## Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORD-Horn Class (1997)

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Venue: | Constraints |

Citations: | 64 - 6 self |

### BibTeX

@ARTICLE{Nebel97solvinghard,

author = {Bernhard Nebel},

title = {Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORD-Horn Class},

journal = {Constraints},

year = {1997},

volume = {1}

}

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### Abstract

While the worst-case 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 attention. In this paper, we will demonstrate that using the ORD-Horn 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 is complete when using the ORD-Horn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORD-Horn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm. Contents 1 Introduction 1 2 Allen's...

### Citations

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698 | A New Method for Solving Hard Satisfiability Problems - Selman, Levesque, et al. - 1996 |

603 | Where the really hard problems are - Cheeseman, Kanefsky, et al. - 1991 |

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171 | Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen’s Interval Algebra - Nebel, Bürckert - 1995 |

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- Allen, Koomen
- 1983
(Show Context)
Citation Context ...l evaluation 1. Introduction Representation of qualitative temporal information and reasoning with it is an integral part of many artificial intelligence tasks, such as general planning (Allen, 1991; =-=Allen and Koomen, 1983), p-=-resentation planning in a multi-media context (Feiner et al., 1993), natural language understanding (Song and Cohen, 1988), and diagnosis of technical systems (N��okel, 1991). Allen's (1983) inter... |

90 | Complexity and Algorithms for Reasoning about Time: A Graph-Theoretic Approach - Golumbic, Shamir - 1993 |

90 | On binary constraint problems - Ladkin, Maddux - 1994 |

82 | Exatt and Approximate Reasoning about Temporal Relations - Beck, Cohen |

78 | On the topography of the genetic fine structure - Benzer - 1961 |

58 | Temporal reasoning and planning - Allen - 1991 |

48 | The Design and Experimental Analysis of Algorithms for Temporal Reasoning - Beek, Manchak - 1996 |

42 |
Effective Solution d Qualitative Interval Constraint Problems
- Ladkin, A
- 1992
(Show Context)
Citation Context ... procedure "path-consistency" transforms a matrix C to b C . The set Split is a subset of A such that path-consistency is complete for ISAT. The algorithm deviates slightly from the one publ=-=ished in (Ladkin and Reinefeld, 1992-=-) in that it makes the choice of the constraint to be processed next nondeterministic, but is otherwise identical. When the algorithm is implemented, a number of design choices are necessary that can ... |

31 |
Increasing tree search e ciency for constraint satisfaction problems
- Haralick, Elliot
- 1980
(Show Context)
Citation Context ... the full calculus, but complete for atomic relations. A more e cient algorithm has been proposed by Ladkin and Reinefeld (1992). This algorithm uses path-consistency as a forward checking technique (=-=Haralick and Elliot, 1980-=-) during the backtrack search, which results in pruning the search tree signi cantly. 2 As pointed out by Ladkin and Reinefeld (1992), this algorithm allows the instantiation of disjunctive relations ... |

30 | Efficient Temporal Reasoning through Timegraphs - Gerevini, Schubert |

25 | Temporarily Distributed Symptoms in Technical Diagnosis - Nokel - 1991 |

23 | The hardest random SAT problems, in - Gent, Walsh - 1994 |

23 | The interpretation of temporal relations in narrative - Song, Cohen - 1988 |

11 | A symbolic approach to interval constraint problems - Ladkin, Reinefeld - 1993 |

10 | Towards coordinated temporal multimedia presentations - Feiner, Litman, et al. - 1993 |

7 | Ladkin and Alexander Reinefeld. Effective solution of qualitative interval constraint problems - Peter - 1992 |

5 | Temporally Distributed Symptoms - Nokel - 1991 |

1 |
Networks of qualitative interval relations: combining circuit consistency and path consistency in the search for a solution
- Isli, Bennaceur
- 1996
(Show Context)
Citation Context ...iburg.de as /pub/documents/papers/ki/allen-csp-solving.programs.tar.gz. 2. A weaker, but more efficient forward-checking technique, called circuit-consistency has been proposed by Isli and Bennaceur (=-=Isli and Bennaceur, 1996-=-). This leads to the exploration of more search nodes, but each forward-check is faster. 3. Note that we obtain a relation algebra if we add complement and union as operations (Ladkin and Maddux, 1994... |

1 |
On the topology of the genetic ne structure
- Benzer
- 1959
(Show Context)
Citation Context ...rk" instances, lead to the same behavior of the backtracking algorithm regardless of whether we use the pointizable subclass or the ORD-Horn class. The DNA sequencing instance from molecular biology (=-=Benzer, 1959-=-) that has been suggested by van Beek and Manchak (1996) is unfortunately not adequate for our purposes because the structure of constraints leads to identical results for P and H (van Beek and Mancha... |