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The Tight Bound of First Fit Decreasing Bin-Packing Algorithm Is FFD(I) ≤ 11/9OPT(I) + 6/9

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Combinatorics, Algorithms, Probabilistic and Experimental Methodologies (ESCAPE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4614))

Abstract

First Fit Decreasing is a classical bin packing algorithm: the items are ordered into their nonincreasing order, and then in this order the next item is always packed into the first bin where it fits. For an instance I let FFD(I) and OPT(I) denote the number of the used bins by algorithm FFD, and an optimal algorithm, respectively. We show in this paper that

$$ FFD(I)\leq 11/9 OPT(I)+6/9, $$
(1)

and that this bound is tight. The tight bound of the additive constant was an open question for many years.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    György Dósa

Authors
  1. György Dósa
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Bo Chen Mike Paterson Guochuan Zhang

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© 2007 Springer-Verlag Berlin Heidelberg

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Dósa, G. (2007). The Tight Bound of First Fit Decreasing Bin-Packing Algorithm Is FFD(I) ≤ 11/9OPT(I) + 6/9. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_1

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  • DOI: https://doi.org/10.1007/978-3-540-74450-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74449-8

  • Online ISBN: 978-3-540-74450-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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