### 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 language | English |
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Pages (from-to) | 1914-1923 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 160 |

Issue number | 13-14 |

DOIs | |

Publication status | Published - szept. 2012 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*,

*160*(13-14), 1914-1923. https://doi.org/10.1016/j.dam.2012.04.012

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

Research output: Article

*Discrete Applied Mathematics*, vol. 160, no. 13-14, pp. 1914-1923. https://doi.org/10.1016/j.dam.2012.04.012

}

TY - JOUR

T1 - On the absolute approximation ratio for First Fit and related results

AU - Boyar, Joan

AU - Dósa, G.

AU - Epstein, Leah

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

KW - Bin packing

KW - First Fit

KW - Next Fit

KW - Worst Fit

UR - http://www.scopus.com/inward/record.url?scp=84862207658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862207658&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2012.04.012

DO - 10.1016/j.dam.2012.04.012

M3 - Article

AN - SCOPUS:84862207658

VL - 160

SP - 1914

EP - 1923

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 13-14

ER -