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)
Artificial Intelligence
On Forward Checking for Non-binary Constraint Satisfaction
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
The difference all-difference makes
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Problem structure in the presence of perturbations
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
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Non-binary constraints are present in many real-world constraint satisfaction problems. Certain classes of these constraints, like the all-different constraint, are "decomposable". That is, they can be represented by binary constraints on the same set of variables. For example, a non-binary all-different constraint can be decomposed into a clique of binary not-equals constraints. In this paper we make a theoretical analysis of local consistency and search algorithms for decomposable constraints. First, we prove a new lower bound for the worst-case time complexity of arc consistency on binary not-equals constraints. We show that the complexity is O(e), where e is the number of constraints, instead of O(ed), with d being the domain size, as previously known. Then, we compare theoretically local consistency and search algorithms that operate on the non-binary representation of decomposable constraints to their counterparts for the binary decomposition. We also extend previous results on arc consistency algorithms to the case of singleton arc consistency.