Abstract
This paper presents new Edge Finding algorithm for discrete cumulative resources, i.e. resources which can process several activities simultaneously up to some maximal capacity C. The algorithm has better time complexity than the current version of this algorithm: \({\mathcal O}(kn {\rm log} n)\) versus \({\mathcal O}(k n^2)\) where n is number of activities on the resource and k is number of distinct capacity demands. Moreover the new algorithm is slightly stronger and it is able to handle optional activities. The algorithm is based on the Θ-tree – a binary tree data structure which already proved to be very useful in filtering algorithms for unary resource constraints.
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References
IBM ILOG CP Optimizer, http://www.ilog.com/products/cpoptimizer/
Philippe Baptiste, C.L.P., Nuijten, W.: Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. Kluwer Academic Publishers, Dordrecht (2001)
Schutt, A., Wolf, A., Schrader, G.: Not-first and not-last detection for cumulative scheduling in \(\uppercase{o}(n^3 \log n)\). In: Umeda, M., Wolf, A., Bartenstein, O., Geske, U., Seipel, D., Takata, O. (eds.) INAP 2005. LNCS (LNAI), vol. 4369, pp. 66–80. Springer, Heidelberg (2006)
Vilím, P.: Max energy filtering algorithm for discrete cumulative resources. In: van Hoeve, W.J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 294–308. Springer, Heidelberg (2009)
Mercier, L., Hentenryck, P.V.: Edge finding for cumulative scheduling. Informs Journal of Computing 20, 143–153 (2008)
Kuhnert, S.: Efficient edge-finding on unary resources with optional activities. In: Proceedings of INAP 2007 and WLP 2007 (2007)
Vilím, P.: Global Constraints in Scheduling. PhD thesis, Charles University in Prague, Faculty of Mathematics and Physics, Department of Theoretical Computer Science and Mathematical Logic (2007)
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Vilím, P. (2009). Edge Finding Filtering Algorithm for Discrete Cumulative Resources in \({\mathcal O}(kn {\rm log} n)\) . In: Gent, I.P. (eds) Principles and Practice of Constraint Programming - CP 2009. CP 2009. Lecture Notes in Computer Science, vol 5732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04244-7_62
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DOI: https://doi.org/10.1007/978-3-642-04244-7_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04243-0
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