Constructive Interval Disjunction

  • Gilles Trombettoni
  • Gilles Chabert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4741)


This paper presents two new filtering operators for numerical CSPs (systems with constraints over the reals) based on constructive disjunction, as well as a new splitting heuristic. The fist operator (CID) is a generic algorithm enforcing constructive disjunction with intervals. The second one (3BCID) is a hybrid algorithm mixing constructive disjunction and shaving, another technique already used with numerical CSPs through the algorithm 3B. Finally, the splitting strategy learns from the CID filtering step the next variable to be split, with no overhead.

Experiments have been conducted with 20 benchmarks. On several benchmarks, CID and 3BCID produce a gain in performance of orders of magnitude over a standard strategy. CID compares advantageously to the 3B operator while being simpler to implement. Experiments suggest to fix the CID-related parameter in 3BCID, offering thus to the user a promising variant of 3B.


Hybrid Algorithm Standard Strategy Splitting Strategy Bisection Point Partial Consistency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barták, R., Erben, R.: A new Algorithm for Singleton Arc Consistency. In: Proc. FLAIRS (2004)Google Scholar
  2. 2.
    Bessière, C., Debruyne, R.: Optimal and Suboptimal Singleton Arc Consistency Algorithms. In: Proc. IJCAI, pp. 54–59 (2005)Google Scholar
  3. 3.
    Debruyne, R., Bessière, C.: Some Practicable Filtering Techniques for the Constraint Satisfaction Problem. In: Proc. IJCAI, pp. 412–417 (1997)Google Scholar
  4. 4.
    Geelen, P.A.: Dual Viewpoint Heuristics for Binary Constraint Satisfaction Problems. In: Proc. ECAI 1992, pp. 31–35 (1992)Google Scholar
  5. 5.
    Granvilliers, L., Benhamou, F.: RealPaver: An Interval Solver using Constraint Satisfaction Techniques. ACM Trans. on Mathematical Software 32(1), 138–156 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Lebbah, Y., Michel, C., Rueher, M.: A Rigorous Global Filtering Algorithm for Quadratic Constraints. Constraints Journal 10(1), 47–65 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Lhomme, O.: Consistency Tech. for Numeric CSPs. In: IJCAI, pp. 232–238 (1993)Google Scholar
  8. 8.
    Lhomme, O.: Quick Shaving. In: Proc. AAAI, pp. 411–415 (2005)Google Scholar
  9. 9.
    Min Li, C., Anbulagan: Heuristics Based on Unit Propagation for Satisfiability Problems. In: Proc. IJCAI, pp. 366–371 (1997)Google Scholar
  10. 10.
    Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)zbMATHGoogle Scholar
  11. 11.
    Neveu, B., Chabert, G., Trombettoni, G.: When Interval Analysis helps Interblock Backtracking. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 390–405. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
  13. 13.
    Refalo, P.: Impact-Based Search Strategies for Constraint Programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    Régin, J.C.: A Filtering Algorithm for Constraints of Difference in CSPs. In: Proc. AAAI, pp. 362–367 (1994)Google Scholar
  15. 15.
    Simonis, H.: Sudoku as a Constraint Problem. In: CP Workshop on Modeling and Reformulating Constraint Satisfaction Problems, pp. 13–27 (2005)Google Scholar
  16. 16.
    Van Hentenryck, P., Michel, L., Deville, Y.: Numerica: A Modeling Language for Global Optimization. MIT Press, Cambridge (1997)Google Scholar
  17. 17.
    Van Hentenryck, P., Saraswat, V., Deville, Y.: Design, Implementation, and Evaluation of the Constraint Language CC(FD). J. Logic Programming 37(1–3), 139–164 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gilles Trombettoni
    • 1
  • Gilles Chabert
    • 2
  1. 1.University of Nice-Sophia and COPRIN Project, INRIA, 2004 route des, lucioles, 06902 Sophia.Antipolis cedex, B.P. 93France
  2. 2.ENSIETA, 2 rue François Verny, 29806 Brest cedex 09France

Personalised recommendations