The Complexity of Constraints on Intervals and Lengths
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Point algebras for temporal reasoning: algorithms and complexity
Artificial Intelligence
Spatial and temporal reasoning: beyond Allen's calculus
AI Communications - Special issue on: Spatial and temporal reasoning
Spatial and temporal reasoning: beyond Allen's calculus
AI Communications - Spatial and Temporal Reasoning
Temporal reasoning component for real-time intelligent decision-support systems
Scientific and Technical Information Processing
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Allen''''s interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen''''s algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NP-complete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.