Speeding Up Weighted Constraint Satisfaction Using Redundant Modeling

  • Y. C. Law
  • J. H. M. Lee
  • M. H. C. Woo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4304)


In classical constraint satisfaction, combining mutually redundant models using channeling constraints is effective in increasing constraint propagation and reducing search space for many problems. In this paper, we investigate how to benefit the same for weighted constraint satisfaction problems (WCSPs), a common soft constraint framework for modeling optimization and over-constrained problems. First, we show how to generate a redundant WCSP model from an existing WCSP using generalized model induction. We then uncover why naively combining two WCSPs by posting channeling constraints as hard constraints and relying on the standard NC* and AC* propagation algorithms does not work well. Based on these observations, we propose m -NC* c and m-AC* c and their associated algorithms for effectively enforcing node and arc consistencies on a combined model with m sub-models. The two notions are strictly stronger than NC* and AC* respectively. Experimental results confirm that applying the 2-NC* c and 2-AC* c algorithms on combined models reduces more search space and runtime than applying the state-of-the-art AC*, FDAC*, and EDAC* algorithms on single models.


Combine Model Constraint Satisfaction Problem Hard Constraint Local Consistency Binary Constraint 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cheng, B., Choi, K., Lee, J., Wu, J.: Increasing constraint propagation by redundant modeling: an experience report. Constraints 4(2), 167–192 (1999)MATHCrossRefGoogle Scholar
  2. 2.
    Schiex, T.: Arc consistency for soft constraints. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 411–424. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Larrosa, J.: Node and arc consistency in weighted CSP. In: Proc. of AAAI 2002, pp. 48–53 (2002)Google Scholar
  4. 4.
    Law, Y., Lee, J.: Model induction: a new source of CSP model redundancy. In: Proc. of AAAI 2002, pp. 54–60 (2002)Google Scholar
  5. 5.
    Larrosa, J., Schiex, T.: In the quest of the best form of local consistency for weighted CSP. In: Proc. of IJCAI 2003, pp. 239–244 (2003)Google Scholar
  6. 6.
    de Givry, S., Heras, F., Zytnicki, M., Larrosa, J.: Existential arc consistency: Getting closer to full arc consistency in weighted CSPs. In: Proc. of IJCAI 2005, pp. 84–89 (2005)Google Scholar
  7. 7.
    Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: hard and easy problems. In: Proc. of IJCAI 1995, pp. 631–637 (1995)Google Scholar
  8. 8.
    Hnich, B., Smith, B., Walsh, T.: Dual modelling of permutation and injection problems. JAIR 21, 357–391 (2004)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Y. C. Law
    • 1
  • J. H. M. Lee
    • 1
  • M. H. C. Woo
    • 1
  1. 1.Department of Computer Science and EngineeringThe Chinese University of Hong KongShatin, N.T.Hong Kong

Personalised recommendations