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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 ..."
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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
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
Tractable Disjunctions of Linear Constraints: Basic Results and Applications to Temporal Reasoning
 Theoretical Computer Science
, 1996
"... We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez an ..."
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Cited by 50 (4 self)
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algorithms for the OrdHorn subclass of Allen's interval formalism. We also show that there is no low level of local consistency that can guarantee global consistency for the OrdHorn subclass. This property distinguishes the OrdHorn subclass from the pointizable subclass (for which strong 5
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 ..."
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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
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 ..."
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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
Global Consistency in Interval Algebra Networks: Tractable Subclasses
 In Proc. ECAI'96
, 1996
"... . Global consistency is an important property in binary constraint satisfaction problems. It implies minimality in the sense that the edges contain all and only the labels that can participate in a global solution, which, for instance, is an important property in querying temporal knowledge bases. A ..."
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Cited by 11 (0 self)
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to any network expressed in either of the two subclasses leads to a globally consistent network. One of the two subclasses covers more than 60% of the ORDHorn subclass. Keywords: Complexity of Reasoning, ConstraintBased Reasoning, Temporal Reasoning. 1 INTRODUCTION Representing and reasoning about
Global Consistency in Interval Algebra Networks: Tractable Subclasses
 In Proc. ECAI'96
, 1996
"... . Global consistency is an important property in binary constraint satisfaction problems. It implies minimality in the sense that the edges contain all and only the labels that can participate in a global solution, which, for instance, is an important property in querying temporal knowledge bases. A ..."
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to any network expressed in either of the two subclasses leads to a globally consistent network. One of the two subclasses covers more than 60% of the ORDHorn subclass. Keywords: Complexity of Reasoning, ConstraintBased Reasoning, Temporal Reasoning. 1 INTRODUCTION Representing and reasoning about
Tractable Disjunctions of Linear Constraints
 Theoretical Computer Science
, 1996
"... We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and inequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and ..."
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reasoning algorithms for the OrdHorn subclass of Allen's interval formalism. This answers an open question posed by Nebel and Burckert. 1 Introduction Linear constraints over the reals have recently been studied in depth by researchers in constraint logic programming (CLP) and constraint databases
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
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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the remaining fifteen subclasses become NPcomplete even if we restrict ourselves to the case of fixed lengths on the durations. We also consider the scheduling problem and the main result is that ORDHorn is the only known maximal subclass for which the scheduling problem is tractable. This extends previous