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Artificial Intelligence
Volume 139, Issue 1, July 2002, Pages 109-132
 
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doi:10.1016/S0004-3702(02)00194-7    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2002 Elsevier Science B.V. All rights reserved.

Accelerating filtering techniques for numeric CSPs

Yahia LebbahE-mail The Corresponding Author, a and Olivier LhommeCorresponding Author Contact Information, E-mail The Corresponding Author, b

a Département Informatique, Faculté des Sciences, Université d'Oran Es-Senia, B.P. 1524, El-M'Naouar Oran, Algeria b ILOG, 1681 route des Dolines, F-06560, Valbonne, France

Received 13 July 2001. 
Available online 12 March 2002.

Abstract

Search algorithms for solving Numeric CSPs (Constraint Satisfaction Problems) make an extensive use of filtering techniques. In this paper1 we show how those filtering techniques can be accelerated by discovering and exploiting some regularities during the filtering process. Two kinds of regularities are discussed, cyclic phenomena in the propagation queue and numeric regularities of the domains of the variables. We also present in this paper an attempt to unify numeric CSPs solving methods from two distinct communities, that of CSP in artificial intelligence, and that of interval analysis.

Author Keywords: Numeric constraint satisfaction problem; Filtering techniques; Propagation; Pruning; Acceleration methods; Nonlinear equations; Interval arithmetic; Interval analysis; Strong consistency; Extrapolation methods

References

1. A. Aitken , On Bernoulli's numerical solution of algebraic equations. Proc. Roy. Soc. Edinburgh 46 (1926), pp. 289–305.

2. G. Alefeld and J. Hezberger, Editors, Introduction to Interval Computations, Academic Press, New York (1983).

3. A. Babichev, O. Kadyrova, T. Kashevarova, A.S. Leshchenko and A.L. Semenov , UniCalc, A novel approach to solving systems of algebraic equations. Reliable Comput. 2 (1993), pp. 29–47.

4. F. Benhamou and L. Granvilliers , Automatic generation of numerical redundancies for non-linear constraint solving. Reliable Computing 3 3 (1997), pp. 335–344. View Record in Scopus | Cited By in Scopus (13)

5. F. Benhamou and W. Older , Applying interval arithmetic to real, integer and boolean constraints. J. Logic Programming 32 1 (1997), pp. 1–24. Abstract | PDF (1260 K) | View Record in Scopus | Cited By in Scopus (60)

6. F. Benhamou, D. McAllester and P. Van Hentenryck , CLP(intervals) revisited. In: Proc. 1994 International Logic Programming Symposium, Ithaca, NY (1994), pp. 124–138.

7. C. Brezinski, Editor, Algorithmes d'Accélération de la Convergence: Étude Numériques, Technip (1978).

8. C. Brezinski, Editor, Introduction à la Pratique du Calcul Numérique, Dunod Université, Dunod, Paris (1988).

9. C. Brezinski and A.C. Matos , Derivation of extrapolation algorithms based on error estimates. J. Comput. Appl. Math. 66 (1996), pp. 5–26. Abstract | PDF (1043 K) | View Record in Scopus | Cited By in Scopus (7)

10. C. Brezinski and R. Zaglia, Editors, Extrapolation MethodsStudies in Computational Mathematics, North-Holland, Amsterdam (1990).

11. C. Brezinski and R. Zaglia , A general extrapolation procedure revisited. Adv. Comput. Math. 2 (1994), pp. 461–477. View Record in Scopus | Cited By in Scopus (0)

12. L. Bordeaux, E. Monfroy and F. Benhamou , Improved bounds on the complexity of kB-consistency. In: Proc. IJCAI-01, Seattle, WA, Morgan Kaufmann, San Mateo, CA (2001), pp. 303–308.

13. B. Botella and P. Taillibert , Interlog: Constraint logic programming on numeric intervals. In: Proc. 3rd International Workshop on Software Engineering, Artificial Intelligence and Expert Systems, Oberammergau (1993).

14. H. Collavizza, F. Delobel and M. Rueher , A note on partial consistencies over continuous domains solving techniques. In: Proc. Fourth International Conference on Principles and Practice of Constraint Programming (CP-98), Springer, Berlin (1998), pp. 147–161.

15. A. Colmerauer, Spécifications de Prolog IV, Tech. Rept., GIA, Faculté des Sciences de Luminy, Marseille, France, 1994.

16. Dassault Electronique, Interlog 1.0: Guide d'utilisation, Tech. Rept., Dassault Electronique, Saint Cloud, France, 1991.

17. E. Davis , Constraint propagation with interval labels. Artificial Intelligence 32 (1987), pp. 281–331. Abstract | PDF (2679 K) | View Record in Scopus | Cited By in Scopus (105)

18. J. Delahaye and B. Germain-Bonne , Résultats négatifs en accélération de la convergence. Numer. Math. 35 (1980), pp. 443–457. View Record in Scopus | Cited By in Scopus (5)

19. B. Faltings , Arc consistency for continuous variables. Artificial Intelligence 60 2 (1994), pp. 363–376. Abstract | PDF (702 K) | View Record in Scopus | Cited By in Scopus (22)

20. B. Faltings and E. Gelle , Local consistency for ternary numeric constraints. In: Proc. IJCAI-97, Nagoya, Japan, Vol. 1 (1997), pp. 392–397.

