Asgeirsson, Eyjólfur Ingi:
*Closed on-line bin packing.*
In: Acta cybernetica, (15) 3.
pp. 361-367. (2002)

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## Abstract

An optimal algorithm for the classical bin packing problem partitions (packs) a given set of items with sizes at most 1 into a smallest number of unit-capacity bins such that the sum of the sizes of the items in each bin is at most 1. Approximation algorithms for this NP-hard problem are called on-line if the items are packed sequentially into bins with the bin receiving a given item being independent of the number and sizes of all items as yet unpacked. Off-line algorithms plan packings assuming full (advance) knowledge of all item sizes. The closed on-line algorithms are intermediate: item sizes are not known in advance but the number n of items is. The uniform model, where the n item sizes are independent uniform random draws from [0,1], commands special attention in the average-case analysis of bin packing algorithms. In this model, the expected wasted space produced by an optimal off-line algorithm is Θ(√n), while that produced by an optimal on-line algorithm is Θ(√n log n)- Surprisingly, an optimal closed on-line algorithm also wastes only s Θ(√n) space on the average. A proof of this last result is the principal contribution of this paper. However, we also identify a class of optimal closed algorithms, extend the main result to other probability models, and give an estimate of the hidden constant factor.

Item Type: | Article |
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Journal or Publication Title: | Acta cybernetica |

Date: | 2002 |

Volume: | 15 |

Number: | 3 |

ISSN: | 0324-721X |

Page Range: | pp. 361-367 |

Language: | angol |

Uncontrolled Keywords: | Természettudomány, Informatika |

Additional Information: | Bibliogr.: p. 366-367.; Abstract |

Date Deposited: | 2016. Oct. 15. 12:25 |

Last Modified: | 2018. Jun. 05. 14:31 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/12684 |

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