Fast parallel constraint satisfaction
Artificial Intelligence
Journal of the ACM (JACM)
Characterising tractable constraints
Artificial Intelligence
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
On the minimality and global consistency of row-convex constraint networks
Journal of the ACM (JACM)
Tractable constraints on ordered domains
Artificial Intelligence
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
On the algebraic structure of combinatorial problems
Theoretical Computer Science
The complexity of maximal constraint languages
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Exploiting Bipartiteness to Identify Yet Another Tractable Subclass of CSP
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Closure Functions and Width 1 Problems
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
A Unifying Framework for Tractable Constraints
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Domain permutation reduction for constraint satisfaction problems
Artificial Intelligence
Representing and solving finite-domain constraint problems using systems of polynomials
Annals of Mathematics and Artificial Intelligence
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The question of determining which sets of constraints give rise to NP-complete problems, and which give rise to tractable problems, is an important open problem in the theory of constraint satisfaction. It has been shown in previous papers that certain sufficient conditions for tractability and NP-completeness can be identified using algebraic properties of relations, and that these conditions can be tested by solving a particular form of constraint satisfaction problem (the so-called indicator problem).This paper describes a program which can solve the relevant indicator problems for arbitrary sets of constraints over small domains, and for some sets of constraints over larger domains. The main innovation in the program is its ability to deal with the many symmetries present in the problem; it also has the ability to preserve symmetries in cases where this speeds up the solution.Using this program, we have systematically investigated the complexity of all individual binary relations over a domain of size four or less, and of all individual ternary relations over a domain of size three or less. This automated analysis includes the derivation of more than 450 000 new NP-completeness results, and precisely identifies the small set of individual relations which cannot be classified as either tractable or NP-complete using the algebraic conditions presented in previous papers.