Abstract
A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach [3 5 8 10 11 12]. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889. It is also shown that the analysis of Harmonic+1 presented in [11] is incorrect; this is a fundamental logical flaw, not an error in calculation or an omitted case. The asymptotic performance ratio of Harmonic+1 is at least 1.59217. Thus Harmonic++ provides the best upper bound for the online bin packing problem to date.
This research was partially supported by an LSU Council on Research summer stipend and by the Research Competitveness Subprogram of the Louisiana Board of Regents.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brown, D. J. A lower bound for on-line one-dimensional bin packing algorithms. Tech. Rep. R-864, Coordinated Sci. Lab., University of Illinois at Urbana-Champaign, 1979.
Coffman, E. G., Garey, M. R., AND Johnson, D. S. Approximation algorithms for bin packing: A survey. In Approximation Algorithms for NP-hard Problems, D. Hochbuam, Ed. PWS Publishing Company, 1997, ch. 2.
Csirik, J. An on-line algorithm for variable-sized bin packing. Acta Informatica 26, 8 (1989), 697–709.
Csirik, J., AND Woeginger, G. On-line packing and covering problems. In On-Line Algorithms—The State of the Art, A. Fiat and G. Woeginger, Eds., Lecture Notes in Computer Science. Springer-Verlag, 1998, ch. 7.
Csirik, J., AND Woeginger, G. Resource augmentation for online bounded space bin packing. In Proceedings of the 27th International Colloquium on Automata, Languages and Programming (Jul 2000), pp. 296–304.
Johnson, D. S. Fast algorithms for bin packing. Journal Computer Systems Science 8 (1974), 272–314.
Johnson, D. S., Demers, A., Ullman, J. D., Garey, M. R., AND Graham, R. L. Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3 (1974), 256–278.
Lee, C., AND Lee, D. A simple on-line bin-packing algorithm. Journal of the ACM 32, 3 (Jul 1985), 562–572.
Liang, F. M. A lower bound for online bin packing. Information Processing Letters 10 (1980), 76–79.
Ramanan, P., Brown, D., Lee, C., AND Lee, D. On-line bin packing in linear time. Journal of Algorithms 10, 3 (Sep 1989), 305–326.
Richey, M. B. Improved bounds for harmoic-based bin packing algorithms. Discrete Applied Mathematics 34 (1991), 203–227.
Seiden, S. S. An optimal online algorithm for bounded space variable-sized bin packing. In Proceedings of the 27th International Colloquium on Automata, Languages and Programming (Jul 2000), pp. 283–295.
VAN Vliet, A. An improved lower bound for online bin packing algorithms. Information Processing Letters 43, 5 (Oct 1992), 277–284.
Yao, A. C. C. New algorithms for bin packing. Journal of the ACM 27 (1980), 207–227.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seiden, S.S. (2001). On the Online Bin Packing Problem. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_20
Download citation
DOI: https://doi.org/10.1007/3-540-48224-5_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42287-7
Online ISBN: 978-3-540-48224-6
eBook Packages: Springer Book Archive