A branch-and-price algorithm for the robust graph coloring problem

Authors:
Claudia Archetti;Nicola Bianchessi;Alain Hertz
Affiliations:
Department of Quantitative Methods, University of Brescia, Brescia, Italy;Department of Information Engineering, University of Brescia, Brescia, Italy;Department of Mathematics and Industrial Engineering, ícole Polytechnique and GERAD, Montréal, Canada
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

Given a graph G, an integer k, and a cost c"u"v associated with all pairs uv of non-adjacent vertices in G, the robust graph coloring problem is to assign a color in {1,...,k} to every vertex of G so that no edge has both endpoints with the same color, and the total cost of the pairs of vertices having the same color is minimum. We propose a branch-and-price algorithm for the solution of this problem. The pricing problem consists in finding a stable set of minimum total weight, and we propose both an exact and a heuristic algorithm for its solution. Computational experiments are reported for randomly generated and benchmark graph coloring instances.