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An exact algorithm for the edge coloring by total labeling problem

Author

Listed:
  • Fabrizio Borghini

    (Universidad de Buenos Aires)

  • Isabel Méndez-Díaz

    (Universidad de Buenos Aires)

  • Paula Zabala

    (Universidad de Buenos Aires)

Abstract

This paper addresses the edge coloring by total labeling graph problem. This is a labeling of the vertices and edges of a graph such that the weights (colors) of the edges, defined by the sum of its label and the labels of its two endpoints, determine a proper edge coloring of the graph. We propose two integer programming formulations and derive valid inequalities which are added as cutting planes on a Branch-and-Cut framework. In order to improve the efficiency of the algorithm, we also develop initial and primal heuristics. The algorithm is tested on random instances and the computational results show that it is very effective in comparison with CPLEX. It is displayed that it reduces both the CPU time (for solved instances) and the final percentage gap (for unsolved instances), and that it is capable of solving instances that are out of the reach of CPLEX.

Suggested Citation

  • Fabrizio Borghini & Isabel Méndez-Díaz & Paula Zabala, 2020. "An exact algorithm for the edge coloring by total labeling problem," Annals of Operations Research, Springer, vol. 286(1), pages 11-31, March.
    • Handle: RePEc:spr:annopr:v:286:y:2020:i:1:d:10.1007_s10479-018-2977-x
    DOI: 10.1007/s10479-018-2977-x
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    References listed on IDEAS

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    1. Pablo Coll & Javier Marenco & Isabel Méndez Díaz & Paula Zabala, 2002. "Facets of the Graph Coloring Polytope," Annals of Operations Research, Springer, vol. 116(1), pages 79-90, October.
    2. 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.
    3. Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1984. "A Cutting Plane Algorithm for the Linear Ordering Problem," Operations Research, INFORMS, vol. 32(6), pages 1195-1220, December.
    4. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2012. "A branch-and-cut procedure for the Udine Course Timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 71-87, April.
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