Closed on-line bin packing

Asgeirsson, Eyjólfur Ingi: Closed on-line bin packing. 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
Journal or Publication Title: Acta cybernetica
Date: 2002
Volume: 15
Number: 3
Page Range: pp. 361-367
ISSN: 0324-721X
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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