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49
Twentyone Large Tractable Subclasses of Allen's Algebra
 ARTIFICIAL INTELLIGENCE
, 1997
"... This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORDHorn subclass. Furthermore, twelve tractable subclasses are identifi ..."
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Cited by 23 (8 self)
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This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORDHorn subclass. Furthermore, twelve tractable subclasses
Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra
 Journal of the ACM
, 1995
"... We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient ..."
Abstract

Cited by 199 (9 self)
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We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method
Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time
, 1997
"... This paper combines two important directions of research in temporal resoning: that of finding maximal tractable subclasses of Allen's interval algebra, and that of reasoning with metric temporal information. Eight new maximal tractable subclasses of Allen's interval algebra are presented, ..."
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Cited by 26 (10 self)
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This paper combines two important directions of research in temporal resoning: that of finding maximal tractable subclasses of Allen's interval algebra, and that of reasoning with metric temporal information. Eight new maximal tractable subclasses of Allen's interval algebra are presented
Maximal Tractable Subclasses of Allen's Interval Algebra: Preliminary Report
 IN AAAI '96
, 1996
"... This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORDHorn subclass. Furthermore, twelve tractable subclasses are identifi ..."
Abstract

Cited by 20 (9 self)
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This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORDHorn subclass. Furthermore, twelve tractable subclasses
Some Observations on Durations, Scheduling and Allen's Algebra
 In Proceedings of the 6th Conference on Constraint Programming (CP'00
, 2000
"... . We continue the study of complexity issues in Allen's algebra extended for handling metric durations. The eighteen known maximal tractable subclasses are studied and we show that three of them can be extended with metric constraints on the durations without sacrificing tractability, while the ..."
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Cited by 5 (3 self)
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tractability results on scheduling in Allen's algebra since we allow far more temporal relations and we allow intervals with uncertain durations. 1 Introduction Representing and reasoning about time has for a long time been acknowledged as one of the core areas of artificial intelligence and a large
A New Proof of Tractability for OR OlWi elations
"... Abstract This paper gives an elementary proof of the tractability of a subclass of temporal relations in Allen's algebra and related temporal calculi, the class of preconvex relations. In Allen's case, this subclass coincides with the class of ORDHorn relations. Nebel and Biirckert defi ..."
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Abstract This paper gives an elementary proof of the tractability of a subclass of temporal relations in Allen's algebra and related temporal calculi, the class of preconvex relations. In Allen's case, this subclass coincides with the class of ORDHorn relations. Nebel and Biirckert
Towards a Complete Classification of Tractability in Point Algebras for Nonlinear Time
 In Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming (CP99
, 1999
"... . Efficient reasoning about temporal constraints over nonlinear time models is vital in numerous application areas, such as planning, distributed systems and cooperating agents. We identify all tractable subclasses of the point algebra for partiallyordered time and examine one large, nontrivial ..."
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Cited by 8 (3 self)
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. Efficient reasoning about temporal constraints over nonlinear time models is vital in numerous application areas, such as planning, distributed systems and cooperating agents. We identify all tractable subclasses of the point algebra for partiallyordered time and examine one large
Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis
 In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI99
, 1999
"... We present a general method for proving tractability of reasoning over disjunctions of jointly exhaustive and pairwise disjoint relations. Examples of these kinds of relations are Allen's temporal interval relations and their spatial counterpart, the RCC8 relations by Randell, Cui, and Cohn. Ap ..."
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Cited by 48 (15 self)
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of reasoning over RCC8 by identifying two large new maximal tractable subsets and show that these two subsets together with b H 8 , the already known maximal tractable subset, are the only such sets for RCC8 that contain all base relations. We also apply our method to Allen's interval algebra and derive
Reasoning about Temporal Relatio A Maximal Tractable Su of Alllen's Interval Algebra*
"... Abstract We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is ..."
Abstract
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Abstract We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method
Computational Complexity of Point Algebras for Nonlinear Time
, 2000
"... Efficient reasoning about temporal constraints over nonlinear time models is vital in numerous application areas, such as planning, distributed systems and cooperating agents. We give a total classification of tractable classes for the point algebra over partially ordered time and examine one large ..."
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Cited by 1 (1 self)
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Efficient reasoning about temporal constraints over nonlinear time models is vital in numerous application areas, such as planning, distributed systems and cooperating agents. We give a total classification of tractable classes for the point algebra over partially ordered time and examine one large
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