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Computational study of valid inequalities for the maximum k-cut problem

Author

Listed:
  • Vilmar Jefté Rodrigues de Sousa

    (Polytechnique Montréal)

  • Miguel F. Anjos

    (Polytechnique Montréal)

  • Sébastien Le Digabel

    (Polytechnique Montréal)

Abstract

We consider the maximum k-cut problem that consists in partitioning the vertex set of a graph into k subsets such that the sum of the weights of edges joining vertices in different subsets is maximized. We focus on identifying effective classes of inequalities to tighten the semidefinite programming relaxation. We carry out an experimental study of four classes of inequalities from the literature: clique, general clique, wheel and bicycle wheel. We considered 10 combinations of these classes and tested them on both dense and sparse instances for $$ k \in \{3,4,5,7\} $$ k ∈ { 3 , 4 , 5 , 7 } . Our computational results suggest that the bicycle wheel and wheel are the strongest inequalities for $$ k=3 $$ k = 3 , and that for $$ k \in \{4,5,7\} $$ k ∈ { 4 , 5 , 7 } the wheel inequalities are the strongest by far. Furthermore, we observe an improvement in the performance for all choices of k when both bicycle wheel and wheel are used, at the cost of 72% more CPU time on average when compared with using only one of them.

Suggested Citation

  • Vilmar Jefté Rodrigues de Sousa & Miguel F. Anjos & Sébastien Le Digabel, 2018. "Computational study of valid inequalities for the maximum k-cut problem," Annals of Operations Research, Springer, vol. 265(1), pages 5-27, June.
    • Handle: RePEc:spr:annopr:v:265:y:2018:i:1:d:10.1007_s10479-017-2448-9
    DOI: 10.1007/s10479-017-2448-9
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    References listed on IDEAS

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    1. Fuda Ma & Jin-Kao Hao, 2017. "A multiple search operator heuristic for the max-k-cut problem," Annals of Operations Research, Springer, vol. 248(1), pages 365-403, January.
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    Cited by:

    1. Cheng Lu & Zhibin Deng, 2021. "A branch-and-bound algorithm for solving max-k-cut problem," Journal of Global Optimization, Springer, vol. 81(2), pages 367-389, October.
    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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