21. E. Freuder , Synthesizing constraint expressions. Comm. ACM 21 (1978), pp. 958–966. View Record in Scopus | Cited By in Scopus (88)

22. E. Freuder , A sufficient condition for backtrack-bounded search. J. ACM 32 4 (1985), pp. 755–761. View Record in Scopus | Cited By in Scopus (54)

23. L. Granvilliers Consistances locales et transformations symboliques de contraintes d'intervalles, Ph.D. Thesis, Université d'Orléans, France (1998).

24. E. Hansen, Editor, Global Optimization Using Interval Analysis, Marcel Dekker, New York (1992).

25. D. Haroud and B. Faltings , Consistency techniques for continuous constraints. Constraints 1 1–2 (1996), pp. 85–118.

26. E. Hyvönen , Constraint reasoning based on interval arithmetic: The tolerance propagation approach. Artificial Intelligence 58 (1992), pp. 71–112. Abstract | PDF (2063 K) | View Record in Scopus | Cited By in Scopus (53)

27. ILOG Solver 4.0, Reference Manual (1997).

28. R.B. Kearfott Rigorous Global Search: Continuous Problems, Kluwer Academic, Dordrecht (1996).

29. V. Kreinovich, A. Lakeyev, J. Rohn and P. Kahl Computational Complexity and Feasibility of Data Processing and Interval Computations, Kluwer, Dordrecht (1998).

30. Y. Lebbah Contribution à la résolution de contraintes par consistence forte, Ph.D. Thesis, Université de Nantes 2, Nantes, France (1994).

31. Y. Lebbah and O. Lhomme , Acceleration methods for numeric CSPs. In: Proc. AAAI-98, Madison, WI (1998), pp. 19–24. View Record in Scopus | Cited By in Scopus (1)

32. O. Lhomme , Consistency techniques for numeric CSPs. In: Proc. IJCAI-93, Chambéry, France (1993), pp. 232–238.

33. O. Lhomme Contribution à la résolution de contraintes sur les réels par propagation d'intervalles, Ph.D. Thesis, Université de Nice—Sophia Antipolis (1994).

34. O. Lhomme, A. Gotlieb and M. Rueher , Dynamic optimization of interval narrowing algorithms. J. Logic Programming 37 1–3 (1998), pp. 165–183. Abstract | PDF (908 K) | View Record in Scopus | Cited By in Scopus (12)

35. O. Lhomme, A. Gotlieb, M. Rueher and P. Taillibert , Boosting the interval narrowing algorithm. In: Proc. 1996 Joint International Conference and Symposium on Logic Programming, MIT Press, Cambridge, MA (1996), pp. 378–392.

36. A. Mackworth , Consistency in networks of relations. Artificial Intelligence 8 1 (1977), pp. 99–118. Abstract | PDF (1121 K) | View Record in Scopus | Cited By in Scopus (460)

37. R. Moore, Editor, Interval Analysis, Prentice Hall, Englewood Cliffs, NJ (1966).

38. A. Neumaier Interval Methods for Systems of EquationsEncyclopedia of Mathematics and its Applications 37, Cambridge University Press, Cambridge, UK (1990).

39. A. Neumaier , A simple derivation of the Hansen-Bliek-Rohn-Ning-Kearfott enclosure for linear interval equations. Reliable Computing 5 (1999), pp. 131–136. View Record in Scopus | Cited By in Scopus (18)

40. W. Older and A. Velino , Extending prolog with constraint arithmetic on real intervals. In: Proc. IEEE Canadian Conference on Electrical and Computer Engineering, IEEE Computer Society Press, Los Alamitos, CA (1990), pp. 14.1.1–14.1.4.

41. J. Puget and P. Van Hentenryck , A constraints satisfaction approach to a circuit design problem. J. Global Optim. 13 1 (1998), pp. 75–93. View Record in Scopus | Cited By in Scopus (11)

42. H. Ratschek and J. Rokne Computer Methods for the Range of FunctionsEllis Horwood Ser.: Math. Appl., Ellis Horwood, Chichester (1984).

43. H. Ratschek and J. Rokne , Experiments using interval analysis for solving a circuit design problem. J. Global Optim. 3 (1993), pp. 501–518. View Record in Scopus | Cited By in Scopus (11)

44. G. Sidebottom and W. Havens Hierarchical arc consistency applied to numeric constraint processing in logic programming, Technical Report CSS-IS TR 91-06, Center for Systems Science, Simon Fraser University, Burnaby, BC (1991).

45. P. Van Hentenryck, D. McAllester and D. Kapur , Solving polynomial systems using branch and prune approach, SIAM. J. Numer. Anal. 34 2 (1997), pp. 797–827. View Record in Scopus | Cited By in Scopus (46)

46. P. Van Hentenryck, L. Michel and Y. Deville Numerica: A Modeling Language for Global Optimization, MIT Press, Cambridge MA (1997).

Corresponding Author Contact Information Corresponding author; email: olhomme@ilog.fr

1 This paper is an extended version of [31].


 
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