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An exact cutting plane algorithm to solve the selective graph coloring problem in perfect graphs

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  • Şeker, Oylum
  • Ekim, Tınaz
  • Taşkın, Z. Caner

Abstract

We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster so that the number of colors needed to color the selected set of vertices is minimized. This problem is known to be NP-hard. In this study, we focus on an exact cutting plane algorithm for selective graph coloring in perfect graphs. Since there exists no suite of perfect graph instances to the best of our knowledge, we also propose an algorithm to randomly (but not uniformly) generate perfect graphs, and provide a large collection of instances available online. We conduct computational experiments to test our method on graphs with varying size and densities, and compare our results with a state-of-the-art algorithm from the literature and with solving an integer programming formulation of the problem by CPLEX. Our experiments demonstrate that our solution strategy significantly improves the solvability of the problem.

Suggested Citation

  • Şeker, Oylum & Ekim, Tınaz & Taşkın, Z. Caner, 2021. "An exact cutting plane algorithm to solve the selective graph coloring problem in perfect graphs," European Journal of Operational Research, Elsevier, vol. 291(1), pages 67-83.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:1:p:67-83
    DOI: 10.1016/j.ejor.2020.09.017
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    References listed on IDEAS

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    1. Wu, Qinghua & Hao, Jin-Kao, 2015. "A review on algorithms for maximum clique problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 693-709.
    2. Demange, Marc & Ekim, Tınaz & Ries, Bernard & Tanasescu, Cerasela, 2015. "On some applications of the selective graph coloring problem," European Journal of Operational Research, Elsevier, vol. 240(2), pages 307-314.
    3. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
    4. Lilian Markenzon & Oswaldo Vernet & Luiz Araujo, 2008. "Two methods for the generation of chordal graphs," Annals of Operations Research, Springer, vol. 157(1), pages 47-60, January.
    5. Hanif D. Sherali & J. Cole Smith, 2001. "Improving Discrete Model Representations via Symmetry Considerations," Management Science, INFORMS, vol. 47(10), pages 1396-1407, October.
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