Abstract

In a minimal binary constraint network, every tuple of a constraint relation can be extended to a solution. It was conjectured that computing a solution to such a network is NP hard. We prove this conjecture. We also prove a conjecture by Dechter and Pearl stating that for k ≥ 2 it is NP-hard to decide whether a constraint network can be decomposed into an equivalent k-ary constraint network, and study related questions.

Keywords

Polynomial Time Constraint Satisfaction Problem Single Solution Propositional Variable Constraint Network 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bessiere, C.: Constraint propagation. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, ch. 3, pp. 29–83 (2006)Google Scholar
  2. 2.
    Cros, H.: Compréhension et apprentissage dans les résaux de contraintes, Université de Montpellier, ”PhD thesis, cited in [1], currently unavailable” (2003)Google Scholar
  3. 3.
    Dechter, R.: From local to global consistency. Artif. Intell. 55(1), 87–108 (1992)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dechter, R.: Constraint processing. Morgan Kaufmann, San Francisco (2003)MATHGoogle Scholar
  5. 5.
    Dechter, R., Pearl, J.: Structure identification in relational data. Artif. Intell. 58, 237–270 (1992)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Fleischanderl, G., Friedrich, G., Haselböck, A., Schreiner, H., Stumptner, M.: Configuring large systems using generative constraint satisfaction. IEEE Intell. Systems 13(4), 59–68 (1998)CrossRefGoogle Scholar
  7. 7.
    Gaur, D.R.: Algorithmic complexity of some constraint satisfaction problems, Master of Science (MSc) Thesis, Simon Fraser University (April 1995), Currently available at: http://ir.lib.sfu.ca/bitstream/1892/7983/1/b17427204.pdf
  8. 8.
    Mackworth, A., Freuder, E.: The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artif. Intelligence 25(1), 65–74 (1985)CrossRefGoogle Scholar
  9. 9.
    Maier, D.: The theory of relational databases. Computer Science Press, Rockville (1983)MATHGoogle Scholar
  10. 10.
    Maier, D., Sagiv, Y., Yannakakis, M.: On the complexity of testing implications of functional and join dependencies. J. ACM 28(4), 680–695 (1981)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Montanari, U.: Networks of constraints: Fundamental properties and applications to picture processing. Information Sciences 7, 95–132 (1974)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Montanari, U., Rossi, F.: Fundamental properties of networks of constraints: A new formulation. In: Kanal, L., Kumar, V. (eds.) Search in Artificial Intelligence, pp. 426–449 (1988)Google Scholar
  13. 13.
    Tsang, E.: Foundations of constraint satisfaction. Academic Press, London (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Georg Gottlob
    • 1
  1. 1.Computer Science Department and Oxford Man InstituteUniversity of OxfordOxfordUK

Personalised recommendations