## Abstract

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems. For the off-line variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing. For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms. We study the general versions of the problems as well as the parameterized versions where there is an upper bound of frac(1, k) on the item sizes, for some integer k.

Original language | English |
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Pages (from-to) | 127-139 |

Number of pages | 13 |

Journal | Theoretical Computer Science |

Volume | 362 |

Issue number | 1-3 |

DOIs | |

State | Published - 11 Oct 2006 |

### Bibliographical note

Funding Information:The work of Boyar, Favrholdt, Kohrt, and Larsen was supported in part by the Danish Natural Science Research Council (SNF). The work of Epstein was supported in part by the Israel Science Foundation (ISF). A preliminary version of this paper appeared in the 15th Internat. Symp. on Fundamentals of Computation Theory, Lecture Notes in Computer Science, Vol. 3623, Springer, Berlin, 2005, pp. 397–408. ∗ Corresponding author. Tel./fax: +45 6550 2338. E-mail addresses: joan@imada.sdu.dk (J. Boyar), lea@math.haifa.ac.il (L. Epstein), lenem@imada.sdu.dk (L.M. Favrholdt), svalle@imada.sdu.dk (J.S. Kohrt), kslarsen@imada.sdu.dk (K.S. Larsen), mortenm@imada.sdu.dk (M.M. Pedersen), sanw@asb.dk (S. WZhlk).

## Keywords

- Approximation
- Bin packing
- Dual bin packing
- On-line

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science