Coloring large graphs based on independent set extraction

Authors:
Qinghua Wu;Jin-Kao Hao
Affiliations:
LERIA, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France;LERIA, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France
Venue:
Computers and Operations Research
Year:
2012

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Abstract

This paper presents an effective approach (EXTRACOL) to coloring large graphs. The proposed approach uses a preprocessing method to extract large independent sets from the graph and a memetic algorithm to color the residual graph. Each preprocessing application identifies, with a dedicated tabu search algorithm, a number of pairwise disjoint independent sets of a given size in order to maximize the vertices removed from the graph. We evaluate EXTRACOL on the 11 largest graphs (with 1000 to 4000 vertices) of the DIMACS challenge benchmarks and show improved results for four very difficult graphs (DSJC1000.9, C2000.5, C2000.9, C4000.5). The behavior of the proposed algorithm is also analyzed.