Graph coloring inequalities from all-different systems
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We explore the idea of obtaining valid inequalities for a 0–1 model from a finite-domain constraint programming formulation of the problem. In particular, we formulate a graph coloring problem as a system of all-different constraints. By analyzing the polyhedral structure of all-different systems, we obtain facet-defining inequalities that can be mapped to valid cuts in the classical 0–1 model of the problem. We focus on cuts corresponding to cycles and webs and show that they are stronger than known cuts for these structures. We also identify path cuts and show they do not strengthen the bound. Computational experiments for a set of benchmark instances reveal that finite-domain cycle cuts often deliver tighter bounds, in less time, than classical 0–1 cuts.
KeywordsGraph coloring Finite-domain variables Facet-defining inequalities
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- 1.Appa, G., Magos, D., Mourtos, I. (2004). Linear programming relaxations of multiple all-different predicates. In J. C. Régin, M. Rueher (Eds.), Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR 2004). Lecture notes in computer science (Vol. 3011, pp. 364–369). Springer.Google Scholar
- 3.Bergman, D., & Hooker, J.N. (2012). Graph coloring facets from all-different systems. In N. Jussien, T. Petit (Eds.), Proceedings of the international workshop on integration of artificial intelligence and operations research techniques in constraint programming for combintaorial optimization problems. CPAIOR: Springer (to appear).Google Scholar
- 5.Genç-Kaya, L., & Hooker, J.N. (2010). The circuit polytope. Manuscript, Carnegie Mellon University.Google Scholar
- 7.Hooker, J.N. (2000). Logic-based methods for optimization: combining optimization and constraint satisfaction. New York: Wiley.Google Scholar
- 8.Hooker, J.N. (2012). Integrated methods for optimization, 2nd edn. Springer.Google Scholar
- 15.Nemhauser, G.L., & Wolsey, L.A. (1999). Integer and combinatorial optimization. New York: Wiley.Google Scholar
- 16.Palubeckis, G. (2008). On the graph coloring polytope. Information Technology and Control, 37, 7–11.Google Scholar
- 19.Yunes, T.H. (2002). On the sum constraint: relaxation and applications. In P. Van Hentenryck (Ed.), Principles and practice of constraint programming (CP 2002). Lecture notes in computer science (Vol. 2470, pp. 80–92). Springer.Google Scholar