Towards a general theory of action and time
Artificial Intelligence
Artificial Intelligence
Constraint propagation algorithms for temporal reasoning: a revised report
Readings in qualitative reasoning about physical systems
Artificial Intelligence - Special issue on knowledge representation
A temporal extension of PROLOG
Journal of Logic Programming
Journal of the ACM (JACM)
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Twenty-one large tractable subclasses of Allen's algebra
Artificial Intelligence
Computational complexity of relating time points with interval
Artificial Intelligence
Tractable approximations for temporal constraint handling
Artificial Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
A relation — algebraic approach to the region connection calculus
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Determining Consistency of Topological Relations
Constraints
Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
parcPlan: A Planning Architecture with Parallel Actions, Resources and Constraints
ISMIS '94 Proceedings of the 8th International Symposium on Methodologies for Intelligent Systems
Satisfiability in Nonlinear Time: Algorithms and Complexity
Proceedings of the Twelfth International Florida Artificial Intelligence Research Society Conference
Reasoning about Binary Topological Relations
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
A complete classification of tractability in RCC-5
Journal of Artificial Intelligence Research
Maximal tractable subclasses of Allen's interval algebra: preliminary report
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Algebras of Approximating Regions
Fundamenta Informaticae - Qualitative Spatial Reasoning
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Categorical methods in qualitative reasoning: the case for weak representations
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
Datalog and constraint satisfaction with infinite templates
Journal of Computer and System Sciences
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Andréka and Maddux [Notre Dame J. Formal Logic 35 (4) 1994] classified the small relation algebras--those with at most 8 elements, or in other terms, at most 3 atomic relations. They showed that there are eighteen isomorphism types of small relation algebras, all representable. For each simple, small relation algebra they computed the spectrum of the algebra, namely the set of cardinalities of square representations of that relation algebra.In this paper we analyze the computational complexity of the problem of deciding the satisfiability of a finite set of constraints built on any small relation algebra. We give a complete classification of the complexities of the general constraint satisfaction problem for small relation algebras. For three of the small relation algebras the constraint satisfaction problem is NP-complete, for the other fifteen small relation algebras the constraint satisfaction problem has cubic (or lower) complexity.We also classify the complexity of the constraint satisfaction problem over fixed finite representations of any relation algebra. If the representation has size two or less then the complexity is cubic (or lower), but if the representation is square, finite and bigger than two then the complexity is NP-complete.