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Backtracking Algorithms for Disjunctions of Temporal Constraints
 Artificial Intelligence
, 1998
"... We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. W ..."
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Cited by 118 (2 self)
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We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints. We have partially ordered those algorithms according to the number of visited search nodes and the number of performed consistency checks. Finally, we have carried out a series of experimental results on the location of the hard region. The results show that hard problems occur at a critical value of the ratio of disjunctions to variables. This value is between 6 and 7. Introduction Reasoning with temporal constraints has been a hot research topic for the last fifteen years. The importance of this problem has been demonstrated in many areas of artifici...
A Complete Classification of Tractability in RCC5
 Journal of Artificial Intelligence Research
, 1997
"... We investigate the computational properties of the spatial algebra RCC5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC5 is known to be NPcomplete but not much is known about its approximately four billion subclasses. We provide a compl ..."
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Cited by 29 (7 self)
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We investigate the computational properties of the spatial algebra RCC5 which is a restricted version of the RCC framework for spatial reasoning. 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 satisfiability for all these subclasses into polynomial and NPcomplete respectively. In the process, we identify all maximal tractable subalgebras which are four in total. 1. Introduction Qualitative spatial reasoning has received a constantly increasing amount of interest in the literature. The main reason for this is, probably, that spatial reasoning has proved to be applicable to realworld problems in, for example, geographical database systems (Egenhofer, 1991; Grigni, Papadias, & Papadimitriou, 1995) and molecular biology (Cui, 1994). In both these applications, the size of the problem instances can be huge, so the complexity of problems and algorithms is a highly...
Temporal Representation and Reasoning in Artificial Intelligence: Issues and Approaches
, 2002
"... this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application ..."
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Cited by 27 (1 self)
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this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application
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, some of them subsuming previously reported tractable algebras. The algebras allow for metric temporal constraints on interval starting or ending points, using the recent framework of Horn DLRs. Two of the algebras can express the notion of sequentiality between intervals, being the first such algebras admitting both qualitative and metric time. 91 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [ Allen, 1991 ] , natural language understanding [ Song and Cohen, 1988 ] and molecular biology [ Benzer, 1959; Golumbic and Shamir, 1993 ] . However, since even the restricted problem of reasoning with pure qualitative ti...
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 are identified, whose maximality is not decided. Four of them can express the notion of sequentiality between intervals, which is not possible in the ORDHorn algebra. All of the algebras are considerably larger than the ORDHorn subclass. The satisfiability algorithm, which is common for all the algebras, is shown to be linear. Furthermore, the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras.
Reasoning about Action in Polynomial Time
, 1997
"... Although many formalisms for reasoning about action exist, surprisingly few approaches have taken computational complexity into consideration. The contributions of this paper are the following: a temporal logic with a restriction for which deciding satisfiability is tractable, a tractable extension ..."
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Cited by 10 (2 self)
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Although many formalisms for reasoning about action exist, surprisingly few approaches have taken computational complexity into consideration. The contributions of this paper are the following: a temporal logic with a restriction for which deciding satisfiability is tractable, a tractable extension for reasoning about action, and NPcompleteness results for the unrestricted problems. Many interesting reasoning problems can be modelled, involving nondeterminism, concurrency and memory of actions. The reasoning process is proved to be sound and complete. 145 1 Introduction Although many formalisms for reasoning about action exist, surprisingly few approaches have taken computational complexity into consideration. One explanation for this might be that many interesting AI problems are (at least) NPhard, and that tractable subproblems that are easily extracted, tend to lack expressiveness. This has led a large part of the AI community to rely on heuristics and incomplete systems to s...
Algorithms and Complexity for Temporal and Spatial Formalisms
, 1997
"... The problem of computing with temporal information was early recognised within the area of artificial intelligence, most notably the temporal interval algebra by Allen has become a widely used formalism for representing and computing with qualitative knowledge about relations between temporal interv ..."
