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On-Line Maximizing the Number of Items Packed in Variable-Sized Bins

  • Leah Epstein
  • Lene M. Favrholdt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2387)

Abstract

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.

Keywords

Empty Space Competitive Ratio Online Algorithm Deterministic Algorithm Large Item 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-Line Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling. Journal of the ACM, 44(3):486–504, 1997. Also in Proc. 25th ACM STOC, 1993, pp. 623-631.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    S. F. Assmann, D. S. Johnson, D. J. Kleitman, and J. Y. Leung. On a Dual Version of the One-Dimensional Bin Packing Problem. Journal of Algorithms, 5:502–525, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 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
  4. 4.
    P. Berman, M. Charikar, and M. Karpinski. On-Line Load Balancing for Related Machines. Journal of Algorithms, 35:108–121, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.Google Scholar
  6. 6.
    J. Boyar and K. S. Larsen. The Seat Reservation Problem. Algorithmica, 25:403–417, 1999zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function: A Generalization of the Competitive Ratio. SIAM Journal on Computing, 31(1):233–258, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. L. Bruno and P. J. Downey. Probabilistic Bounds for Dual Bin-Packing. Acta Informatica, 22:333–345, 1985.zbMATHMathSciNetGoogle Scholar
  9. 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
  10. 10.
    Y. Cho and S. Sahni. Bounds for List Schedules on Uniform Processors. SIAM Journal on Computing, 9:91–103, 1988.CrossRefMathSciNetGoogle Scholar
  11. 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. 12.
    J. Csirik and J. B. G. Frenk. A Dual Version of Bin Packing. Algorithms Review, 1:87–95, 1990.Google Scholar
  13. 13.
    J. Csirik and V. Totik. On-Line Algorithms for a Dual Version of Bin Packing. Discr. Appl. Math., 21:163–167, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    J. Csirik and G. Woeginger. On-Line Packing and Covering Problems. In Amos Fiat and Gerhard J. Woeginger, editors, Online Algorithms, volume 1442 of LNCS, chapter 7, pages 147–177. Springer-Verlag, 1998.CrossRefGoogle Scholar
  15. 15.
    R. L. Graham. Bounds for Certain Multiprocessing Anomalies. Bell Systems Technical Journal, 45:1563–1581, 1966.Google Scholar
  16. 16.
    E. G. Coffman Jr. and J. Y. Leung. Combinatorial Analysis of an Efficient Algorithm for Processor and Storage Allocation. SIAM Journal on Computing, 8(2):202–217, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    E. G. Coffman Jr. J. Y. Leung, and D. W. Ting. Bin Packing: Maximizing the Number of Pieces Packed. Acta Informatica, 9:263–271, 1978.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    J. Y. Leung. Fast Algorithms for Packing Problems. PhD thesis, Pennsylvania State University, 1977.Google Scholar
  19. 19.
    S. Martello and P. Toth. Knapsack Problems. John Wiley and Sons, Chichester, 1990.zbMATHGoogle Scholar
  20. 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. 21.
    A. C. Yao. Towards a Unified Measure of Complexity. Proc. 12th ACM Symposium on Theory of Computing, pages 222–227, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Leah Epstein
    • 1
  • Lene M. Favrholdt
    • 2
  1. 1.The Interdisciplinary CenterSchool of Computer ScienceHerzliyaIsrael
  2. 2.Department of Mathematics and Computer ScienceUniversity of SouthernDenmark

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