An adaptive memory algorithm for the k-coloring problem

  • Authors:

  • Philippe Galinier;Alain Hertz;Nicolas Zufferey

  • Affiliations:

  • Department of Computer Science, ícole Polytechnique de Montréal, Canada;Department of Mathematics and Industrial Engineering, ícole Polytechnique de Montréal, Canada;Département d'opérations et systèmes de décision, Université Laval, Canada

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2008

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Abstract

Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,...,k}) to each vertex of G so that no edge has both endpoints with the same color. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory. At each iteration, the information contained in the central memory is used for producing an offspring solution which is then possibly improved using a local search algorithm. The so obtained solution is finally used to update the central memory. We describe in this paper an adaptive memory algorithm for the k-coloring problem. Computational experiments give evidence that this new algorithm is competitive with, and simpler and more flexible than, the best known graph coloring algorithms.