Logic-Based Methods for Optimization
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
On the Sum Constraint: Relaxation and Applications
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Representations of the all_different Predicate of Constraint Satisfaction in Integer Programming
INFORMS Journal on Computing
Integrated Methods for Optimization (International Series in Operations Research & Management Science)
A cutting plane algorithm for graph coloring
Discrete Applied Mathematics
On the system of two all_different predicates
Information Processing Letters
On the Facial Structure of the Alldifferent System
SIAM Journal on Discrete Mathematics
A polyhedral approach to the alldifferent system
Mathematical Programming: Series A and B
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We explore the idea of obtaining valid inequalities for a 0-1 model from a 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 alldiff 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 cyclic structures and show that they are stronger than known cuts. For example, when an existing separation algorithm identifies odd hole cuts, we can supply stronger cuts with no additional calculation. In addition, we generalize odd hole cuts to odd cycle cuts that are stronger than any collection of odd hole cuts.