Variable space search for graph coloring

  • Authors:

  • Alain Hertz;Matthieu Plumettaz;Nicolas Zufferey

  • Affiliations:

  • ícole Polytechnique de Montréal, Département de mathématiques et de génie industriel, Montréal (QC) H3C 3A7, Canada;ícole Polytechnique Fédérale de Lausanne (EPFL), Chaire de Recherche Opérationnelle Sud-Est (ROSE), CH-1015 Lausanne, Switzerland;HEC-Université de Genève, Faculté des Sciences íconomiques et Sociales, 1211 Genève 4, Switzerland

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

Quantified Score

Hi-index 0.05

Visualization

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. We propose a new local search methodology, called Variable Space Search, which we apply to the k-coloring problem. The main idea is to consider several search spaces, with various neighborhoods and objective functions, and to move from one to another when the search is blocked at a local optimum in a given search space. The k-coloring problem is thus solved by combining different formulations of the problem which are not equivalent, in the sense that some constraints are possibly relaxed in one search space and always satisfied in another. We show that the proposed algorithm improves on every local search used independently (i.e., with a unique search space), and is competitive with the currently best coloring methods, which are complex hybrid evolutionary algorithms.