### Abstract

We consider the On-Line Dual Bin Packing problem where we have a fixed number n of bins of equal size and a sequence of items. The goal is to maximize the number of items that are packed in the bins by an on-line algorithm. An investigation of First-Fit and an algorithm called Log shows that, in the special case where all sequences can be completely packed by an optimal off-line algorithm, First-Fit has a constant competitive ratio, but Log does not. In contrast, if there is no restriction on the input sequences, Log is exponentially better than First-Fit. This is the first separation of this sort with a difference of more than a constant factor. We also design randomized and deterministic algorithms for which the competitive ratio is constant on sequences which the optimal off-line algorithm can pack using at most αn bins, if α is constant and known to the algorithm in advance.

Original language | English |
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Journal | Nordic Journal of Computing |

Volume | 8 |

Issue number | 4 |

Pages (from-to) | 463-472 |

Number of pages | 10 |

ISSN | 1236-6064 |

Publication status | Published - 2001 |

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## Cite this

Boyar, J., Favrholdt, L. M., Larsen, K. S., & Nielsen, M. N. (2001). The Competitive Ratio for On-Line Dual Bin Packing with Restricted Input Sequences.

*Nordic Journal of Computing*,*8*(4), 463-472.