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Encyclopedia of Algorithms pp 1858–1860Cite as

Robust Bin Packing

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Years and Authors of Summarized Original Work

  • 2009; Epstein, Levin

  • 2013; Jansen, Klein

Problem Definition

Consider the classical online bin packing problem, where items of sizes in (0, 1] arrive over time. At the arrival of each item, it has to be assigned to a bin of capacity 1 such that the total size of all items in the bin does not exceed its capacity. The objective is to minimize the number of used bins.

Online bin packing was introduced by Ullman [10] and has seen enormous research since then (see the survey of Seiden [9] for an overview). The quality of an online algorithm is typically measured by the asymptotic performance guarantee of the algorithm divided by the optimal offline solution and is called the (asymptotic) competitive ratio. In the case of online bin packing, the best known algorithm has an asymptotic competitive ratio of 1. 58889 (see [9]). On the other hand, it was shown that no algorithm can achieve a ratio better than 1. 54037 (see [1]).

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Recommended Reading

  1. Balogh J, Békési J, Galambos G (2010) New lower bounds for certain classes of bin packing algorithms. In: Workshop on approximation and online algorithms (WAOA), Liverpool. LNCS, vol 6534, pp 25–36

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  2. Cook W, Gerards A, Schrijver A, Tardos E (1986) Sensitivity theorems in integer linear programming. Math Program 34(3):251–264

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  3. Epstein L, Levin A (2009) A robust APTAS for the classical bin packing problem. Math Program 119(1):33–49

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  4. Epstein L, Levin A (2013) Robust approximation schemes for cube packing. SIAM J Optim 23(2):1310–1343

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  5. Fernandez de la Vega W, Lueker G (1981) Bin packing can be solved within 1 +ε in linear time. Combinatorica 1(4):349–355

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  6. Ivković Z, Lloyd E (1998) Fully dynamic algorithms for bin packing: being (mostly) myopic helps. SIAM J Comput 28(2):574–611

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  7. Jansen K, Klein K (2013) A robust AFPTAS for online bin packing with polynomial migration. In: International colloquium on automata, languages, and programming (ICALP), Riga, pp 589–600

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  8. Sanders P, Sivadasan N, Skutella M (2009) Online scheduling with bounded migration. Math Oper Res 34(2):481–498

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  9. Seiden S (2002) On the online bin packing problem. J ACM 49(5):640–671

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  10. Ullman J (1971) The performance of a memory allocation algorithm. Technical report, Princeton University

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Author information

Authors and Affiliations

  1. University Kiel, Kiel, Germany

    Kim-Manuel Klein

Authors
  1. Kim-Manuel Klein
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Correspondence to Kim-Manuel Klein .

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Editors and Affiliations

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

    Ming-Yang Kao

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Klein, KM. (2016). Robust Bin Packing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_492

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