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Bin Packing

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 1997; Coffman, Garay, Johnson

Problem Definition

In the one‐dimensional bin packing problem, one is given a list \( { L = (a_1,a_2,\ldots,a_n) } \) of items, each item a i having a size \( { s(a_i) \in (0,1] } \). The goal is to pack the items into a minimum number of unit-capacity bins, that is, to partition the items into a minimum number of sets, each having total size of at most 1. This problem is NP-hard, and so much of the research on it has concerned the design and analysis of approximation algorithms, which will be the subject of this article.

Although bin packing has many applications, it is perhaps most important for the role it has played as a proving ground for new algorithmic and analytical techniques. Some of the first worst- and average-case results for approximation algorithms were proved in this domain, as well as the first lower bounds on the competitive ratios of online algorithms. Readers interested in a more detailed...

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Recommended Reading

  1. Bentley JL, Johnson DS, Leighton FT, McGeoch CC (1983) An experimental study of bin packing. In: Proceedings of the 21st annual Allerton conference on communication, control, and computing, Urbana, University of Illinois, 1983, pp 51–60

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  2. Bentley JL, Johnson DS, Leighton FT, McGeoch CC, McGeoch LA (1984) Some unexpected expected behavior results for bin packing. In: Proceedings of the 16th annual ACM symposium on theory of computing. ACM, New York, pp 279–288

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  3. Coffman EG Jr, Courcoubetis C, Garey MR, Johnson DS, McGeoch LA, Shor PW, Weber RR, Yannakakis M (1991) Fundamental discrepancies between average-case analyses under discrete and continuous distributions. In: Proceedings of the 23rd annual ACM symposium on theory of computing, New York, 1991. ACM Press, New York,pp 230–240

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  4. Coffman EG Jr, Garey MR, Johnson DS (1997) Approximation algorithms for bin-packing: a survey. In: Hochbaum D (ed) Approximation algorithms for NP-hard problems. PWS Publishing, Boston, pp 46–93

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  5. Coffman EG Jr, Johnson DS, Shor PW, Weber RR (1997) Bin packing with discrete item sizes, part II: tight bounds on first fit. Random Struct Algorithms 10:69–101

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Author information

Authors and Affiliations

  1. Department of Computer Science, Columbia University, New York, NJ, USA

    David S. Johnson

  2. AT&T Laboratories, Algorithms and Optimization Research Department, Florham Park, NJ, USA

    David S. Johnson

Authors
  1. David S. Johnson
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Johnson, D.S. (2016). Bin Packing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_49

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