Skip to main content
SpringerLink
Log in

Approaches to the incremental detection of implicit equalities with the revised simplex method

  • Conference paper
  • First Online:
Principles of Declarative Programming (ALP 1998, PLILP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1490))

Abstract

This paper deals with the incremental detection of implicit equalities using the revised simplex method. This algorithm is more efficient and more suitable to practical problems than the tableau method usually applied in constraint logic programming. We describe and discuss the adaptation to the revised simplex of three approaches: the CLP (R), the Prolog III, and the quasi-dual one. All of these have been integrated into the constraint logic programming language Athena based on a revised simplex method over exact-precision rationals. This system is used to compare these methods on a set of typical CLP problems over linear constraints.

A part of this work was done when the author was in Laboratoire d'informatique de Marseille, Faculte des sciences de Luminy, 13009 Marseille — France

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ilog Planner, User Manual. ILOG, S.A., Paris, France, November 1996.

    Google Scholar 

  2. Frédéric Benhamou and TouraÏvane. Prolog IV: langage et algorithmes. In JFPL'95: IVèmes Journées Francophones de Programmation en Logique, pages 51–65, Dijon, France, 1995. Teknea.

    Google Scholar 

  3. H. Beringer and B. de Backer. Combinatorial problem solving in constraint logic programming with cooperating solvers. In Logic Programming: Formal Methods and Practical Applications. Elsevier Science Publishers, 1994.

    Google Scholar 

  4. D. Bertsimas and J. N. Tsitsiklis. Introduction to Linear Optimization. Athena Scientific, Belmont, Massachusetts, 1997.

    Google Scholar 

  5. V. Chvatal. Linear Programming. W.H. Freeman and Company, New York, 1983.

    Google Scholar 

  6. A. Colmerauer. An introduction to Prolog III. Communications of the ACM, 33(7):69–91, July 1990.

    Article  Google Scholar 

  7. A. Colmerauer. Naive resolution of non-linear constraints. In Frederic Benhamou and Alain Colmerauer, editors, Constraint Logic Programming: Selected Research, pages 89–112. MIT Press, 1993.

    Google Scholar 

  8. A. Colmerauer. Spécifications de Prolog IV. Technical report, Laboratoire d'Informatique de Marseille, 1996.

    Google Scholar 

  9. Michel Henrion. Les algorithmes numériques de Prolog III. Technical report, Prologia, 1989.

    Google Scholar 

  10. C. Holzbaur. A specialized incremental solved form algorithm for systems of linear inequalities. Technical Report TR-94-07, Austrian Research Institute for Artificial Intelligence, Vienna, 1994.

    Google Scholar 

  11. J.-L. Imbert and P. van Hentenryck. On the handling of disequations in CLP over linear rational arithmetic. In Frederic Benhamou and Alain Colmerauer, editors, Constraint Logic Programming: Selected Research, pages 49–72. MIT Press, 1993.

    Google Scholar 

  12. J. Jaffar, S. Michaylov, P. Stuckey, and R.H.C. Yap. The CLP(R) language and system. Transactions on Programming Languages and Systems, 14(3), July 1992.

    Google Scholar 

  13. J-L Lassez. Parametric queries, linear constraints and variable elimination. In DISCO 90, LNCS 429, pages 164–173. Springer-Verlag Lecture Notes in Computer Science, 1990.

    Google Scholar 

  14. J-L Lassez. Querying constraints. In Proceedings of the ACM Conference on Principles of Database Systems, Nashville, 1990.

    Google Scholar 

  15. J-L Lassez and K. McAloon. A canonical form for generalised linear constraints. Journal of Symbolic Computation, (1):1–24, 1992.

    Google Scholar 

  16. P. Refalo. Resolution et implication de contraintes lineaires en programmation logique par constraintes. Ph.D Thesis. Laboratoire d'informatique de Marseille, Marseille, 1997.

    Google Scholar 

  17. P. Refalo and P. van Hentenryck. CLP(R lin) revised. In Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 1–14, Bonn, Germany, 1996.

    Google Scholar 

  18. P. J. Stuckey. Incremental linear constraint solving and implicit equalities. ORSA Journal of Computing, 3(4):269–274, 1991.

    MATH  Google Scholar 

  19. J. Telgen. Redundancy and Linear Programs. Mathematical Centre Tracts, 1981. number 137.

    Google Scholar 

  20. P. van Hentenryck and T. Graf. Standard forms for rational linear arithmetics in constraint logic programming. In The International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida, January 1990.

    Google Scholar 

  21. P. van Hentenryck and V. Ramachandran. Backtracking without trailling in CLP(R lin). ACM Transaction on Programming Langages and Systems, 1(1):0–0, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ILOG, S.A., 9 rue de Verdun, BP 85, 94253, Gentilly, France

    Philippe Refalo

Authors
  1. Philippe Refalo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Catuscia Palamidessi Hugh Glaser Karl Meinke

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Refalo, P. (1998). Approaches to the incremental detection of implicit equalities with the revised simplex method. In: Palamidessi, C., Glaser, H., Meinke, K. (eds) Principles of Declarative Programming. ALP PLILP 1998 1998. Lecture Notes in Computer Science, vol 1490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056634

Download citation

  • DOI: https://doi.org/10.1007/BFb0056634

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65012-6

  • Online ISBN: 978-3-540-49766-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation