Abstract
Overload checking is an important method for unary as well as for cumulative resource constraints in constraint-based scheduling, as it tests for a sufficient inconsistency property. While an algorithm with time complexity \({\cal O}(n \log n)\) exists that is known for unary resource constraints, to our knowledge no such algorithms have been established to date for overload checking in cumulative constraints on n tasks. In this paper, an \({\cal O}(n \log n)\) overload checking algorithm is presented as well as its application to a more specific problem domain: the non-overlapping placement of n rectangles in a two-dimensional area. There, the runtime complexity of overload checking is \({\cal O}(n^3 \log n)\).
The work presented in this paper is funded by the European Union (EFRE) and the state of Berlin within the framework of the research project “inubit MRP”, grant no. 10023515.
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References
Baptiste, P., le Pape, C., Nuijten, W.: Constraint-Based Scheduling. In: International Series in Operations Research & Management Science, vol. 39. Kluwer Academic Publishers, Dordrecht (2001)
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)
Beldiceanu, N., Contjean, E.: Introducing global constraints in CHIP. Mathematical and Computer Modelling 12, 97–123 (1994)
Caseau, Y., Laburthe, F.: Improved CLP scheduling with task intervals. In: van Hentenryck, P. (ed.) Proceedings of the Eleventh International Conference on Logic Programming, ICLP 1994, pp. 369–383. MIT Press, Cambridge (1994)
Caseau, Y., Laburthe, F.: Cumulative scheduling with task intervals. In: Maher, M.J. (ed.) Proceedings of the 13th Joint International Conference and Syposium on Logic Programming - JICSLP 1996, pp. 363–377. MIT Press, Cambridge (1996)
Hoche, M., Müller, H., Schlenker, H., Wolf, A.: Firstcs - A Pure Java Constraint Programming Engine. In: Hanus, M., Hofstedt, P., Wolf, A. (eds.) 2nd International Workshop on Multiparadigm Constraint Programming Languages – MultiCPL 2003, September 29 (2003), uebb.cs.tu-berlin.de/MultiCPL03/Proceedings.MultiCPL03.RCoRP03.pdf
Vilím, P.: O(n logn) filtering algorithms for unary resource constraint. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 335–347. Springer, Heidelberg (2004)
Vilím, P., Barták, R., Čepek, O.: Unary resource constraint with optional activities. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 62–76. Springer, Heidelberg (2004)
Wolf, A.: Pruning while sweeping over task intervals. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 739–753. Springer, Heidelberg (2003)
Wolf, A., Schlenker, H.: Realizing the alternative resources constraint. In: Seipel, D., Hanus, M., Geske, U., Bartenstein, O. (eds.) INAP/WLP 2004. LNCS, vol. 3392, pp. 185–199. Springer, Heidelberg (2005)
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Wolf, A., Schrader, G. (2006). \({\cal O}(n \log n)\) Overload Checking for the Cumulative Constraint and Its Application. In: Umeda, M., Wolf, A., Bartenstein, O., Geske, U., Seipel, D., Takata, O. (eds) Declarative Programming for Knowledge Management. INAP 2005. Lecture Notes in Computer Science(), vol 4369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11963578_8
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DOI: https://doi.org/10.1007/11963578_8
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