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A Note on Partial Consistencies over Continuous Domains

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Principles and Practice of Constraint Programming — CP98 (CP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1520))

Abstract

This paper investigates the relations among different partial consistencies which have been proposed for pruning the domains of the variables in constraint systems over the real numbers. We establish several properties of the filtering achieved by the algorithms based upon these partial consistencies. Especially, we prove that:

  1. 1)

    2B—Consistency (or Hull consistency) algorithms actually yield a weaker pruning than Box-consistency;

  2. 2)

    3B—Consistency algorithms perform a stronger pruning than Box-consistency.

This paper also provides an analysis of both the capabilities and the inherent limits of the filtering algorithms which achieve these partial consistencies.

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References

  1. F. Benhamou, D. Mc Allester, and P. Van Hentenryck. CLP(Intervals) Revisited. in Proc. Logic Programming: Proceedings of the 1994 International Symposium, MIT Press, (1994).

    Google Scholar 

  2. F. Benhamou and W. Older. Applying interval arithmetic to real, integer and boolean constraints. Journal of Logic Programming, (1997).

    Google Scholar 

  3. C. Bliek. Computer Methods for Design Automation. PhD thesis, Massachusetts Institute of Technology, 1992.

    Google Scholar 

  4. R.P. Brent. A FORTRAN multiple-precision arithmetic package ACM Trans. on Math. Software, 4, no 1, 57–70, 1978.

    Article  Google Scholar 

  5. J.C. Cleary. Logical arithmetic. Future Computing Systems, 2(2):125–149, 1987.

    Google Scholar 

  6. B. Faltings. Arc-consistency for continuous variables. Artificial Intelligence, vol. 65, pp. 363–376, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. C. Freuder. Synthesizing constraint expressions. Communications of the ACM, 21:958–966, November 1978.

    Google Scholar 

  8. L. Granvilliers. On the combination of Box-consistency and Hull-consistency. Workshop “Non binary constraints”, ECAI-98, Brighton, 23–28 August 1998.

    Google Scholar 

  9. E. Hansen. Global optimization using interval analysis. Marcel Dekker, NY, 1992.

    MATH  Google Scholar 

  10. Hoon Hong and Volker Stahl. Safe starting regions by fixed points and tightening. Computing, 53:323–335, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  11. E. Hyvönen. Constraint reasoning based on interval arithmetic: the tolerance propagation approach. Artificial Intelligence, vol. 58, pp. 71–112, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  12. H. Hong, V. Stahl. Safe Starting Regions by Fixed Points and Tightening. Computing, vol. 53, pp 323–335, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. H. M. Lee and M. H. van Emden. Interval computation as deduction in CHIP. Journal of Logic Programming, 16: 3–4, pp. 255–276, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  14. O. Lhomme. Consistency techniques for numeric CSPs. in Proc. IJCAI93, Chambery, (France), pp. 232–238, (August 1993).

    Google Scholar 

  15. O. Lhomme. Contribution á la résolution de contraintes sur les réels par propagation d’intervalles. PhD Thesis, University of Nice Sophia Antipolis-CNRS, Route des Colles, B.P. 145, 06903 Sophia Antipolis Cedex, France, 1994.

    Google Scholar 

  16. O. Lhomme and M. Rueher. Application des techniques CSP au raisonnement sur les intervalles. RIA (Dunod), vol. 11:3, pp. 283–312, 1997.

    MATH  Google Scholar 

  17. A. Mackworth. Consistency in networks of relations. Artificial Intelligence, vol. 8, no. 1, pp. 99–118, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  18. U. Montanari. Networks of constraints: Fundamental properties and applications to picture processing. Information Science, 7(2):95–132, 1974.

    Article  MathSciNet  Google Scholar 

  19. R. Moore, Interval Analysis. Prentice Hall, 1966.

    Google Scholar 

  20. A. Neumaier. Interval methods for systems of equations. Cambridge University Press, 1990.

    Google Scholar 

  21. W.J. Older and A. Velino. Extending prolog with constraint arithmetic on real intervals. In Proc. of IEEE Canadian conference on Electrical and Computer Engineering. IEEE Computer Society Press, 1990.

    Google Scholar 

  22. W. Older and A. Vellino. Constraint arithmetic on real intervals. in Constraint Logic Programming: Selected Research, eds., Frédéric Benhamou and Alain Colmerauer. MIT Press, (1993).

    Google Scholar 

  23. Prologia PrologIV Constraints inside. Parc technologique de Luminy Case 919 13288 Marseille cedex 09 (France), 1996.

    Google Scholar 

  24. M. Rueher, C. Solnon. Concurrent Cooperating Solvers within the Reals. Reliable Computing. Kluwer Academic Publishers, Vol. 3:3, pp. 325–333, 1997.

    Article  MATH  Google Scholar 

  25. E. Tsang. Foundations of Constraint Satisfaction. Academic Press, 1993.

    Google Scholar 

  26. P. Van Hentenryck, Y. Deville, and L. Michel. Numerica. A modeling language for global optimization. MIT Press, 1997.

    Google Scholar 

  27. P. Van Hentenryck, D. McAllester, and D. Kapur. Solving Polynomial Systems Using a Branch and Prune Aprroach. SIAM Journal (forthcomming).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Université de Nice-Sophia-Antipolis, I3S ESSI, 930, route des Colles, B.P. 145, 06903, Sophia-Antipolis, France

    Héléne Collavizza, FranÇois Delobel & Michel Rueher

Authors
  1. Héléne Collavizza
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  2. FranÇois Delobel
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  3. Michel Rueher
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Editor information

Editors and Affiliations

  1. School of Computing and Information Technology, Griffith University, Nathan, Queensland, 4111, Australia

    Michael Maher

  2. ILOG S.A., 9, rue de Verdun, BP 85, F-94253, Gentilly Cedex, France

    Jean-Francois Puget

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© 1998 Springer-Verlag Berlin Heidelberg

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Collavizza, H., Delobel, F., Rueher, M. (1998). A Note on Partial Consistencies over Continuous Domains. In: Maher, M., Puget, JF. (eds) Principles and Practice of Constraint Programming — CP98. CP 1998. Lecture Notes in Computer Science, vol 1520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49481-2_12

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  • DOI: https://doi.org/10.1007/3-540-49481-2_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65224-3

  • Online ISBN: 978-3-540-49481-2

  • eBook Packages: Springer Book Archive

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