Effective solution of qualitative interval constraint problems

Ladkin, Peter B.; Reinefeld, Alexander

doi:10.1016/0004-3702(92)90106-8

Cited by 79 publications

(39 citation statements)

References 9 publications

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“…This considerably reduces the branching factor of the search tree. Instead of splitting each relation into all of its base relations, they can be split into sub-relations contained in T [126]. The average branching factor of the resulting search tree depends on how well T splits the relations of 2 � .…”

Section: Qualitative Spatial Representation and Reasoningmentioning

confidence: 99%

Qualitative Spatial Representation and Reasoning

2002

Qualitative Spatial Reasoning With Topological Information

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Section: Qualitative Spatial Representation and Reasoningmentioning

confidence: 99%

Qualitative Spatial Representation and Reasoning

2002

Qualitative Spatial Reasoning With Topological Information

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“…Analysis has revealed [28] that whereas the path consistency determined by constraint propagation is O(n3), full consistency is an NP-hard problem. Other studies suggest that clever implementation and good heuristics can provide solutions to full consistency with close to O(n 3) performance in the vast majority of cases [16,15].…”

Section: Introductionmentioning

confidence: 99%

“…In view of the need for carrying out constraint propagation efficiently, several investigators have suggested improvements on the basic algorithm ( [1,9,16,15], among others). The most fundamental efficiency is achieved by storing the compositions of the atomic relations in a look-up table, making the processing of each pair of relations a sequence of lookups and logical (disjunction and conjunction) or set (union and intersection) operations.…”

Section: Introductionmentioning

confidence: 99%

Lattice structure of temporal interval relations

Anger

Rodríguez

1996

Appl Intell

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Due to increasing interest in representation of temporal knowledge, automation of temporal reasoning, and analysis of distributed systems, literally dozens of temporal models have been proposed and explored during the last decade. Interval-based temporal models are especially appealing when reasoning about events with temporal extent but pose special problems when deducing possible relationships among events. The paper delves deeply into the structure of the set of atomic relations in a class of temporal interval models assumed to satisfy density and homogeneity properties. An order structure is imposed on the atomic relations of a given model allowing the characterization of the compositions of atomic relations (or even lattice intervals) as lattice intervals. By allowing the utilization of lattice intervals rather than individual relations, this apparently abstract result explicitly leads to a concrete approach which speeds up constraint propagation algorithms.

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“…This direct encoding scheme for IA networks can be derived from our 1-D support encoding scheme by replacing the SUP clauses with conflict (CON) clauses. If we represent SUP clauses between a triple of intervals (i < k < j) as a 3D array of allowable values for the CSP variable X ij given the values of X ik and X kj , then the corresponding CON clauses are defined as: (10) where…”

Section: The Sat Direct Encodingmentioning

confidence: 99%

“…Existing reasoning techniques are generally based on the backtracking approach (proposed by Ladkin and Reinefeld [10]), which uses path consistency as forward checking. Although this approach has been further improved [13,20], it and its variants still rely on path consistency checking at each step to prune the search space.…”

Section: Introductionmentioning

confidence: 99%

Towards an Efficient SAT Encoding for Temporal Reasoning

Pham

Thornton

Sattar

2006

Principles and Practice of Constraint Programming - CP 2006

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Abstract. In this paper, we investigate how an IA network can be effectively encoded into the SAT domain. We propose two basic approaches to modelling an IA network as a CSP: one represents the relations between intervals as variables and the other represents the relations between end-points of intervals as variables. By combining these two approaches with three different SAT encoding schemes, we produced six encoding schemes for converting IA to SAT. These encodings were empirically studied using randomly generated IA problems of sizes ranging from 20 to 100 nodes. A general conclusion we draw from these experimental results is that encoding IA into SAT produces better results than existing approaches. Further, we observe that the phase transition region maps directly from the IA encoding to each SAT encoding, but, surprisingly, the location of the hard region varies according to the encoding scheme. Our results also show a fixed performance ranking order over the various encoding schemes.

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Effective solution of qualitative interval constraint problems

Cited by 79 publications

References 9 publications

Qualitative Spatial Representation and Reasoning

Qualitative Spatial Representation and Reasoning

Lattice structure of temporal interval relations

Towards an Efficient SAT Encoding for Temporal Reasoning

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