### Abstract

We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K-Bounded Best Fit algorithms (BBF_{K}). They are based on the Θ (n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ (n log n) First Fit algorithm. Unlike the Next-K Fit 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 though 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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Pages (from-to) | 115-138 |

Number of pages | 24 |

Journal | Algorithmica (New York) |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2001 |

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### Keywords

- Best Fit
- Bin packing
- First Fit
- On-line algorithms

### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

### Cite this

*Algorithmica (New York)*,

*31*(2), 115-138. https://doi.org/10.1007/s00453-001-0041-7