Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
From local to global consistency
Artificial Intelligence
On the minimality and global consistency of row-convex constraint networks
Journal of the ACM (JACM)
Closure properties of constraints
Journal of the ACM (JACM)
Constraint tightness and looseness versus local and global consistency
Journal of the ACM (JACM)
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Synthesizing constraint expressions
Communications of the ACM
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
Tractable tree convex constraint networks
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Consistency and set intersection
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Journal of Artificial Intelligence Research
Two hardness results on feedback vertex sets
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
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In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This approach not only simplifies the understanding of and unifies many existing consistency results, but also directs the study of consistency to that of set intersection properties in many situations, as demonstrated by the results on the convexity and tightness of constraints in this paper. Specifically, we identify a new class of tree convex constraints where local consistency ensures global consistency. This generalizes row convex constraints. Various consistency results are also obtained on constraint networks where only some, in contrast to all in the existing work, constraints are tight.