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
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References
Ilog Planner, User Manual. ILOG, S.A., Paris, France, November 1996.
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.
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.
D. Bertsimas and J. N. Tsitsiklis. Introduction to Linear Optimization. Athena Scientific, Belmont, Massachusetts, 1997.
V. Chvatal. Linear Programming. W.H. Freeman and Company, New York, 1983.
A. Colmerauer. An introduction to Prolog III. Communications of the ACM, 33(7):69–91, July 1990.
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.
A. Colmerauer. Spécifications de Prolog IV. Technical report, Laboratoire d'Informatique de Marseille, 1996.
Michel Henrion. Les algorithmes numériques de Prolog III. Technical report, Prologia, 1989.
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.
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.
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.
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.
J-L Lassez. Querying constraints. In Proceedings of the ACM Conference on Principles of Database Systems, Nashville, 1990.
J-L Lassez and K. McAloon. A canonical form for generalised linear constraints. Journal of Symbolic Computation, (1):1–24, 1992.
P. Refalo. Resolution et implication de contraintes lineaires en programmation logique par constraintes. Ph.D Thesis. Laboratoire d'informatique de Marseille, Marseille, 1997.
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.
P. J. Stuckey. Incremental linear constraint solving and implicit equalities. ORSA Journal of Computing, 3(4):269–274, 1991.
J. Telgen. Redundancy and Linear Programs. Mathematical Centre Tracts, 1981. number 137.
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.
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.
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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
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DOI: https://doi.org/10.1007/BFb0056634
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