Skip to main content

A Parametric Propagator for Discretely Convex Pairs of Sum Constraints

  • Conference paper
Book cover Principles and Practice of Constraint Programming (CP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,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.

This work is supported by grants 2011-6133 and 2012-4908 of the Swedish Research Council (VR). We thank the reviewers for their constructive comments.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Mathematical and Computer Modelling 20(12), 97–123 (1994)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  3. Bonfietti, A., Lombardi, M.: The weighted average constraint. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 191–206. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Fujishige, S.: Submodular Functions and Optimization. In: Annals of Discrete Mathematics, 2nd edn., Elsevier (2005)

    Google Scholar 

  5. Gent, I.P.: The recomputation manifesto. CoRR, abs/1304.3674 (2013)

    Google Scholar 

  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. 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. OscaR Team. OscaR: Scala in OR (2012), https://bitbucket.org/oscarlib/oscar

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Régin, J.-C.: Cost-based arc consistency for global cardinality constraints. Constraints 7(3-4), 387–405 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  16. Schaus, P.: Solving balancing and bin-packing problems with constraint programming, PhD Thesis, Université catholique de Louvain, Belgium (2009)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  18. Schaus, P., Régin, J.-C.: Bound-consistent spread constraint, application to load balancing in nurse to patient assignments (submitted)

    Google Scholar 

  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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Monette, JN., Beldiceanu, N., Flener, P., Pearson, J. (2013). A Parametric Propagator for Discretely Convex Pairs of Sum Constraints. In: Schulte, C. (eds) Principles and Practice of Constraint Programming. CP 2013. Lecture Notes in Computer Science, vol 8124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40627-0_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40627-0_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40626-3

  • Online ISBN: 978-3-642-40627-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics