Arc and path consistence revisited
Artificial Intelligence
Comments on Mohr and Henderson's path consistency algorithm
Artificial Intelligence
Arc-consistency and arc-consistency again
Artificial Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
Using inference to reduce arc consistency computation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Solution Techniques for Constraint Satisfaction Problems: Foundations
Artificial Intelligence Review
Cyclic consistency: a local reduction operation for binary valued constraints
Artificial Intelligence
Path consistency on triangulated constraint graphs
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Making AC-3 an optimal algorithm
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
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Within the framework of constraint programming, particulary concerning the Constraint Satisfaction Problems (CSPs), the techniques of preprocessing based on filtering algorithms were shown to be very important for the search phase. In particular, two filtering methods have been studied, these methods exploit two properties of local consistency: arc-and path-consistency. Concerning the arc-consistency methods, there is a linear time algorithm (in the size of the problem) which is efficient in practice (Bessière, Freuder, & Régin 1995). But the limitations of the arc-consistency algorithms requires often filtering methods with higher order like path-consistency filterings. The best path-consistency algorithm proposed is PC-6, a natural generalization of AC-6 (Bessière 1994) to path-consistency (Chmeiss & Jégou 1995)(Chmeiss 1996). Its time complexity is O(n3 d3) and its space complexity is O(n3 d2), where n is the number of variables and d is the size of domains. We have remarked that PC-6, though it is widely better than PC-4 (Han & Lee 1988), was not very efficient in practice, specialy for those classes of problems that require an important. space to be run. Therefore, we propose here a new path-consistency algorithm called PC-7, its space complexity is O(n2 d2) but its time complexity is O(n3 d4) i.e. worse than that of PC-6. However, the simplicity of PC-7 as well as the data structures used for its implementation offer really a higher performance than PC-6. Furthermore, it turns out that when the size of domains is a constant of the problems, the time complexity of PC-7 becomes, like PC-6, optimal i.e. O(n3).