Skip to main content
SpringerLink
Log in

The average-case analysis of some on-line algorithms for bin packing

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

In this paper we give tighter bounds than were previously known for the performance of the bin packing algorithms Best Fit and First Fit when the inputs are uniformly distributed on [0, 1]. We also give a general lower bound for the performance of any on-line bin packing algorithm on this distribution. We prove these results by analyzing optimal matchings on points randomly distributed in a unit square. We give a new lower bound for the up-right matching problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Ajtai, J. Komlós andG. Tusnády, On optimal matchings,Combinatorica 4 (1983), 259–264.

    Google Scholar 

  2. J. L. Bentley, D. S. Johnson, F. T. Leighton andC. C. McGeoch, An experimental study of bin packing,Proc. 21st Ann. Allerton Conf. on Communication, Control, and Computing, University of Illinois, Urbana IL, (1983), 51–60.

    Google Scholar 

  3. J. L. Bentley, D. S. Johnson, F. T. Leighton, C. C. McGeoch andL. McGeoch, Some unexpected expected behavior results for bin packing,Proc. 16th ACM Symp. on Theory of Computing, (1984), 279–288.

  4. J. L. Bentley andC. C. McGeoch,personal communications.

  5. D. J. Brown, A lower bound for on-line one-dimensional bin packing algorithms,Technical Report R 86,Coordinated Science Lab., U. of Illinois, Urbana, IL, 1979.

  6. E. G. Coffman, Jr., M. R. Garey andD. S. Johnson, Approximation algorithms for bin packing — an updated survey,Algorithm Design for Computer System Design, (G. Ausiello, M. Lucertini and P. Serafini, eds.), Springer—Verlag, New York, (1984), 49–106.

    Google Scholar 

  7. E. G. Coffman, Jr., M. Hofri, K. So andA. C. Yao, A stochastic model of bin packing,Information and Control 44 (1980), 105–115.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. M. Dudley, Empirical and Poisson processes on classes of sets or functions too large for central limit theorems,Z. Wahrsch. verw. Gebiete 61 (1982), 355–368.

    Article  MATH  MathSciNet  Google Scholar 

  9. W. Fernandez de la Vega andG. S. Lueker, Bin packing can be solved within 1 +ε in linear time,Combinatorica 1 (1981), 349–355.

    MATH  MathSciNet  Google Scholar 

  10. G. N. Frederickson, Probabilistic analysis for simple one- and two-dimensional bin packing algorithms,Inf. Proc. Letters 11 (1980), 156–161.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. M. Hammersley, A few seedlings of research,Proc. 6th Berkeley Symp. on Mathematical Statistics and Probability,1 (1970), 345–394.

    Google Scholar 

  12. D. S. Johnson,Near-optimal bin packing algorithms, Ph. D. Thesis, Massachusetts Institute of Technology, June 1973, Project MAC TR—109.

  13. D. S. Johnson, A. Demers, J. D. Ullman, M. R. Garey andR. L. Graham, Worst-case performance bounds for simple one-dimensional packing algorithms,SIAM J. of Computing 3 (1974), 299–325.

    Article  MathSciNet  Google Scholar 

  14. N. Karmarkar, Probabilistic analysis of some bin-packing algorithms,Proc. 23rd IEEE Symp. on Foundations of Computer Science, (1982), 107–111.

  15. N. Karmarkar andR. M. Karp, An efficient approximation scheme for the one-dimensional bin packing problem,Proc. 23rd IEEE Symp. on Foundations of Computer Science, (1982), 312–320.

  16. W. Knödel, A bin packing algorithm with complexity 0 (n logn) and performance 1 in the stochastic limit,Mathematical Foundations of Computer Science 1981, Lecture Notes in Computer Science 118, (J. Gruska and M. Chytil, eds.), Springer, Berlin, (1981), 369–378.

    Google Scholar 

  17. R. M. Karp, M. Luby andA. Marchetti-Spaccamela, Probabilistic analysis of multi-dimensional bin packing problems,Proc. 16th ACM Symp. on Theory of Computing, (1984), 289–298.

  18. F. T. Leighton andC. E. Leiserson, Wafer-scale integration of systolic arrays,Proc. 23rd IEEE Symp. on Foundations of Computer Science, (1982), 297–311.

  19. F. T. Leighton andP. W. Shor, Tight bounds for minimax grid matching, with applications to the average case analysis of algorithms.Proc. 18th ACM Symp. on Theory of Computing, (1986), 91–103.

  20. F. M. Liang, A lower bound for on-line bin packing,Inf. Proc. Letters 10 (1980), 76–79.

    Article  MATH  Google Scholar 

  21. G. S. Lueker, An average-case analysis of bin packing with uniformly distributed item sizes,report No. 181, Department of Information and Computer Science, U. of California, Irvine, CA, 1982.

  22. G. S. Lueker, personal communication.

Download references

Author information

Authors and Affiliations

  1. Mathematical Science Research Institute, 1000 Centennial Drive, 94720, Berkeley, CA

    Peter W. Shor

Authors
  1. Peter W. Shor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

A preliminary version of this paper appeared inProc. 25th IEEE Symposium on Foundations of Computer Science, 193–200.

This research was done while the author was at the Massachusetts Institute of Technology Dept. of Mathematics and was supported by a NSF Graduate Fellowship and by Air Force grant OSR-82-0326.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shor, P.W. The average-case analysis of some on-line algorithms for bin packing. Combinatorica 6, 179–200 (1986). https://doi.org/10.1007/BF02579171

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579171

AMS subject classification (1980)

Search

Navigation