On-Line Maximizing the Number of Items Packed in Variable-Sized Bins
We study an on-line bin packing problem. A fixed number n of bins, possibly of different sizes, are given. The items arrive on-line, and the goal is to pack as many items as possible. It is known that there exists a legal packing of the whole sequence in the n bins. We consider fair algorithms that reject an item, only if it does not fit in the empty space of any bin. We show that the competitive ratio of any fair, deterministic algorithm lies between 1/2 and 2/3, and that a class of algorithms including Best-Fit has a competitive ratio of exactly n/2n−1.
KeywordsEmpty Space Competitive Ratio Online Algorithm Deterministic Algorithm Large Item
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- 3.Y. Azar, J. Boyar, L. Epstein, L. M. Favrholdt, K. S. Larsen, and M. N. Nielsen. Fair versus Unrestricted Bin Packing. Algorithmica (to appear). Preliminary version at SWAT 2000, volume 1851 of LNCS: 200–213, Springer-Verlag, 2000.Google Scholar
- 5.A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.Google Scholar
- 9.C. Chekuri and S. Khanna. A PTAS for the Multiple Knapsack Problem. In Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 213–222, 2000.Google Scholar
- 11.E. G. Coffman, Jr., M. R. Garey, and D. S. Johnson. Approximation Algorithms for Bin Packing: A Survey. In Dorit S. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems, chapter 2, pages 46–93. PWS Publishing Company, 1997.Google Scholar
- 12.J. Csirik and J. B. G. Frenk. A Dual Version of Bin Packing. Algorithms Review, 1:87–95, 1990.Google Scholar
- 15.R. L. Graham. Bounds for Certain Multiprocessing Anomalies. Bell Systems Technical Journal, 45:1563–1581, 1966.Google Scholar
- 18.J. Y. Leung. Fast Algorithms for Packing Problems. PhD thesis, Pennsylvania State University, 1977.Google Scholar
- 20.J. Sgall. On-Line Scheduling. In A. Fiat and G. J. Woeginger, editors, Online Algorithms: The State of the Art, volume 1442 of LNCS, pages 196–231. Springer-Verlag, 1998.Google Scholar
- 21.A. C. Yao. Towards a Unified Measure of Complexity. Proc. 12th ACM Symposium on Theory of Computing, pages 222–227, 1980.Google Scholar