### 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 |
---|---|

Pages (from-to) | 2810-2816 |

Number of pages | 7 |

Journal | Discrete Applied Mathematics |

Volume | 156 |

Issue number | 14 |

DOIs | |

Publication status | Published - Jul 28 2008 |

### Fingerprint

### Keywords

- Bin packing
- Worst-case analysis

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Applied Mathematics*,

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

**Random-order bin packing.** / Coffman, Edward G.; Csirik, J.; Rónyai, L.; Zsbán, Ambrus.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 156, no. 14, pp. 2810-2816. https://doi.org/10.1016/j.dam.2007.11.004

}

TY - JOUR

T1 - Random-order bin packing

AU - Coffman, Edward G.

AU - Csirik, J.

AU - Rónyai, L.

AU - Zsbán, Ambrus

PY - 2008/7/28

Y1 - 2008/7/28

N2 - 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.

AB - 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.

KW - Bin packing

KW - Worst-case analysis

UR - http://www.scopus.com/inward/record.url?scp=50649124439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50649124439&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2007.11.004

DO - 10.1016/j.dam.2007.11.004

M3 - Article

AN - SCOPUS:50649124439

VL - 156

SP - 2810

EP - 2816

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 14

ER -