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Bin packing: Maximizing the number of pieces packed

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Summary

We consider a variant of the classical one-dimensional bin-packing problem: The number of bins is fixed and the object is to maximize the number of pieces packed from some given set. Both problems have applications in processor and storage allocation in computer systems in addition to a broad application in operations research.

It can easily be shown that both problems are NP-complete; our approach will be to propose and analyze very fast heuristics. We consider a class of algorithms and bound the performance of an arbitrary algorithm in that class. Finally we propose an algorithm, the first-fit-increasing algorithm, and analyze its running time and relative performance.

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References

  1. Coffman, E.G., Garey, M.R., Johnson, D.S.: An application of bin-packing to multiprocessor scheduling. SIAM J. Comput. (to appear)

  2. Coffman, E.G., Jr., Leung, J.Y-T., Ting, D.: Bin-packing: Maximizing the number of pieces packed. Technical Report, Computer Science Dept., The Pennsylvania State Univ., 1976

  3. Graham, R.L.: Bounds on the performance of scheduling algorithms. In: Computer and job-shop scheduling theory (E.G. Coffman, ed.). New York:Wiley 1976

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  4. Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3 299–326 (1974)

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Columbia University, 10027, New York, NY, USA

    E. G. Coffman Jr.

  2. Computer Science Department, Virginia Polytechnic University, 24060, Blacksburg, VA, USA

    J. Y. -T. Leung

  3. Bell Laboratories, 07733, Holmdel, NJ, USA

    D. W. Ting

Authors
  1. E. G. Coffman Jr.
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  2. J. Y. -T. Leung
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  3. D. W. Ting
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Additional information

This research was supported in part by NSF Grant No. 28290

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Coffman, E.G., Leung, J.Y.T. & Ting, D.W. Bin packing: Maximizing the number of pieces packed. Acta Informatica 9, 263–271 (1978). https://doi.org/10.1007/BF00288885

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  • DOI: https://doi.org/10.1007/BF00288885

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