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Cited by 3 (2 self)
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The problem of computing with temporal information was early recognised within the area of artificial intelligence, most notably the temporal interval algebra by Allen has become a widely used formalism for representing and computing with qualitative knowledge about relations between temporal intervals. However, the computational properties of the algebra and related formalisms are known to be bad: most problems (like satisfiability) are NPhard. This thesis contributes to finding restrictions (as weak as possible) on Allen's algebra and related temporal formalisms (the pointinterval algebra and extensions of Allen's algebra for metric time) for which the satisfiability problem can be computed in polynomial time. Another research area utilising temporal information is that of reasoning about action, which treats the problem of drawing conclusions based on the knowledge about actions having been performed at certain time points (this amounts to solving the infamous frame problem). One ...
Satisfiability in Nonlinear Time: Algorithms and Complexity
 in: Proceedings of the Florida Artificial Intelligence Research Society conference
, 1999
"... rrodriguQnsLgov Most work on temporal interval relations and associated automated reasoning methods assumes linear (totally ordered) time. Although checking the consistency of temporal interval constraint networks is known to be NPhard in general, many tractable subclasses of lineartime temporal ..."
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Cited by 3 (0 self)
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rrodriguQnsLgov Most work on temporal interval relations and associated automated reasoning methods assumes linear (totally ordered) time. Although checking the consistency of temporal interval constraint networks is known to be NPhard in general, many tractable subclasses of lineartime temporal relations are known for which a standard O(ns) constraint propagation algorithm actually determines the global consistency. In the very special case in which the relations are all ~pointizable, " meaning that the network can be replaced by an equivalent point constraint network (on the start and finish points of the intervals), an O(n21 algorithm to check consistency exists. This paper explores the situation in nonlinear temporal models, showing that the familiar results no longer pertain. In particular, the paper shows that for networks of point relations in partially ordered time, the usual constraint propagation approach does not determine global consistency, although for the branching time model, the question remains open. Nonetheless, the paper presents an O(na) algorithm for consistency of a significant subset of the pointizable temporal interval relations in a general partially ordered time model. Beyond checking consistency, for the consistent case the algorithm produces am example scenario satisfying all the given constraints. The latter result benefits planning applications, where actual quantitative values cam be assigned to the intervals.
A Comparison of PointBased Approaches to Qualitative Temporal Reasoning
 In Proceedings of the AAAI National Conference on Artificial Intelligence
, 1999
"... We address the problem of implementing general, qualitative, pointbased temporal reasoning. Given a database of assertions concerning relative occurrences of points in time, we are interested in various operations on this database, including compiling the assertions into a representation that su ..."
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Cited by 3 (0 self)
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We address the problem of implementing general, qualitative, pointbased temporal reasoning. Given a database of assertions concerning relative occurrences of points in time, we are interested in various operations on this database, including compiling the assertions into a representation that supports efficient reasoning, determining whether a database is consistent, and computing the strongest entailed relation between two points. We begin by specifying a set of operations and their corresponding algorithms, applicable to general pointbased temporal domains. We next consider a specialpurpose reasoner, based on seriesparallel graphs, which performs very well in a temporal domain with a particular restricted structure. We discuss the notion of a metagraph, which encapsulates local structure inside metaedges and uses special purpose algorithms within such local structures, to obtain a fast general pointbased reasoner. That is, specifically, we use a very fast, seriesparallel graph reasoner to speed up general pointbased reasoning. We also analyse the TimeGraph reasoner of Gerevini and Schubert. For purposes of comparison, we have implemented four approaches: a generic pointbased reasoner, the generic pointbased reasoner with a ranking heuristic, a reasoner based on seriesparallel graphs, and a version of Gerevini and Schubert's TimeGraph reasoner. We compare these different approaches, as well as the original TimeGraphII reasoner of Gerevini and Schubert, on different data sets. We conclude that the seriesparallel graph reasoner provides the best overall performance: our results show that it dominated on domains exhibiting structure, and it degraded gracefully when conditions were less than ideal, in that it did worse than the generic appr...