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Bin Packing

1997; Coffman, Garay, Johnson

  • Reference work entry
Encyclopedia of Algorithms

Keywords and Synonyms

Cutting stock problem                  

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 coverage than is possible here are...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Algorithms and Optimization Research Department, AT&T Labs, Florham Park, NJ, USA

    David S. Johnson

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  1. David S. Johnson
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Johnson, D. (2008). Bin Packing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_49

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