A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Tree clustering for constraint networks (research note)
Artificial Intelligence
Characterising tractable constraints
Artificial Intelligence
On the minimality and global consistency of row-convex constraint networks
Journal of the ACM (JACM)
Tractable constraints on ordered domains
Artificial Intelligence
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Fundamental properties of neighbourhood substitution in constraint satisfaction problems
Artificial Intelligence
Constraint tightness and looseness versus local and global consistency
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The Brélaz Heuristic and Optimal Static Orderings
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Neighborhood-Based Variable Ordering Heuristics for the Constraint Satisfaction Problem
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
Typed guarded decompositions for constraint satisfaction
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
A new hybrid tractable class of soft constraint problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Hybrid tractability of valued constraint problems
Artificial Intelligence
On guaranteeing polynomially bounded search tree size
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
A characterisation of the complexity of forbidding subproblems in binary Max-CSP
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
The tractability of CSP classes defined by forbidden patterns
Journal of Artificial Intelligence Research
Many-to-many interchangeable sets of values in CSPs
Proceedings of the 28th Annual ACM Symposium on Applied Computing
Eliminating redundancy in CSPs through merging and subsumption of domain values
ACM SIGAPP Applied Computing Review
Variable elimination in binary CSP via forbidden patterns
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The Constraint Satisfaction Problem (CSP) is a central generic problem in artificial intelligence. Considerable progress has been made in identifying properties which ensure tractability in such problems, such as the property of being tree-structured. In this paper we introduce the broken-triangle property, which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure. We show that the broken-triangle property is conservative (i.e., it is preserved under domain reduction and hence under arc consistency operations) and that there is a polynomial-time algorithm to determine an ordering of the variables for which the broken-triangle property holds (or to determine that no such ordering exists). We also present a non-conservative extension of the broken-triangle property which is also sufficient to ensure tractability and can also be detected in polynomial time. We show that both the broken-triangle property and its extension can be used to eliminate variables, and that both of these properties provide the basis for preprocessing procedures that yield unique closures orthogonal to value elimination by enforcement of consistency. Finally, we also discuss the possibility of using the broken-triangle property in variable-ordering heuristics.