Skip to main content
Springer Nature Link
Log in

Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class

  • Published:
Constraints Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Allen, J. F., & Koomen, J. A. (1983). Planning using a temporal world model. In Proceedings of the 8th International Joint Conference on Artificial Intelligence (IJCAI-83), pages 741–747.

  2. Allen, J. F. (1983). Maintaining knowledge about temporal intervals. In Communications of the ACM 26(11):832–843.

    Google Scholar 

  3. Allen, J. F. (1991). Temporal reasoning and planning. In J. F. Allen, H. A. Kautz, R. N. Pelavin, and J. D. Tenenberg, editors, Reasoning about Plans, pages 1–67, Morgan Kaufmann.

  4. Benzer, S. (1959). On the topology of the genetic fine structure. In Proc. Nat. Acad. Sci. USA 45:1607–1620.

    Google Scholar 

  5. Cheeseman, P., Kanefsky, B., & Taylor, W. M. (1991). Where the really hard problems are. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), pages 331–337.

  6. Feiner, S. K., Litman, D. J., McKeown, K. R., & Passonneau, R. J. (1993). Towards coordinated temporal multimedia presentation. In M. Maybury, editor, Intelligent Multi Media. AAAI Press.

  7. Gent, I. P., & Walsh, T. (1994). The hardest random SAT problems. In B. Nebel and L. Dreschler-Fischer, editors, KI-94: Advances in Artificial Intelligence, pages 355–366, Springer-Verlag.

  8. Gerevini, A., & Schubert, L. (1993). Efficient temporal reasoning through timegraphs. In Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), pages 648–654.

  9. Golumbic, M. C., & Shamir, R. (1993). Complexity and algorithms for reasoning about time: A graphtheoretic approach. In Journal of the Association for Computing Machinery 40(5):1128–1133.

    Google Scholar 

  10. Haralick, R. M., & Elliot, G. L. (1980). Increasing tree search efficiency for constraint satisfaction problems. In Artificial Intelligence 14:263–313.

    Google Scholar 

  11. Isli, A., & Bennaceur, H. (1996). Networks of qualitative interval relations: Combining circuit consistency and path consistency in the search for a solution. In Proceedings of Third International Workshop on Temporal Representation and Reasoning.

  12. Ladkin, P. B., & Maddux, R. (1994). On binary constraint problems. In Journal of the Association for Computing Machinery 41(3):435–469.

    Google Scholar 

  13. Ladkin, P. B., & Reinefeld, A. (1992). Effective solution of qualitative interval constraint problems. In Artificial Intelligence 57(1):105–124.

    Google Scholar 

  14. Ladkin, P. B., & Reinefeld, A. (1993). A symbolic approach to interval constraint problems. In J. Calmet and J. A. Campbell, editors, Artificial Intelligence and Symbolic Mathematical Computing, volume 737 of Lecture Notes in Computer Science, pages 65–84, Springer-Verlag.

  15. Montanari, U. (1974). Networks of constraints: Fundamental properties and applications to picture processing. In Information Science 7:95–132.

    Google Scholar 

  16. Nebel, B., & Bürckert, H-J. (1995). Reasoning about temporal relations: A maximal tractable subclass of Allen's interval algebra. In Journal of the Association for Computing Machinery 42(1):43–66.

    Google Scholar 

  17. Nökel, K. (1991). Temporally Distributed Symptoms in Technical Diagnosis, Volume 517 of Lecture Notes in Artificial Intelligence. Springer-Verlag.

  18. Selman, B., Levesque, H. J., & Mitchell, D. (1992). A new method for solving hard satisfiability problems. In Proceedings of the 10th National Conference of the American Association for Artificial Intelligence (AAAI-92), pages 440–446.

  19. Song, F., & Cohen, R. (1988). The interpretation of temporal relations in narrative. In Proceedings of the 7th National Conference of the American Association for Artificial Intelligence (AAAI-88), pages 745–750.

  20. van Beek, P., & Cohen, R. (1990). Exact and approximate reasoning about temporal relations. In Computational Intelligence 6:132–144.

    Google Scholar 

  21. van Beek, P., & Manchak, D. W. (1996). The design and experimental analysis of algorithms for temporal reasoning. In Journal of Artificial Intelligence Research 4:1–18.

    Google Scholar 

  22. Vilain, M. B., & Kautz, H. A. (1986). Constraint propagation algorithms for temporal reasoning. In Proceedings of the 5th National Conference of the American Association for Artificial Intelligence (AAAI-86), pages 377–382.

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Albert-Ludwigs-Universität Freiburg, Am Flughafen 17, D-79110, Freiburg, Germany

    Bernhard Nebel

Authors
  1. Bernhard Nebel
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nebel, B. Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class. Constraints 1, 175–190 (1997). https://doi.org/10.1007/BF00137869

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00137869

Keywords