Arc and path consistence revisited
Artificial Intelligence
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
Characterising tractable constraints
Artificial Intelligence
On the minimality and global consistency of row-convex constraint networks
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Constraint satisfaction over connected row-convex constraints
Artificial Intelligence
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Directed constraint networks: a relational framework for causal modeling
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 2
Constraints, consistency and closure
Artificial Intelligence
Simple randomized algorithms for tractable row and tree convex constraints
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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We identify a property of constraints called smoothness, and present an extremely simple randomized algorithm for solving smooth constraints. The complexity of the algorithm is much less than the lower bound for establishing path-consistency, and because smoothness is shown to be identical to connected row-convexity (CRC) for the case of binary constraints, the time and space complexity of solving CRC constraints is improved. Central to our algorithm is the relationship of smooth constraints to random walks on directed graphs. We also provide simple deterministic algorithms to test for the smoothness of a given CSP under given domain orderings of the variables. Finally, we show that some other known tractable constraint languages, like the set of implicational constraints, and the set of binary integer linear constraints, are special cases of smooth constraints, and can therefore be solved much more efficiently than the traditional time and space complexities attached with them.