This paper presents a sweep based algorithm for the k-dimensional cumulative constraint, which can operate in filtering mode as well as in greedy assignment mode. Given n tasks and k resources, this algorithm has a worst-case time complexity of O(kn 2) but scales well in practice. In greedy assignment mode, it handles up to 1 million tasks with 64 resources in one single constraint in SICStus. In filtering mode, on our benchmarks, it yields a speed-up of about k 0.75 when compared to its decomposition into k independent cumulative constraints.


Active Task Early Start Late Start Sweep Algorithm Single Sweep 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. International Series in Operations Research and Management Science. Kluwer (2001)Google Scholar
  2. 2.
    Beldiceanu, N., Carlsson, M.: Sweep as a generic pruning technique applied to the non-overlapping rectangles constraint. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 377–391. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Thiel, S.: Sweep synchronisation as a global propagation mechanism. Computers and Operations Research 33(10), 2835–2851 (2006)zbMATHCrossRefGoogle Scholar
  4. 4.
    Carlsson, M., et al.: SICStus Prolog User’s Manual. SICS, 4.2.1 edn. (2012),
  5. 5.
    Freuder, E., Lee, J., O’Sullivan, B., Pesant, G., Rossi, F., Sellman, M., Walsh, T.: The future of CP. Personal communication (2011)Google Scholar
  6. 6.
    Kameugne, R., Fotso, L.P., Scott, J., Ngo-Kateu, Y.: A quadratic edge-finding filtering algorithm for cumulative resource constraints. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 478–492. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Kolisch, R., Sprecher, A.: PSPLIB – a project scheduling problem library. European Journal of Operational Research 96, 205–216 (1996)CrossRefGoogle Scholar
  8. 8.
    Letort, A., Beldiceanu, N., Carlsson, M.: A scalable sweep algorithm for the cumulative constraint. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 439–454. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    O’Sullivan, B.: CP panel position - the future of CP. Personal communication (2011)Google Scholar
  10. 10.
    Régin, J.C., Rezgui, M.: Discussion about constraint programming bin packing models. In: AI for Data Center Management and Cloud Computing. AAAI (2011)Google Scholar
  11. 11.
    ROADEF: Challenge 2012 machine reassignment (2012),
  12. 12.
    Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Why cumulative decomposition is not as bad as it sounds. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 746–761. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  14. 14.
    Choco Team: Choco: an open source Java CP library. Research report 10-02-INFO, Ecole des Mines de Nantes (2010),
  15. 15.
    Vilím, P.: Edge finding filtering algorithm for discrete cumulative resources in \({\mathcal O}(kn {\rm log} n)\). In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 802–816. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Vilím, P.: Timetable edge finding filtering algorithm for discrete cumulative resources. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 230–245. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Arnaud Letort
    • 1
  • Mats Carlsson
    • 2
  • Nicolas Beldiceanu
    • 1
  1. 1.TASC team(EMN-INRIA,LINA) Mines de NantesFrance
  2. 2.SICSKistaSweden

Personalised recommendations