### Abstract

We present a sequence of new linear-time, bounded-space, online bin packing algorithms, the K-Bounded Best Fit algorithms (BBF_{K}), which are based on the ⊙(nlogn) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the ⊙(n logn) First Fit algorithm. Unlike those algorithms, whose asymptotic worst-case ratios approach the limiting value of 17/10 from above as K → ∞ but never reach it, these new algorithms have worst-case ratio 17/10 for all K ≥ 2. They also have substantially better average performance than their bounded-space competition, as we have determined based on extensive experimental results, summarized here, for instances with item sizes drawn independently and uniformly from intervals of the form (0,u], 0 < u ≤ 1. Indeed, for each u < 1, it appears that there exists a fixed memory bound K(u) such that BBF_{K(u)} obtains significantly better packings on average than does the First Fit algorithm, even thought the latter requires unbounded storage and has a significantly greater running time. For u = 1, BBF_{K} can still outperform First Fit (and essentially equal Best Fit) if K is allowed to grow slowly. We provide both theoretical and experimental results concerning the growth rates required.

Original language | English |
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Title of host publication | Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 |

Publisher | Association for Computing Machinery |

Pages | 309-319 |

Number of pages | 11 |

ISBN (Print) | 0897913760 |

Publication status | Published - Mar 1 1991 |

Event | 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 - San Francisco, United States Duration: Jan 28 1991 → Jan 30 1991 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 |
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Country | United States |

City | San Francisco |

Period | 1/28/91 → 1/30/91 |

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### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991*(pp. 309-319). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery.