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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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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. A well
A Tractable Subclass of Fuzzy Constraint Networks
"... Abstract. The Fuzzy Constraint Networks model, a generalization of the Disjunctive Temporal Fuzzy Constraint Networks, is a framework that allows representing and reasoning with fuzzy qualitative and quantitative complex constraints. However, its general complexity is exponential, and we need to fin ..."
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to find tractable subclasses. In this paper we propose two algorithms to deal with a tractable subclass named SeriesParallel Fuzzy Constraint Networks. 1
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.
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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. Another, computational, advantage of a globally consistent network is that finding a solution can be done in a backtrackfree manner. In this paper, we propose two new subclasses of the interval algebra for which pathconsistency is sufficient to ensure global consistency, i.e. pathconsistency applied
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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. Another, computational, advantage of a globally consistent network is that finding a solution can be done in a backtrackfree manner. In this paper, we propose two new subclasses of the interval algebra for which pathconsistency is sufficient to ensure global consistency, i.e. pathconsistency applied
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
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
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
Exploiting Bipartiteness to Identify Yet Another Tractable Subclass of CSP
 PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING—CP’99, VOLUME 1713 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1999
"... The class of constraint satisfaction problems (CSPs) over finite domains has been shown to be NPcomplete, but many tractable subclasses have been identified in the literature. In this paper we are interested in restrictions on the types of constraint relations in CSP instances. By a result of Je ..."
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Cited by 1 (0 self)
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The class of constraint satisfaction problems (CSPs) over finite domains has been shown to be NPcomplete, but many tractable subclasses have been identified in the literature. In this paper we are interested in restrictions on the types of constraint relations in CSP instances. By a result
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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is sufficient for deciding satisfiability. Further, using an extensive machinegenerated case analysis, we show that the ORDHorn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain
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