Abstract
We propose a novel algorithm for computing the number of ordered integer partitions with upper bounds. This problem’s task is to compute the number of distributions of z balls into n urns with constrained capacities \(i_1,\hdots,i_n\) (see [10]). Besides the fact that this elementary urn problem has no known combinatoric solution, it is interesting because of its applications in the theory of database preferences as described in [3] and [9]. The running time of our algorithm depends only on the number of urns and not on their capacities as in other previously known algorithms.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andrews, G.E.: The Theory of Partitions, 1st edn. Cambridge University Press (1998)
Conway, H., Guy, R.: The Book of Numbers, 1st edn. Copernicus (1995)
Endres, M.: Semi-Skylines and Skyline Snippets - Theory and Applications. Books on Demand (2011)
von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 1st edn. Cambridge University Press (2003)
Hardy, G., Wright, E.: An Introduction to the Theory of Numbers, 3rd edn. Oxford University Press (1954)
Knuth, D.E.: Johann Faulhaber and Sums of Powers. Math. Comp. 61(203), 277–294 (1993)
Knuth, D.E.: Seminumerical Algorithms, 3rd edn. Addison-Wesley (1997)
Matoušek, J., Nešetřil, J.: Invitation to Discrete Mathematics. Springer (2002)
Preisinger, T.: Graph-based Algorithms for Pareto Preference Query. Books on Demand (2009)
Wirsching, G.: Balls in constrained urns and cantor-like sets. Zeitschrift für Analysis und ihre Anwendungen 17, 979–996 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Glück, R., Köppl, D., Wirsching, G. (2013). Computational Aspects of Ordered Integer Partition with Upper Bounds. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds) Experimental Algorithms. SEA 2013. Lecture Notes in Computer Science, vol 7933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38527-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-38527-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38526-1
Online ISBN: 978-3-642-38527-8
eBook Packages: Computer ScienceComputer Science (R0)