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124
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
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
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
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
A LinearProgramming Approach to Temporal Reasoning
 IN PROCEEDINGS OF AAAI96
, 1996
"... We present a new formalism, Horn Disjunctive Linear Relations (Horn DLRs), for reasoning about temporal constraints. We prove that deciding satisfiability of sets of Horn DLRs is polynomial by exhibiting an algorithm based upon linear programming. Furthermore, we prove that most other approache ..."
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Cited by 26 (6 self)
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We present a new formalism, Horn Disjunctive Linear Relations (Horn DLRs), for reasoning about temporal constraints. We prove that deciding satisfiability of sets of Horn DLRs is polynomial by exhibiting an algorithm based upon linear programming. Furthermore, we prove that most other
A fast algorithm and lower bound for temporal reasoning
"... We introduce two new tractable temporal constraint languages, which both strictly contain the class OrdHorn of Bürkert and Nebel. The presented algorithms decide whether a given set of constraints from these languages is consistent in time that is quadratic in the input size; this also yields a new ..."
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Cited by 2 (2 self)
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new algorithm for OrdHorn constraints, where the best known algorithms also have quadratic running time. We also prove that the two languages are maximally tractable, i.e., if we add a new temporal relation to one of these constraint languages, the corresponding constraint satisfaction problem
A Unifying Approach to Temporal Constraint Reasoning
 Artificial Intelligence
"... We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs ..."
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Cited by 37 (10 self)
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DLRs, which have a polynomialtime satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORDHorn algebra by Nebel and Burckert and the simple temporal constraints by Dechter et al. Thus, DLRs is a suitable
On finding a solution in temporal constraint satisfaction problems
 In Proceedings of IJCAI97
, 1997
"... Computing a consistent interpretation of the variables involved in a set of temporal constraints is an important task for many areas of AI requiring temporal reasoning. We focus on the important classes of the qualitative relations in Nebel and Biirckert's ORDHorn algebra, and of the metric co ..."
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Cited by 10 (0 self)
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Computing a consistent interpretation of the variables involved in a set of temporal constraints is an important task for many areas of AI requiring temporal reasoning. We focus on the important classes of the qualitative relations in Nebel and Biirckert's ORDHorn algebra, and of the metric
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
Results 1  10
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124