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

•The selective graph coloring problem in perfect graphs.•An exact cutting plane algorithm.•A perfect graph generation algorithm.•An extensive computational assessment. We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph t...

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Veröffentlicht in:European journal of operational research Jg. 291; H. 1; S. 67 - 83
Hauptverfasser: Şeker, Oylum, Ekim, Tınaz, Taşkın, Z. Caner
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.05.2021
Schlagworte:
Cutting plane algorithm
Graph theory
Partition coloring
Perfect graph generation
Selective graph coloring
Perfect graph generation
Graph theory
Selective graph coloring
Cutting plane algorithm
Partition coloring
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•The selective graph coloring problem in perfect graphs.•An exact cutting plane algorithm.•A perfect graph generation algorithm.•An extensive computational assessment. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2020.09.017