Skip to main content
SpringerLink
Log in

Multidimensional Cube Packing

  • Published:
Algorithmica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo SP, Brazil

    Yoshiharu Kohayakawa & Yoshiko Wakabayashi

  2. Instituto de Computação, Universidade Estadual de Campinas, Caixa Postal 6176, 13084-971 Campinas SP, Brazil

    Flavio Keidi Miyazawa

  3. Verity, Inc., 892 Ross Drive, Sunnyvale, CA 94089, USA

    Prabhakar Raghavan

Authors
  1. Yoshiharu Kohayakawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Flavio Keidi Miyazawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Prabhakar Raghavan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yoshiko Wakabayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yoshiharu Kohayakawa, Flavio Keidi Miyazawa, Prabhakar Raghavan or Yoshiko Wakabayashi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kohayakawa, Y., Miyazawa, F., Raghavan, P. et al. Multidimensional Cube Packing. Algorithmica 40, 173–187 (2004). https://doi.org/10.1007/s00453-004-1102-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-004-1102-5

Search

Navigation