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Computing

, Volume 52, Issue 3, pp 281–297 | Cite as

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

  • G. Galambos
  • A. van Vliet
Article

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.

AMS Subject Classifications

90B35 90C27 

Key words

Combinatorial problems on-line bin packing suboptimal algorithms 

Untere Schranken für 1-, 2- und 3-dimensionale Bin-Packungsprobleme

Zusammenfassung

In dieser Arbeit untersuchen wir asymptotische untere Schranken von on-line Algorithmen für verschiedene Arten des Bin-Packungsproblems. Kürzlich haben Galambos und Frenk einen einfachen Beweis der unteren Schranke 1.536... für das eindimensionale Packungsproblem angegeben. Ausgehend von ihren Überlegungen präsentieren wir eine allgemeine Technik zur Herleitung unterer Schranken auch für andere Packungsprobleme. Wir verwenden diese Technik, um neue untere Schranken für das zweidimensionale (1,802...) und das dreidimensionale (1,974...) Packungsproblem zu beweisen.

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References

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • G. Galambos
    • 1
  • A. van Vliet
    • 2
  1. 1.Department of Computer ScienceJGYTFSzegedHungary
  2. 2.Econometric InstituteErasmus University RotterdamRotterdamThe Netherlands

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