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Online Bin Packing: Old Algorithms and New Results

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Language, Life, Limits (CiE 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8493))

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Abstract

In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. FirstFit and BestFit algorithms are simple online algorithms introduced in early seventies, when it was also shown that their asymptotic approximation ratio is equal to 1.7. We present a simple proof of this bound and survey recent developments that lead to the proof that also the absolute approximation ratio of these algorithms is exactly 1.7. More precisely, if the optimum needs opt bins, the algorithms use at most \(\lfloor1.7\cdot\) OPT \(\rfloor\) bins and for each value of opt, there are instances that actually need so many bins. We also discuss bounded-space bin packing, where the online algorithm is allowed to keep only a fixed number of bins open for future items. In this model, a variant of BestFit also has asymptotic approximation ratio 1.7, although it is possible that the bound is significantly smaller if also the offline solution is required to satisfy the bounded-space restriction.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, Computer Science Institute of Charles University, Praha, Czech Republic

    Jiří Sgall

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  1. Jiří Sgall
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Editors and Affiliations

  1. College of Science, Department of Computer Science, Swansea University, SA2 8PP, Swansea, UK

    Arnold Beckmann

  2. Department of Algorithms and Their Applications, Eötvös Loránd University, Pázmány Péter sétány 1/c,, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  3. Computer Science Institute, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Sgall, J. (2014). Online Bin Packing: Old Algorithms and New Results. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds) Language, Life, Limits. CiE 2014. Lecture Notes in Computer Science, vol 8493. Springer, Cham. https://doi.org/10.1007/978-3-319-08019-2_38

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  • DOI: https://doi.org/10.1007/978-3-319-08019-2_38

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08018-5

  • Online ISBN: 978-3-319-08019-2

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