Tree Decomposition with Function Filtering

  • Martí Sánchez
  • Javier Larrosa
  • Pedro Meseguer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3709)

Abstract

Besides search, complete inference methods can also be used to solve soft constraint problems. Their main drawback is the high spatial complexity. To improve its practical usage, we present an approach to decrease memory consumtion in tree decomposition methods, a class of complete inference algorithms. This approach, called function filtering, allows to detect and remove some tuples that appear to be consistent (with a cost below the upper bound) but that will become inconsistent (with a cost exceeding the upper bound) when extended to other variables. Using this idea, we have developed new algorithms CTEf, MCTEf and IMCTEf, standing for cluster, mini-cluster and iterative mini-cluster tree elimination with function filtering. We demonstrate empirically the benefits of our approach.

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References

  1. 1.
  2. 2.
  3. 3.
    Bertele, U., Brioschi, F.: Nonserial Dynamic Programming. AC. Press (1972)Google Scholar
  4. 4.
    Cabon, B., Givry, S., Verfaillie, G.: Anytime lower bounds for constraint violation minimization problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 117–131. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    de Givry, S., Verfaillie, G., Schiex, T.: Bounding the optimum of constraint optimization problems. In: Proceedings of the 3th Conference on Principles and Practice of Constraint Programming, Schloss Hagenberg, Austria, pp. 405–419Google Scholar
  6. 6.
    Dechter, R.: Constraint Processing. Elsevier, Amsterdam (2003)Google Scholar
  7. 7.
    Dechter, R., Kask, K., Larrosa, J.: A general scheme for multiple lower bound computation in constraint optimization. In: Proceedings of the 6th Conference on Principles and Practice of Constraint Programming, pp. 346–360 (2001)Google Scholar
  8. 8.
    Dechter, R., Pearl, J.: Network-based heuristics for constraint satisfaction problems. Artificial Intelligence 34, 1–38 (1987)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Dechter, R., Pearl, J.: Tree clustering for constraints networks. Artifical Intelligence 38 (1989)Google Scholar
  10. 10.
    Dechter, R.: Bucket elimination: A unifying framework for reasoning. Artifical Intelligence 113, 41–85 (1999)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Larkin, D., Dechter, R.: Bayesian inference in the presence of determinism (2003)Google Scholar
  12. 12.
    Bensana, E., Lemaitre, M., Verfaillie, G.: Earth observation satellite management. Constraints 4, 293–299 (1999)MATHCrossRefGoogle Scholar
  13. 13.
    Larrosa, J.: Node and arc consistency in weighted csp. In: Proc. AAAI (2002)Google Scholar
  14. 14.
    Larrosa, J., Morancho, E., Niso, D.: On the practical applicability of bucket elimination: Still-life as a case study. Journal of Artificial Intelligence Research (2005)Google Scholar
  15. 15.
    Larrosa, J., Schiex, T.: Solving weighted csp by maintaining arc consistency. Artificial Intelligence 159 (2004)Google Scholar
  16. 16.
    Sanchez, M., Meseguer, P., Larrosa, J.: Improving the applicability of adaptive consistency. In: Proceedings of the 10th Conference on Principles and Practice of Constraint Programming, Toronto, Canda (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Martí Sánchez
    • 1
  • Javier Larrosa
    • 2
  • Pedro Meseguer
    • 1
  1. 1.Institut d’Investigació en Intel.ligència ArtificialConsejo Superior de Investigaciones CientíficasBellaterraSpain
  2. 2.Dep. Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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