Abstract
We introduce an on-line model for a class of hand-making games such as Rummy and Mah-Jang. An input is a sequence of items, u 1,..., u i,... such that 0 < |ui| ≤ 1.0. When u i is given, the on-line player puts it into the bin and can discard any selected items currently in the bin (including u i) under the condition that the total size of the remaining items is at most one. The goal is to make this total size as close to 1.0 as possible when the game ends. We also discuss the multi-bin model, where the player can select a bin out of the k ones which u i is put into. We prove tight bounds for the competitive ratio of this problem, both for k = 1 and k ≥ 2.
supported in part by Scientific Research Grant, Ministry of Japan, No. 13480081.
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
J. Csirik, G. Galambos, and G. Turán, “A lower bound on on-line algorithms for decreasing lists,” Proc. EURO VI, 1984.
J. Csirik, and G. Woeginger, “Resource argumentation for online bounded space bin packing,” Proc. ICALP 2000, pp. 296–304, 2000.
M. M. Halldórsson, “Online coloring known graphs,” Electronic J. Combinatorics, Vol. 7, R7, 2000. http://www.combinatorics.org.
M. M. Halldórsson, K. Iwama, S. Miyazaki, and S. Taketomi, “Online independent sets,” Proc. COCOON 2000, pp. 202–209, 2000.
D. S. Johnson, A. Demers, J. D. Ullman, M. R. Garey, and R. L. Graham, “Worst-case performance bounds for simple one-dimensional packing algorithms,” SIAM Journal on Computing, Vol. 3(4), pp. 299–325, 1974.
G. S. Lueker, “Average-case analysis of off-line and on-line knapsack problems,” Proc. Sixth Annual ACM-SIAM SODA, pp. 179–188, 1995.
A. Marchetti-Spaccamela and C. Vercellis, “Stochastic on-line knapsack problems,” Math. Programming, Vol. 68(1, Ser. A), pp. 73–104, 1995.
S. S. Seiden, “On the online bin packing problem,” Proc. ICALP 2001, pp. 237–248, 2001.
S. S. Seiden, “An optimal online algorithm for bounded space variable-sized bin packing,” Proc. ICALP 2000, pp. 283–295, 2000.
A. van Vliet, “On the asymptotic worst case behavior of harmonic fit,” J. Algorithms, Vol. 20, pp. 113–136, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Iwama, K., Taketomi, S. (2002). Removable Online Knapsack Problems. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_26
Download citation
DOI: https://doi.org/10.1007/3-540-45465-9_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43864-9
Online ISBN: 978-3-540-45465-6
eBook Packages: Springer Book Archive