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Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms

By G. Galambos and A. (André) van Vliet

Abstract

In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536 ... lower bound for the 1-dimensional bin packing problem. Following their ideas, we present a general technique that can be used to derive lower bounds for other bin packing problems as well. We apply this technique to prove new lower bounds for the 2-dimensional (1.802...) and 3-dimensional (1.974...) bin packing problem

Topics: AMS Subject Classifications: 90B35, 90C27, bin packing, Combinatorial problems, on-line, suboptimal algorithms
Year: 1994
DOI identifier: 10.1007/BF02246509
OAI identifier: oai:repub.eur.nl:71894

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