## 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 | |

State | Published - Sep 2012 |

### Bibliographical note

Funding Information:The first author was partially supported by the Danish Council for Independent Research, Natural Sciences . The second author was partially supported by Project K-TET_10-1-2011-0064833, Algorithms and Visualization for difficult combinatorial optimization problems .

## Keywords

- Bin packing
- First Fit
- Next Fit
- Worst Fit

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics