Abstract
This paper presents a sweep based algorithm for the cumulative constraint, which can operate in filtering mode as well as in greedy assignment mode. Given n tasks, this algorithm has a worst-case time complexity of O(n2). In practice, we use a variant with better average-case complexity but worst-case complexity of O(n2 logn), which goes down to O(n logn) when all tasks have unit duration, i.e. in the bin-packing case. Despite its worst-case time complexity, this algorithm scales well in practice, even when a significant number of tasks can be scheduled in parallel. It handles up to 1 million tasks in one single cumulative constraint in both Choco and SICStus.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling 17(7), 57–73 (1993)
Beldiceanu, N., Carlsson, M., Poder, E., Sadek, R., Truchet, C.: A Generic Geometrical Constraint Kernel in Space and Time for Handling Polymorphic k-Dimensional Objects. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 180–194. Springer, Heidelberg (2007)
Beldiceanu, N., Carlsson, M.: A New Multi-resource cumulatives Constraint with Negative Heights. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 63–79. Springer, Heidelberg (2002)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational geometry - algorithms and Applications. Springer (1997)
Carlsson, M., et al.: SICStus Prolog User’s Manual. SICS, 4.2.1 edn. (2012), http://www.sics.se/sicstus
Freuder, E., Lee, J., O’Sullivan, B., Pesant, G., Rossi, F., Sellman, M., Walsh, T.: The future of CP. Personal communication (2011)
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)
Hermenier, F., Lorca, X., Menaud, J.M., Muller, G., Lawall, J.: Entropy: a consolidation manager for clusters. In: VEE 2009, pp. 41–50. ACM (2009)
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)
O’Sullivan, B.: CP panel position - the future of CP. Personal communication (2011)
Pape, C.L.: Des systèmes d’ordonnacement flexibles et opportunistes. Ph.D. thesis, Université Paris IX (1988) (in French)
Régin, J.C., Rezgui, M.: Discussion about constraint programming bin packing models. In: AI for Data Center Management and Cloud Computing. AAAI (2011)
ROADEF: Challenge 2012 machine reassignment (2012), http://challenge.roadef.org/2012/en/index.php
Schaus, P., Deville, Y.: A global constraint for bin-packing with precedences: application to the assembly line balancing problem. In: AAAI 2008, pp. 369–374. AAAI Press (2008)
Schulte, C.: Comparing trailing and copying for constraint programming. In: Schreye, D.D. (ed.) ICLP 1999, pp. 275–289. The MIT Press (1999)
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)
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)
Shaw, P.: A Constraint for Bin Packing. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 648–662. Springer, Heidelberg (2004)
Team, C.: Choco: an open source Java CP library. Research report 10-02-INFO, Ecole des Mines de Nantes (2010), http://choco.emn.fr/
Vilím, P.: Edge Finding Filtering Algorithm for Discrete Cumulative Resources in O(kn logn). In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 802–816. Springer, Heidelberg (2009)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Letort, A., Beldiceanu, N., Carlsson, M. (2012). A Scalable Sweep Algorithm for the cumulative Constraint. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-33558-7_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33557-0
Online ISBN: 978-3-642-33558-7
eBook Packages: Computer ScienceComputer Science (R0)