Algorithmica

, Volume 40, Issue 3, pp 173–187

Multidimensional Cube Packing

Article

DOI: 10.1007/s00453-004-1102-5

Cite this article as:
Kohayakawa, Y., Miyazawa, F., Raghavan, P. et al. Algorithmica (2004) 40: 173. doi:10.1007/s00453-004-1102-5

Abstract

We consider the d-dimensional cube packing problem (d-CPP): given a list L of d-dimensional cubes and (an unlimited quantity of) d-dimensional unit-capacity cubes, called bins, find a packing of L into the minimum number of bins. We present two approximation algorithms for d-CPP, for fixed d. The first algorithm has an asymptotic performance bound that can be made arbitrarily close to 2 – (1/2)d . The second algorithm is an improvement of the first and has an asymptotic performance bound that can be made arbitrarily close to 2 – (2/3)d . To our knowledge, these results improve the bounds known so far for d = 2 and d = 3, and are the first results with bounds that are not exponential in the dimension.

Approximation algorithms Multidimensional bin packing Asymptotic performance 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo SPBrazil
  2. 2.Instituto de Computação, Universidade Estadual de Campinas, Caixa Postal 6176, 13084-971 Campinas SPBrazil
  3. 3.Verity, Inc., 892 Ross Drive, Sunnyvale, CA 94089USA

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