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Tractable Combinations of Global Constraints

  • David A. Cohen
  • Peter G. Jeavons
  • Evgenij Thorstensen
  • Stanislav Živný
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)

Abstract

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems.

Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.

Keywords

Constraint Programming Constraint Satisfaction Problem Counting Function Global Constraint Constraint Problem 
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.
    Aschinger, M., Drescher, C., Friedrich, G., Gottlob, G., Jeavons, P., Ryabokon, A., Thorstensen, E.: Optimization methods for the partner units problem. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 4–19. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Aschinger, M., Drescher, C., Gottlob, G., Jeavons, P., Thorstensen, E.: Structural decomposition methods and what they are good for. In: Schwentick, T., Dürr, C. (eds.) Proc. STACS 2011. LIPIcs, vol. 9, pp. 12–28 (2011)Google Scholar
  3. 3.
    Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. Journal of the ACM 30, 479–513 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Beldiceanu, N.: Pruning for the minimum constraint family and for the number of distinct values constraint family. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 211–224. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Bessiere, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of reasoning with global constraints. Constraints 12(2), 239–259 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bessiere, C., Katsirelos, G., Narodytska, N., Quimper, C.-G., Walsh, T.: Decomposition of the NValue constraint. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 114–128. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Bulatov, A., Jeavons, P., Krokhin, A.: Classifying the complexity of constraints using finite algebras. SIAM Journal on Computing 34(3), 720–742 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bulatov, A.A., Marx, D.: The complexity of global cardinality constraints. Logical Methods in Computer Science 6(4(4)), 1–27 (2010)Google Scholar
  9. 9.
    Chen, H., Grohe, M.: Constraint satisfaction with succinctly specified relations. Journal of Computer and System Sciences 76(8), 847–860 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cohen, D.A., Green, M.J., Houghton, C.: Constraint representations and structural tractability. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 289–303. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Cohen, D.A., Jeavons, P., Gyssens, M.: A unified theory of structural tractability for constraint satisfaction problems. Journal of Computer and System Sciences 74(5), 721–743 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Dalmau, V., Kolaitis, P.G., Vardi, M.Y.: Constraint satisfaction, bounded treewidth, and finite-variable logics. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 223–254. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artificial Intelligence 38(3), 353–366 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Freuder, E.C.: Complexity of k-tree structured constraint satisfaction problems. In: Proc. AAAI, pp. 4–9. AAAI Press / The MIT Press (1990)Google Scholar
  15. 15.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman (1979)Google Scholar
  16. 16.
    Gent, I.P., Jefferson, C., Miguel, I.: MINION: A fast, scalable constraint solver. In: Proc. ECAI 2006, pp. 98–102. IOS Press (2006)Google Scholar
  17. 17.
    Gottlob, G., Leone, N., Scarcello, F.: A comparison of structural CSP decomposition methods. Artificial Intelligence 124(2), 243–282 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Gottlob, G., Leone, N., Scarcello, F.: Hypertree decompositions and tractable queries. Journal of Computer and System Sciences 64(3), 579–627 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Green, M.J., Jefferson, C.: Structural tractability of propagated constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 372–386. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Grohe, M.: The complexity of homomorphism and constraint satisfaction problems seen from the other side. Journal of the ACM 54(1), 1–24 (2007)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gyssens, M., Jeavons, P.G., Cohen, D.A.: Decomposing constraint satisfaction problems using database techniques. Artificial Intelligence 66(1), 57–89 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Hermenier, F., Demassey, S., Lorca, X.: Bin repacking scheduling in virtualized datacenters. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 27–41. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    van Hoeve, W.J., Katriel, I.: Global constraints. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, Foundations of Artificial Intelligence, vol. 2, ch. 6, pp. 169–208. Elsevier (2006)Google Scholar
  24. 24.
    Kutz, M., Elbassioni, K., Katriel, I., Mahajan, M.: Simultaneous matchings: Hardness and approximation. Journal of Computer and System Sciences 74(5), 884–897 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Marx, D.: Tractable hypergraph properties for constraint satisfaction and conjunctive queries. In: Proc. STOC 2010, pp. 735–744. ACM (2010)Google Scholar
  26. 26.
    Quimper, C.G., López-Ortiz, A., van Beek, P., Golynski, A.: Improved algorithms for the global cardinality constraint. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 542–556. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  27. 27.
    Rosen, K.H., Michaels, J.G., Gross, J.L., Grossman, J.W., Shier, D.R. (eds.): Handbook of Discrete and Combinatorial Mathematics. Discrete Mathematics and Its Applications. CRC Press (2000)Google Scholar
  28. 28.
    Rossi, F., van Beek, P., Walsh, T. (eds.): The Handbook of Constraint Programming. Elsevier (2006)Google Scholar
  29. 29.
    Samer, M., Szeider, S.: Tractable cases of the extended global cardinality constraint. Constraints 16(1), 1–24 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Wallace, M.: Practical applications of constraint programming. Constraints 1, 139–168 (1996)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Wallace, M., Novello, S., Schimpf, J.: ECLiPSe: A platform for constraint logic programming. ICL Systems Journal 12(1), 137–158 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • David A. Cohen
    • 1
  • Peter G. Jeavons
    • 2
  • Evgenij Thorstensen
    • 2
  • Stanislav Živný
    • 3
  1. 1.Department of Computer ScienceRoyal Holloway, University of LondonUK
  2. 2.Department of Computer ScienceUniversity of OxfordUK
  3. 3.Department of Computer ScienceUniversity of WarwickUK

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