A Parametric Propagator for Discretely Convex Pairs of Sum Constraints

  • Jean-Noël Monette
  • Nicolas Beldiceanu
  • Pierre Flener
  • Justin Pearson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)

Abstract

We introduce a propagator for abstract pairs of Sum constraints, where the expressions in the sums respect a form of convexity. This propagator is parametric and can be instantiated for various concrete pairs, including Deviation, Spread, and the conjunction of Sum and Count. We show that despite its generality, our propagator is competitive in theory and practice with state-of-the-art propagators.

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References

  1. 1.
    Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Mathematical and Computer Modelling 20(12), 97–123 (1994)CrossRefMATHGoogle Scholar
  2. 2.
    Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Among, common and disjoint constraints. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS (LNAI), vol. 3978, pp. 29–43. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Bonfietti, A., Lombardi, M.: The weighted average constraint. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 191–206. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Fujishige, S.: Submodular Functions and Optimization. In: Annals of Discrete Mathematics, 2nd edn., Elsevier (2005)Google Scholar
  5. 5.
    Gent, I.P.: The recomputation manifesto. CoRR, abs/1304.3674 (2013)Google Scholar
  6. 6.
    Harvey, W., Schimpf, J.: Bounds consistency techniques for long linear constraints. In: Proceedings of TRICS 2002, the Workshop on Techniques foR Implementing Constraint programming Systems, pp. 39–46 (2002)Google Scholar
  7. 7.
    Murota, K.: Recent developments in discrete convex analysis. In: Cook, W., Lovász, L., Vygen, J. (eds.) Research Trends in Combinatorial Optimization, pp. 219–260. Springer (2009)Google Scholar
  8. 8.
    OscaR Team. OscaR: Scala in OR (2012), https://bitbucket.org/oscarlib/oscar
  9. 9.
    Pesant, G., Régin, J.-C.: SPREAD: A balancing constraint based on statistics. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 460–474. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Petit, T., Beldiceanu, N., Lorca, X.: A generalized arc-consistency algorithm for a class of counting constraints. In: IJCAI 2011, pp. 643–648. AAAI Press (2011), revised edition available at http://arxiv.org/abs/1110.4719
  11. 11.
    Petit, T., Régin, J.-C., Beldiceanu, N.: A Θ(n) bound-consistency algorithm for the increasing sum constraint. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 721–728. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Puget, J.-F.: Improved bound computation in presence of several clique constraints. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 527–541. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Razakarison, N., Beldiceanu, N., Carlsson, M., Simonis, H.: GAC for a linear inequality and an atleast constraint with an application to learning simple polynomials. In: SoCS 2013, AAAI Press (2013)Google Scholar
  14. 14.
    Régin, J.-C.: Cost-based arc consistency for global cardinality constraints. Constraints 7(3-4), 387–405 (2002)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Régin, J.-C., Petit, T.: The objective sum constraint. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 190–195. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Schaus, P.: Solving balancing and bin-packing problems with constraint programming, PhD Thesis, Université catholique de Louvain, Belgium (2009)Google Scholar
  17. 17.
    Schaus, P., Deville, Y., Dupont, P.: Bound-consistent deviation constraint. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 620–634. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Schaus, P., Régin, J.-C.: Bound-consistent spread constraint, application to load balancing in nurse to patient assignments (submitted)Google Scholar
  19. 19.
    Schulte, C., Stuckey, P.J.: When do bounds and domain propagation lead to the same search space? ACM Transactions on Programming Languages and Systems 27(3), 388–425 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-Noël Monette
    • 1
  • Nicolas Beldiceanu
    • 2
  • Pierre Flener
    • 1
  • Justin Pearson
    • 1
  1. 1.Dept. of Information TechnologyUppsala UniversityUppsalaSweden
  2. 2.TASC Team (CNRS/INRIA)Mines de NantesNantesFrance

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