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Bin Packing with Rejection Revisited

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Approximation and Online Algorithms (WAOA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4368))

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Abstract

We consider the following generalization of bin packing. Each item is associated with a size bounded by 1, as well as a rejection cost, that an algorithm must pay if it chooses not to pack this item. The cost of an algorithm is the sum of all rejection costs of rejected items plus the number of unit sized bins used for packing all other items.

We first study the offline version of the problem and design an APTAS for it. This is a non-trivial generalization of the APTAS given by Fernandez de la Vega and Lueker for the standard bin packing problem. We further give an approximation algorithm of absolute approximation ratio \(\frac 32\), this value is best possible unless P= NP.

Finally, we study an online version of the problem. For the bounded space variant, where only a constant number of bins can be open simultaneously, we design a sequence an algorithms whose competitive ratios tend to the best possible asymptotic competitive ratio. We show that our algorithms have the same asymptotic competitive ratios as these known for the standard problem, whose ratios tend to Π ∞ ≈1.691. Furthermore, we introduce an unbounded space algorithm which achieves a much smaller asymptotic competitive ratio. All our results improve upon previous results of Dósa and He.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Leah Epstein

Authors
  1. Leah Epstein
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

  2. Research Academic Computer Technology Institute &, Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Greece

    Christos Kaklamanis

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© 2007 Springer-Verlag Berlin Heidelberg

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Epstein, L. (2007). Bin Packing with Rejection Revisited. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_12

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  • DOI: https://doi.org/10.1007/11970125_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69513-4

  • Online ISBN: 978-3-540-69514-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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