Lower Bounds for Non-binary Constraint Optimization Problems

  • Pedro Meseguer
  • Javier Larrosa
  • Martí Sánchez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)


The necessity of non-binary constraint satisfaction algorithms is increasing because many real problems are inherently nonbinary. Considering overconstrained problems (and Partial Forward Checking as the solving algorithm), we analyze several lower bounds proposed in the binary case, extending them for the non-binary case. We show that techniques initially developed in the context of reversible DAC can be applied in the general case, to deal with constraints of any arity. We discuss some of the issues raised for non-binary lower bounds, and we study their computational complexity. We provide experimental results of the use of the new lower bounds on overconstrained random problems, including constraints with different weights.


Constraint Satisfaction Problem Soft Constraint Limited Version Future Variable Current Partial Assignment 
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  1. 1.
    M. S. Affane and H. Bennaceur. A weighted arc consistency technique for Max-CSP. In Proc. of the 13 th ECAI, 209–213, 1998.Google Scholar
  2. 2.
    C. Bessiere, P. Meseguer, E.C. Freuder, and J. Larrosa. On forward checking for non-binary constraint satisfaction. In Non-binary constraints Workshop, IJCAI-99, 1999.Google Scholar
  3. 3.
    S. Bistarelli, U. Montanari and F. Rossi. Constraint Solving over Semirings. In Proc. of the 14 th IJCAI, 1995.Google Scholar
  4. 4.
    E.C. Freuder and R.J. Wallace. Partial constraint satisfaction. Artificial Intelligence, 58:21–70, 1992.CrossRefMathSciNetGoogle Scholar
  5. 5.
    J. Larrosa. Boosting search with variable elimination. In Proc. of the 6 th CP, 291–305, 2000.Google Scholar
  6. 6.
    J. Larrosa and P. Meseguer. Exploiting the use of DAC in Max-CSP. In Proc. of the 2 th CP, 308–322, 1996.Google Scholar
  7. 7.
    J. Larrosa, P. Meseguer, and T. Schiex. Maintaining reversible dac for max-csp. Artificial Intelligence, 107:149–163, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Larrosa and R. Dechter. On the dual representation of non-binary semiringbased CSPs. In Modelling and Solving Soft Constraints Workshop, CP-00, 2000.Google Scholar
  9. 9.
    P. Meseguer. Lower bounds for non-binary Max-CSP. In Modelling and Solving Constraint Problems Workshop, ECAI-00, August 2000.Google Scholar
  10. 10.
    J.C. Régin, T. Petit, C. Bessiére and J.F. Puget. An original constraint based approach for solving over constrained problems. In Proc. of the 6 th CP, 543–548, September 2000.Google Scholar
  11. 11.
    T. Schiex, H. Fargier and G. Verfaillie. Valued Constraint Satisfaction Problems: hard and easy problems. In Proc. of the 14 th IJCAI, 631–637, 1995.Google Scholar
  12. 12.
    T. Schiex. Maximizing the reversible DAC lower bound in Max-CSP is NP-hard. INRA Tec. Report 1998/02.Google Scholar
  13. 13.
    T. Schiex. Arc consistency for soft constraints In Proc. of the 6 th CP, 411–424, 2000.Google Scholar
  14. 14.
    B. Smith. Phase transition and the mushy region in constraint satisfaction problems. In Proc. of the 11 th ECAI, 100–104, 1994.Google Scholar
  15. 15.
    G. Verfaillie, M. Lemaître, and T. Schiex. Russian doll search. In Proc. of the 13 th AAAI, 181–187, 1996.Google Scholar
  16. 16.
    R. Wallace. Directed arc consistency preprocessing. In M. Meyer, editor, Selected papers from the ECAI-94 Workshop on Constraint Processing, number 923 in LNCS, 121–137. Springer, Berlin, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Pedro Meseguer
    • 1
  • Javier Larrosa
    • 2
  • Martí Sánchez
    • 1
  1. 1.IIIA-CSICCampus UABBellaterraSpain
  2. 2.Dep. LSIUPCBarcelonaSpain

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