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

  • Authors:

  • Joseph Wun-Tat Chan;Prudence W. H. Wong;Fencol C. C. Yung

  • Affiliations:

  • King’s College London, Department of Computer Science, London, UK;University of Liverpool, Department of Computer Science, Liverpool, UK;University of Hong Kong, Department of Computer Science, Hong Kong, Hong Kong

  • Venue:
  • Algorithmica
  • Year:
  • 2009

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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 1b≤2 and the achievable competitive ratio.