On variable sized vector packing

Epstein, Leah: On variable sized vector packing. Acta cybernetica, (16) 1. pp. 47-56. (2003)

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Abstract

One of the open problems in on-line packing is the gap between the lower bound Ω(l) and the upper bound O(d) for vector packing of d-dimensional items into d-dimensional bins. We address a more general packing problem with variable sized bins. In this problem, the set of allowed bins contains the traditional "all-1" vector, but also a finite number of other d-dimensional vectors. The study of this problem can be seen as a first step towards solving the classical problem. It is not hard to see that a simple greedy algorithm achieves competitive ratio O(d) for every set of bins. We show that for all small ε > 0 there exists a set of bins for which the competitive ratio is 1 + ε. On the other hand we show that there exists a set of bins for which every deterministic or randomized algorithm has competitive ratio Ω(d). We also study one special case for d = 2.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2003
Volume: 16
Number: 1
Page Range: pp. 47-56
ISSN: 0324-721X
Language: angol
Uncontrolled Keywords: Természettudomány, Informatika
Additional Information: Bibliogr.: 56. p.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Apr. 10. 15:38
URI: http://acta.bibl.u-szeged.hu/id/eprint/12708

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