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Probabilistic Analysis of Online (Class-Constrained) Bin Packing and Bin Covering

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Abstract

We study online algorithms for bin packing and bin covering in two different probabilistic settings in which the item sizes are drawn randomly or the items are adversarial but arrive in random order. We prove several results on the expected performance of well-known online algorithms in these settings. In particular, we prove that the simple greedy algorithm Dual Next-Fit for bin covering performs in the random-order setting strictly better than in the worst case, proving a conjecture by Christ et al. (Theoret Comput Sci 556:71–84, 2014).

Additionally we also study class-constrained bin packing and bin covering. In these problems, each item has not only a size but also a color and there are constraints on the number of different colors in each bin. These problems have been studied before in the classical worst-case model and we provide the first probabilistic analysis of these problems. We prove for several simple online algorithms bounds on their expected performance in the two probabilistic models discussed above. We observe that in the case of class constrained bin packing for several algorithms their performance differs with respect to the two probabilistic performance measures.

This research was supported by ERC Starting Grant 306465 (BeyondWorstCase).

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Authors and Affiliations

  1. Department of Computer Science, University of Bonn, Bonn, Germany

    Carsten Fischer & Heiko Röglin

Authors
  1. Carsten Fischer
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  2. Heiko Röglin
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Correspondence to Carsten Fischer .

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Editors and Affiliations

  1. Stony Brook University, Stony Brook, New York, USA

    Michael A. Bender

  2. Rutgers University, New Brunswick, New Jersey, USA

    Martín Farach-Colton

  3. Pace University, New York, New York, USA

    Miguel A. Mosteiro

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Fischer, C., Röglin, H. (2018). Probabilistic Analysis of Online (Class-Constrained) Bin Packing and Bin Covering. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_34

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  • DOI: https://doi.org/10.1007/978-3-319-77404-6_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77403-9

  • Online ISBN: 978-3-319-77404-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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