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On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis

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Abstract

We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson. This problem is a generalization of the bin packing problem in which items may arrive and depart from the packing dynamically. The main result in this paper is a lower bound of 2.5 on the achievable competitive ratio, improving the best known 2.428 lower bound, and revealing that packing items of restricted form like unit fractions (i.e., of size 1/k for some integer k), for which a 2.4985-competitive algorithm is known, is indeed easier.

We also investigate the resource augmentation version of the problem where the on-line algorithm can use bins of size b (>1) times that of the optimal off-line algorithm. An interesting result is that we prove b=2 is both necessary and sufficient for the on-line algorithm to match the performance of the optimal off-line algorithm, i.e., achieve 1-competitiveness. Further analysis gives a trade-off between the bin size multiplier 1<b≤2 and the achievable competitive ratio.

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Authors and Affiliations

  1. Department of Computer Science, King’s College London, London, UK

    Joseph Wun-Tat Chan

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Prudence W. H. Wong

  3. Department of Computer Science, University of Hong Kong, Hong Kong, Hong Kong

    Fencol C. C. Yung

Authors
  1. Joseph Wun-Tat Chan
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  2. Prudence W. H. Wong
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  3. Fencol C. C. Yung
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Corresponding author

Correspondence to Prudence W. H. Wong.

Additional information

Communicated by Danny Chen and D.T. Lee.

J.W.-T. Chan’s research is partly supported by Hong Kong RGC Grant HKU5172/03E when the author was with the Department of Computer Science, University of Hong Kong, Hong Kong.

P.W.H. Wong’s research is partly supported by Nuffield Foundation Grant NAL/01004/G.

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Chan, J.WT., Wong, P.W.H. & Yung, F.C.C. On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis. Algorithmica 53, 172–206 (2009). https://doi.org/10.1007/s00453-008-9185-z

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  • DOI: https://doi.org/10.1007/s00453-008-9185-z

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