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Online square and cube packing

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Abstract

In online square packing, squares of different sizes arrive online and need to be packed into unit squares which are called bins. The goal is to minimize the number of bins used. Online cube packing is defined analogously. We show an upper bound of 2.2697 and a lower bound of 1.6406 for online square packing, and an upper bound of 2.9421 and a lower bound of 1.6680 for online cube packing. The upper bound for squares can be further reduced to 2.24437 using a computer proof. These results improve on the previously known results for the two problems. We also show improved lower bounds for higher dimensions.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Leah Epstein

  2. Fakultät für Informatik, Universität Karlsruhe, Germany

    Rob van Stee

Authors
  1. Leah Epstein
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  2. Rob van Stee
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Correspondence to Leah Epstein.

Additional information

Preliminary versions of different parts of this paper appeared in Proc. Symp. Discr. Alg. 2004 (SODA 2004) and Proc. Eur. Symp. Alg. 2004 (ESA 2004).

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Epstein, L., van Stee, R. Online square and cube packing. Acta Informatica 41, 595–606 (2005). https://doi.org/10.1007/s00236-005-0169-z

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  • DOI: https://doi.org/10.1007/s00236-005-0169-z

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