### Abstract

The average-case analysis of algorithms usually assumes independent, identical distributions for the inputs. In [C. Kenyon, Best-fit bin-packing with random order, in: Proc. of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 1996, pp. 359-364] Kenyon introduced the random-order ratio, a new average-case performance metric for bin packing heuristics, and gave upper and lower bounds for it for the Best Fit heuristics. We introduce an alternative definition of the random-order ratio and show that the two definitions give the same result for Next Fit. We also show that the random-order ratio of Next Fit equals to its asymptotic worst-case, i.e., it is 2.

Original language | English |
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Pages (from-to) | 2810-2816 |

Number of pages | 7 |

Journal | Discrete Applied Mathematics |

Volume | 156 |

Issue number | 14 |

DOIs | |

Publication status | Published - júl. 28 2008 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*156*(14), 2810-2816. https://doi.org/10.1016/j.dam.2007.11.004