Abstract
Systems combining an interval narrowing solver and a linear programming solver can tackle constraints over the reals that none of these solvers can handle on their own. In this paper we introduce a cooperating scheme where an interval narrowing solver and a linear programming solver work concurrently. Information exchanged by the solvers is therefore handled as soon as it becomes available. Moreover, to improve the pruning, the linear programming solver computes the actual range of values of each variable with respect to the subset of linear constraints. To validate the proposed architecture a prototype system-named CCC-has been developed. Several examples are given to illustrate the gain in speed and precision we can expect with CCC.
Similar content being viewed by others
References
Benhamou, F., Mc Allester, D., and Van Hentenryck, P.: CLP (Intervals) Revisited, in: Proc. ILPS'94, MIT Press, 1994.
Benhamou, F. and Older, W.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints, Journal of Logic Programming (1994).
Beringer, H. and de Backer, B.: Combinatorial Problem Solving in Constraint Logic Programming with Cooperative Solvers, in: Beierle, C. and Plumer, L. (eds), Logic Programming: Formal Methods and Practical Applications, Elsevier Science Publishers, 1995.
Chiu, C. K. and Lee, J. H. M.: Towards Practical Interval Constraint Logic Programming, in: Proc. ILPS'94, MIT Press, 1994, pp. 109–123.
Chiu, C. K. and Lee, J.H.M.: Efficient Linear Equality Solving in Constraint Logic Programming, Research Report, Dep. of Computer Sciences, The Chinese University of Hong Hong, 1996.
Chvatal, V.: Linear Programming, W. H. Freeman and Co, 1983.
Colmerauer, A.: An Introduction to PROLOG-III, Communications of the ACM 33 (7) (1990), pp. 69–90.
Davis, E.: Constraint Propagation with Interval Labels, Artificial Intelligence 32 (1987), pp. 281–331.
Hong, H.: Confluency of Cooperative Constraint Solvers, Technical Report, Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 1994.
Jaffar, J. and Maher, M.: Constraint Logic Programming: A Survey, Journal of Logic Programming 19 (20) (1994), pp. 503–581.
Lhomme, O.: Consistency Techniques for Numeric CSPs, in: Proc. IJCAI93, Chambery, France, 1993, pp. 232–238.
Lhomme, O., Gotlieb, A., Rueher, M., and Taillibert, P.: Boosting the Interval Narrowing Algorithm, in: Proc. JICSLP'96, MIT Press, 1996, pp. 378–392.
Marti, P. and Rueher, M.: A Distributed Cooperating Constraints Solving System, Special Issue of IJAIT (International Journal on Artificial Intelligence Tools) 4 (1–2) (1995), pp. 93–113.
Older, W. and Vellino, A.: Constraint Arithmetic on Real Intervals, in: Benhamou, F. and Colmerauer, A. (eds), Constraint Logic Programming: Selected Research, MIT Press, 1993.
Podelski, A. (ed.): Constraint Programming: Basics and Trends, LNCS 910, Springer Verlag, 1995, pp. 1–21 (Châtillon-sur-Seine Spring School, France, 1994).
PrologIA. PrologIV—Constraint Inside (Handbook of PrologIV), Parc Technologique de Luminy—Case 919, 13288 Marseille cedex 09, France, 1996.
Refalo, P. and Van Hentenryck, P.: CLP(Rlin ) Revisited, in: Proc. JICSLP'96, MIT Press, 1996, pp. 22–36.
Rueher, M.: An Architecture for Cooperating Constraint Solvers on Reals, in [15].
Saraswat, V. A.: Concurrent Constraint Programming, MIT Press, 1993.
Smolka, G.: An Oz Primer, DFKI Report, http://ps-www.dfki.uni-sb.de/oz/.
Van Hentenryck, P., Mc Allester, D., and Kapur, D.: Solving Polynomial Systems Using Branch and Prune Approach, SIAM Journal, to appear.
Van Hentenryck, P., Saraswat, V. A., and Deville, Y.: Design, Implementation, and Evaluation of the Constraint Language cc(FD), in [15].
Waltz, D. L.: Generating Semantic Descriptions from Drawings of Scenes with Shadows, Tech. Report AI-TR-271, MIT Cambridge, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rueher, M., Solnon, C. Concurrent Cooperating Solvers over Reals. Reliable Computing 3, 325–333 (1997). https://doi.org/10.1023/A:1009939327927
Issue Date:
DOI: https://doi.org/10.1023/A:1009939327927