New Results on the Queens_n2 Graph Coloring Problem
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For the Queens_n2 graph coloring problems no chromatic numbers are available for n > 9 except where n is not a multiple of 2 or 3. In this paper we propose an exact algorithm that takes advantage of the particular structure of these graphs. The algorithm works on the independent sets of the graph rather than on the vertices to be colored. It combines branch and bound, for independent set assignment, with a clique based filtering procedure. A first experimentation of this approach provided the coloring number values ranging for n = 10 to n = 14.
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- Caramia, M. and P. Dell'Olmo. (2001). “Iterative Coloring Extension of a Maximum Clique.” Naval Research Logistic 48(6), 518–550.Google Scholar
- Caramia, M. and P. Dell'Olmo. (2002). “Constraint Propagation in Graph Coloring.” Journal of Heuristic 8, 83–107.Google Scholar
- Chiarandini, M. and T. Stützle. (2002). “An Application of Iterated Local Searchto Graph Coloring Problem.” In Mehrotra, A., Johnson, D.S., and Trick, M. (eds.), Proceedings of the Computational Symposium on Graph Coloringand its Generalizations. Ithaca, New York, USA, pp. 112–125.Google Scholar
- Gardner, M. (1995). Further Mathematical Diversions: The Paradox of the Unexpected Hanging and Others. Mathematical Association of America.Google Scholar
- Hamiez, J.P. (2002). “Coloration de Graphes et Planification de Rencontressportives: Heuristiques, Algorithmes et Analyses.” PhD thesis, Universitéd'Angers.Google Scholar
- Kochenberger, G., F. Glover, B. Alidaee, and C. Rego. (to appear). “An Unconstrained Quadratic Binary Program-ming Approach to the Vertex Coloring Problem.” Annals of Operations Research.Google Scholar
- Mehrotra, A. and M.A. Trick. (1996). A Column Generation Approach for Graph Coloring.” INFORMS Journal of Computing 8(4), 344–354.Google Scholar
- Sabin, D. and E. Freuder. (1994). “Contradicting Conventional Wisdom in Con-Straint Satisfaction.” In ECAI'94, Amsterdam, pp. 125–129.Google Scholar