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118
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 195 (8 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
Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORDHorn Class
 Constraints
, 1997
"... While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attent ..."
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Cited by 68 (6 self)
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attention. In this paper, we will demonstrate that using the ORDHorn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm
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
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 9 (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
RCC5 and its Tractable Subclasses
, 1996
"... We investigate the computational properties of the spatial algebra RCC5 which is a restricted version of the RCC framework. The satisfiability problem for RCC5 is known to be NPcomplete but not much is known about its approximately four billion subclasses. We provide a complete classification of ..."
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We investigate the computational properties of the spatial algebra RCC5 which is a restricted version of the RCC framework. The satisfiability problem for RCC5 is known to be NPcomplete but not much is known about its approximately four billion subclasses. We provide a complete classification
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 52 (3 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
A New Tractable Subclass of the Rectangle Algebra
 PROCEEDINGS OF THE 16TH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1999
"... This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak pre ..."
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Cited by 17 (1 self)
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This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak preconvexity and strong preconvexity. It introduces afterwards the fundamental operations of intersection, composition and inversion and demonstrates that the concept of weak preconvexity is preserved by the operation of composition whereas the concept of strong preconvexity is preserved by the operation of intersection. Finally, fitting the propagation techniques conceived to solve interval networks, it shows that the polynomial pathconsistency algorithm is a decision method for the problem of proving the consistency of strongly preconvex rectangle networks.
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
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