a ‘two-level’ variant that arises in mobile wireless communications. We show that an exact algorithm based on intelligent preprocessing, cutting planes and symmetry-breaking is capable of solving small- and medium-size instances to proven optimality, and providing strong lower bounds for larger instances.

Suggested Citation

  • Jamie Fairbrother & Adam N. Letchford & Keith Briggs, 2018. "A two-level graph partitioning problem arising in mobile wireless communications," Computational Optimization and Applications, Springer, vol. 69(3), pages 653-676, April.
    • Handle: RePEc:spr:coopap:v:69:y:2018:i:3:d:10.1007_s10589-017-9967-9
    DOI: 10.1007/s10589-017-9967-9
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    References listed on IDEAS

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    1. M. Deza & M. Grötschel & M. Laurent, 1992. "Clique-Web Facets for Multicut Polytopes," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 981-1000, November.
    2. Bissan Ghaddar & Miguel Anjos & Frauke Liers, 2011. "A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem," Annals of Operations Research, Springer, vol. 188(1), pages 155-174, August.
    3. Adam N. Letchford, 2001. "On Disjunctive Cuts for Combinatorial Optimization," Journal of Combinatorial Optimization, Springer, vol. 5(3), pages 299-315, September.
    4. Karen Aardal & Stan Hoesel & Arie Koster & Carlo Mannino & Antonio Sassano, 2007. "Models and solution techniques for frequency assignment problems," Annals of Operations Research, Springer, vol. 153(1), pages 79-129, September.
    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. Cheng Lu & Zhibin Deng & Shu-Cherng Fang & Wenxun Xing, 2023. "A New Global Algorithm for Max-Cut Problem with Chordal Sparsity," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 608-638, May.
    2. Vilmar Jefté Rodrigues de Sousa & Miguel F. Anjos & Sébastien Le Digabel, 2019. "Improving the linear relaxation of maximum k-cut with semidefinite-based constraints," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(2), pages 123-151, June.

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