Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Lower Bounds for Online Bin Packing

  • Rob van SteeEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_493

Years and Authors of Summarized Original Work

  • 1992; van Vliet

  • 2012; Balogh, Békési, Galambos

Problem Definition

In the online bin packing problem, a sequence of items with sizes in the interval (0, 1] arrive one by one and need to be packed into bins, so that each bin contains items of total size at most 1. Each item must be irrevocably assigned to a bin before the next item becomes available. The algorithm has no knowledge about future items. There is an unlimited supply of bins available, and the goal is to minimize the total number of used bins (bins that receive at least one item).

The most common performance measure for online bin packing algorithms is the asymptotic performance ratio, or asymptotic competitive ratio, which is defined as
$$\displaystyle{ R_{\mathrm{ASY}}(A) :=\mathop{\lim \sup }\limits_{ n \rightarrow \infty }\!\left \{\!\mathop{\max }\limits_{L}\!\left \{\left .\!\!\frac{A(L)} {n} \right \vert \!\mbox{ OPT}(L)\! =\! n\right \}\!\right \}\!. }$$

Keywords

Bin packing Competitive analysis Lower bounds Online algorithms 
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Recommended Reading

  1. 1.
    Balogh J, Békési J, Galambos G (2012) New lower bounds for certain bin packing algorithms. Theor Comput Sci 440–441:1–13MathSciNetzbMATHCrossRefGoogle Scholar
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    Brown DJ (1979) A lower bound for on-line one-dimensional bin packing algorithms. Technical report R-864, Coordinated Science Laboratory, UrbanaGoogle Scholar
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    Liang FM (1980) A lower bound for online bin packing. Inf Process Lett 10:76–79zbMATHCrossRefGoogle Scholar
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    Seiden SS (2002) On the online bin packing problem. J ACM 49(5):640–671MathSciNetzbMATHCrossRefGoogle Scholar
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    Sylvester JJ (1880) On a point in the theory of vulgar fractions. Am J Math 3:332–335MathSciNetzbMATHCrossRefGoogle Scholar
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    van Vliet A (1992) An improved lower bound for on-line bin packing algorithms. Inf Process Lett 43:277–284MathSciNetzbMATHCrossRefGoogle Scholar
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    Yao AC-C (1980) New algorithms for bin packing. J ACM 27:207–227MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.University of LeicesterLeicesterUK