## Efficient Algorithms for Qualitative Reasoning about Time (1995)

Venue: | Artificial Intelligence |

Citations: | 32 - 6 self |

### BibTeX

@ARTICLE{Gerevini95efficientalgorithms,

author = {Alfonso Gerevini and Lenhart Schubert},

title = {Efficient Algorithms for Qualitative Reasoning about Time},

journal = {Artificial Intelligence},

year = {1995},

volume = {74},

pages = {207--248}

}

### OpenURL

### Abstract

Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PA-relations) and on a major extension to include binary disjunctions of PA-relations (PA-disjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PA-r...

### Citations

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Citation Context ...ther approaches based on graph algorithms have been proposed whose main characteristic is that of providing better performance in practice compared to the more traditional constraint-based approaches =-=[9, 12, 14, 15, 17, 18, 19, 28]-=-. The present paper follows a similar direction. Our goal is to efficiently manage large data sets of qualitative temporal relations including at least the pointizable relations and disjointness relat... |

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Citation Context ...oom and Allen [43] comparing the performance of Timegraph I and II with several temporal reasoning systems based on constraint propagation algorithms -- TimeLogic [23], MATS [22], Tachyon [6] and TMM =-=[9, 10]-=- -- in which the timegraph approach proved by far the most efficient for large data sets generated for the TRAINS world [1]. (TMM came closest to matching TG-II's performance, but does not handle 6= o... |

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Citation Context ...cent experiments conducted by Yampratoom and Allen [43] comparing the performance of Timegraph I and II with several temporal reasoning systems based on constraint propagation algorithms -- TimeLogic =-=[23]-=-, MATS [22], Tachyon [6] and TMM [9, 10] -- in which the timegraph approach proved by far the most efficient for large data sets generated for the TRAINS world [1]. (TMM came closest to matching TG-II... |

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Citation Context ...over 100,000 queries on 100 randomly generated timegraphs with 500 points and 4000 relations was 2.8 milliseconds. Finally, we should mention some recent experiments conducted by Yampratoom and Allen =-=[43]-=- comparing the performance of Timegraph I and II with several temporal reasoning systems based on constraint propagation algorithms -- TimeLogic [23], MATS [22], Tachyon [6] and TMM [9, 10] -- in whic... |

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Citation Context ...eated the problem quite satisfactorily. In fact, the correctness of the algorithm proposed by van Beek [37, 38] is based on a lemma whose proof as given in [39] turns out to be incorrect. However, in =-=[16]-=- we provide a new proof for the lemma which shows that van Beek's algorithm is indeed correct. In [18] the 6= relations are only partially treated as the proposed algorithms cannot derive some strict ... |

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Citation Context ...n perform a search in the set of the 2 m possible ways of choosing the disjuncts (for m disjunctions). This search is necessarily exponential in the worst case (assuming P6=NP) since, as we proved in =-=[13], the prob-=-lem of determining the consistency of a D-timegraph is NP-complete even when the allowed disjunctions are limited to "not between" relations (i.e. 3-point relations of the form xR 1 wzR 2 x,... |

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