A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Constraint propagation algorithms for temporal reasoning: a revised report
Readings in qualitative reasoning about physical systems
From local to global consistency
Proceedings of the eighth biennial conference of the Canadian Society for Computational Studies of Intelligence on CSCSI-90
Artificial Intelligence - Special issue on knowledge representation
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Synthesizing constraint expressions
Communications of the ACM
Structural disambiguation with constraint propagation
ACL '90 Proceedings of the 28th annual meeting on Association for Computational Linguistics
The complexity of recognizing polyhedral scenes
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Approximation algorithms for temporal reasoning
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
An efficient arc consistency algorithm for a class of CSP problems
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Directed constraint networks: a relational framework for causal modeling
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 2
Journal of Computer and System Sciences
Constraints, consistency and closure
Artificial Intelligence
Topological reasoning between complex regions in databases with frequent updates
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Journal of Artificial Intelligence Research
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Constraint networks have been shown to be useful in formulating such diverse problems as scene labeling, natural language parsing, and temporal reasoning. Given a constraint network, we often wish to (i) find a solution that satisfies the constraints and (ii) find the corresponding minimal network where the constraints are as explicit as possible. Both tasks are known to be NP-complete in the general case. Task (i) is usually solved using a backtracking algorithm, and task (ii) is often solved only approximately by enforcing various levels of local consistency. In this paper, we identify a property of binary constraints called row convexity and show its usefulness in deciding when a form of local consistency called path consistency is sufficient to guarantee a network is both minimal and decomposable. Decomposable networks have the property that a solution can be found without backtracking. We show that the row convexity property can be tested for efficiently and we show, by examining applications of constraint networks discussed in the literature, that our results are useful in practice. Thus, we identify a large class of constraint networks for which we can solve both tasks (i) and (ii) efficiently.