Tight results for Next Fit and Worst Fit with resource augmentation

  • Authors:

  • Joan Boyar;Leah Epstein;Asaf Levin

  • Affiliations:

  • Department of Mathematics and Computer Science, University of Southern Denmark, 5230 Odense M, Denmark;Department of Mathematics, University of Haifa, 31905 Haifa, Israel;Chaya fellow. Faculty of Industrial Engineering and Management, The Technion, 32000 Haifa, Israel

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b1, is compared to an optimal packing into bins of size 1, we give a complete analysis of the asymptotic approximation ratio of WF and of NF, and use it to show that WF is strictly better than NF for any 1=2, and for b=1.