Network Flow Problems in Constraint Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Groups and Constraints: Symmetry Breaking during Search
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Constraint Programming Contribution to Benders Decomposition: A Case Study
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
The parameterized complexity of global constraints
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Breaking symmetries in all different problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Static and dynamic structural symmetry breaking
Annals of Mathematics and Artificial Intelligence
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Filtering algorithms for the NVALUE constraint
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Parameterized Complexity
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Lexicographic constraints are commonly used to break variable symmetries. In the general case, the number of constraint to be posted is potentially exponential in the number of variables. For injective problems (AllDiff), Puget's method[12] breaks all variable symmetries with a linear number of constraints. In this paper we assess the number of constraints for "almost" injective problems. We propose to characterize them by a parameter μ based on Global Cardinality Constraint as a generalization of the AllDiff constraint. We show that for almost injective problems, variable symmetries can be broken with no more than $\binom{n}{\mu}$ constraints which is XP in the framework of parameterized complexity. When only ν variables can take duplicated values, the number of constraints is FPT in μ and ν.