On the absolute approximation ratio for First Fit and related results

Joan Boyar, G. Dósa, Leah Epstein

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We revisit three famous bin packing algorithms, namely Next Fit (NF), Worst Fit (WF) and First Fit (FF). We compare the approximation ratio of these algorithms as a function of the total size of the input items α. We give a complete analysis of the worst case behavior of WF and NF, and determine the ranges of α for which FF has a smaller approximation ratio than WF and NF. In addition, we prove a new upper bound of 127≈1.7143 on the absolute approximation ratio of FF, improving over the previously known upper bound of 1.75, given by Simchi-Levi. This property of FF is in contrast to the absolute approximation ratios of WF and NF, which are both equal to 2.

Original languageEnglish
Pages (from-to)1914-1923
Number of pages10
JournalDiscrete Applied Mathematics
Volume160
Issue number13-14
DOIs
Publication statusPublished - Sep 2012

Fingerprint

Bins
Approximation
Upper bound
Bin Packing
Range of data

Keywords

  • Bin packing
  • First Fit
  • Next Fit
  • Worst Fit

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

On the absolute approximation ratio for First Fit and related results. / Boyar, Joan; Dósa, G.; Epstein, Leah.

In: Discrete Applied Mathematics, Vol. 160, No. 13-14, 09.2012, p. 1914-1923.

Research output: Contribution to journalArticle

Boyar, Joan ; Dósa, G. ; Epstein, Leah. / On the absolute approximation ratio for First Fit and related results. In: Discrete Applied Mathematics. 2012 ; Vol. 160, No. 13-14. pp. 1914-1923.
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