A generic arc-consistency algorithm and its specializations
Artificial Intelligence
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Linear Formulation of Constraint Programming Models and Hybrid Solvers
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
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CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
The range and roots constraints: specifying counting and occurrence problems
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Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
The range constraint: algorithms and implementation
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The parameterized complexity of global constraints
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Circuit complexity and decompositions of global constraints
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Decompositions of all different, global cardinality and related constraints
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
ILP'11 Proceedings of the 21st international conference on Inductive Logic Programming
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A wide range of counting and occurrence constraints can be specified with just two global primitives: the Range constraint, which computes the range of values used by a sequence of variables, and the Roots constraint, which computes the variables mapping onto a set of values. We focus here on the Roots constraint. We show that propagating the Roots constraint completely is intractable. We therefore propose a decomposition which can be used to propagate the constraint in linear time. Interestingly, for all uses of the Roots constraint we have met, this decomposition does not destroy the global nature of the constraint as we still prune all possible values. In addition, even when the Roots constraint is intractable to propagate completely, we can enforce bound consistency in linear time simply by enforcing bound consistency on the decomposition. Finally, we show that specifying counting and occurrence constraints using Roots is effective and efficient in practice on two benchmark problems from CSPLib.