On dynamic bin packing: an improved lower bound and resource augmentation analysis

  • Authors:

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

  • Affiliations:

  • Department of Computer Science, University of Hong Kong, Hong Kong;Department of Computer Science, University of Liverpool, UK;Department of Computer Science, University of Hong Kong, Hong Kong

  • Venue:
  • COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
  • Year:
  • 2006

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Abstract

We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson [7]. 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 [3], and revealing that packing items of restricted form like unit fractions (i.e., of size 1/k for some integer k), which can guarantee a competitive ratio 2.4985 [3], is indeed easier. We also investigate the resource augmentation analysis on 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 is made to give a trade-off between the bin size multiplier b and the achievable competitive ratio.