Strip Packing vs. Bin Packing

  • Authors:
  • Xin Han;Kazuo Iwama;Deshi Ye;Guochuan Zhang

  • Affiliations:
  • School of Informatics, Kyoto University, Kyoto 606-8501, Japan;School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Mathematics, Zhejiang University, China

  • Venue:
  • AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2007

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Abstract

In this paper we establish a general algorithmic framework between bin packing and strip packing, with which we achieve the same asymptotic bounds by applying bin packing algorithms to strip packing. More precisely we obtain the following results: (1) Any offline bin packing algorithm can be applied to strip packing maintaining the same asymptotic worst-case ratio. Thus using FFD (First Fit Decreasing Height) as a subroutine, we get a practical (simple and fast) algorithm for strip packing with an upper bound 11/9. (2) A class of Harmonic-based algorithms for bin packing can be applied to online strip packing maintaining the same asymptotic competitive ratio. It implies online strip packing admits an upper bound of 1.58889 on the asymptotic competitive ratio. This significantly improves the previously best bound of 1.6910 and affirmatively answers an open question posed in [5] .