Advertisement

Motivation

The global cardinality constraint (gcc) [7], written as
$$ cardinality(x,J;l,u),x_{j}\in D_{j},j\in J, $$
states that each value d is received by at least l d and by at most u d of the variables {x j :j ∈ J}, where \(d\in D={\mathop{\textstyle \bigcup }}_{j\in J}D_{j}=\{0,\ldots ,|D|-1\};\) also, 0 ≤ l d  ≤ u d and u d  ≥ 1 for all d ∈ D. The gcc has several applications [2, 10], thus having been studied from the Constraint Programming community mainly for accomplishing various forms of consistency [4, 6–8] or for examining the tractability of a natural generalization [9].

Keywords

Convex Hull Constraint Satisfaction Problem Facial Structure European Social Fund Identical Term 
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.
    Bergman, D., Hooker, J.N.: Graph Coloring Facets from All-Different Systems. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 50–65. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Bulatov, A.A., Marx, D.: Constraint Satisfaction Problems and Global Cardinality Constraints. Communications of the ACM 53, 99–106 (2010)CrossRefGoogle Scholar
  3. 3.
    Hooker, J.N.: Integrated Methods for Optimization. International Series in Operations Research & Management Science. Springer (2012)Google Scholar
  4. 4.
    Katriel, I., Thiel, S.: Complete Bound Consistency for the Global Cardinality Constraint. Constraints 10, 191–217 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Magos, D., Mourtos, I.: On the facial structure of the AllDifferent system. SIAM Journal on Discrete Mathematics 25, 130–158 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Quimper, C.G., Golynski, A., López-Ortiz, A., van Beek, P.: An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint. Constraints 10, 115–135 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Regin, J.C.: Generalized arc consistency for global cardinality constrain. In: Proceedings of AAAI 1996, pp. 209–215 (1996)Google Scholar
  8. 8.
    Regin, J.C.: Cost-Based Arc Consistency for Global Cardinality Constraints. Constraints 7, 387–405 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Samer, M., Szeider, S.: Tractable cases of the extended global cardinality constraint. Constraints 16, 1–24 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    van Beek, P., Wilken, K.: Fast optimal instruction scheduling for single-issue processors with arbitrary latencies. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 625–639. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ioannis Mourtos
    • 1
  1. 1.Department of Management Science and TechnologyAthens University of Economics and BusinessAthensGreece

Personalised recommendations