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Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
 Journal of the ACM
, 2001
"... 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 c ..."
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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 NPcomplete. 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.
Reasoning About Temporal Constraints: Classifying The Complexity In Allen's Algebra By Using An Algebraic Technique
, 2001
"... Allen's interval algebra is one of the best established formalisms for temporal reasoning. We study those fragments of Allen's algebra that contain a basic relation distinct from the equality relation. We prove that such a fragment is either NPcomplete or else contained in some already kn ..."
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Cited by 3 (0 self)
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Allen's interval algebra is one of the best established formalisms for temporal reasoning. We study those fragments of Allen's algebra that contain a basic relation distinct from the equality relation. We prove that such a fragment is either NPcomplete or else contained in some already known tractable subalgebra. We obtain this result by giving a new uniform description of known maximal tractable subalgebras and then systematically using an algebraic technique for description of maximal subalgebras with a given property. This approach avoids the need for extensive computerassisted search.
The Complexity of Constraints on Intervals and Lengths
 In Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science (STACS2002
, 2002
"... We study intervalvalued constraint satisfaction problems (CSPs), in which the aim is to find an assignment of intervals to a given set of variables subject to constraints on the relative positions of intervals. One interesting question concerning... ..."
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Cited by 2 (1 self)
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We study intervalvalued constraint satisfaction problems (CSPs), in which the aim is to find an assignment of intervals to a given set of variables subject to constraints on the relative positions of intervals. One interesting question concerning...
A Complete Classification of Complexity in Allen's Algebra
 In Proc. IJCAI01
, 2001
"... We study fragments of Allen's algebra that contain a basic relation distinct from the equality relation. ..."
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We study fragments of Allen's algebra that contain a basic relation distinct from the equality relation.