A Framework for Decision-Based Consistencies

  • Jean-François Condotta
  • Christophe Lecoutre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6876)

Abstract

Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (generalized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by \(S^{\phi}_{\Delta}\) Open image in new window , Open image in new window and Open image in new window , study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this general framework provides us with a better insight into decision-based consistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones.

Keywords

Decision Mapping Unary Constraint Strong Consistency Constraint Network Negative Decision 
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.

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References

  1. 1.
    Apt, K.R.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)CrossRefMATHGoogle Scholar
  2. 2.
    Bennaceur, H., Affane, M.S.: Partition-k-AC: An efficient filtering technique combining domain partition and arc consistency. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 560–564. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Bessiere, C.: Constraint propagation. In: Handbook of Constraint Programming, ch. 3. Elsevier, Amsterdam (2006)Google Scholar
  4. 4.
    Bessiere, C., Debruyne, R.: Theoretical analysis of singleton arc consistency and its extensions. Artificial Intelligence 172(1), 29–41 (2008)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bessiere, C., Stergiou, K., Walsh, T.: Domain filtering consistencies for non-binary constraints. Artificial Intelligence 72(6-7), 800–822 (2008)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Carlier, J., Pinson, E.: Adjustments of heads and tails for the job-shop problem. European Journal of Operational Research 78, 146–161 (1994)CrossRefMATHGoogle Scholar
  7. 7.
    Condotta, J.-F., Lecoutre, C.: A class of df-consistencies for qualitative constraint networks. In: Proceedings of KR 2010, pp. 319–328 (2010)Google Scholar
  8. 8.
    Debruyne, R., Bessiere, C.: From restricted path consistency to max-restricted path consistency. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 312–326. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Debruyne, R., Bessiere, C.: Some practical filtering techniques for the constraint satisfaction problem. In: Proceedings of IJCAI 1997, pp. 412–417 (1997)Google Scholar
  10. 10.
    Debruyne, R., Bessiere, C.: Domain filtering consistencies. Journal of Artificial Intelligence Research 14, 205–230 (2001)MathSciNetMATHGoogle Scholar
  11. 11.
    Dechter, R.: Constraint processing. Morgan Kaufmann, San Francisco (2003)MATHGoogle Scholar
  12. 12.
    Freuder, E.C., Elfe, C.: Neighborhood inverse consistency preprocessing. In: Proceedings of AAAI 1996, pp. 202–208 (1996)Google Scholar
  13. 13.
    Lecoutre, C.: Constraint networks: techniques and algorithms. ISTE/Wiley (2009)Google Scholar
  14. 14.
    Lecoutre, C., Cardon, S., Vion, J.: Conservative dual consistency. In: Proceedings of AAAI 2007, pp. 237–242 (2007)Google Scholar
  15. 15.
    Lecoutre, C., Cardon, S., Vion, J.: Second-order consistencies. Journal of Artificial Intelligence Research (JAIR) 40, 175–219 (2011)MathSciNetMATHGoogle Scholar
  16. 16.
    Lecoutre, C., Prosser, P.: Maintaining singleton arc consistency. In: Proceedings of CPAI 2006 Workshop held with CP 2006, pp. 47–61 (2006)Google Scholar
  17. 17.
    Lhomme, O.: Quick shaving. In: Proceedings of AAAI 2005, pp. 411–415 (2005)Google Scholar
  18. 18.
    Martin, P., Shmoys, D.B.: A new approach to computing optimal schedules for the job-shop scheduling problem. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 389–403. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  19. 19.
    Stergiou, K.: Heuristics for dynamically adapting propagation. In: Proceedings of ECAI 2008, pp. 485–489 (2008)Google Scholar
  20. 20.
    Stergiou, K., Walsh, T.: Inverse consistencies for non-binary constraints. In: Proceedings of ECAI 2006, pp. 153–157 (2006)Google Scholar
  21. 21.
    Szymanek, R., Lecoutre, C.: Constraint-level advice for shaving. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 636–650. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    van Dongen, M.R.C.: Beyond singleton arc consistency. In: Proceedings of ECAI 2006, pp. 163–167 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jean-François Condotta
    • 1
  • Christophe Lecoutre
    • 1
  1. 1.CRIL - CNRS, UMR 8188Univ Lille Nord de France, ArtoisLensFrance

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