Online Bin Packing of Squares and Cubes

Leah Epstein, Loay Mualem

Research output: Contribution to journalArticlepeer-review


In the d-dimensional online bin packing problem, d-dimensional cubes of positive sizes no larger than 1 are presented one by one to be assigned to positions in d-dimensional unit cube bins. In this work, we provide improved upper bounds on the asymptotic competitive ratio for square and cube bin packing problems, where our bounds do not exceed 2.0885 and 2.5735 for square and cube packing, respectively. To achieve these results, we adapt and improve a previously designed harmonic-type algorithm, and apply a different method for defining weight functions. We detect deficiencies in the state-of-the-art results by providing counter-examples to the current best algorithms and their analysis, where the claimed bounds were 2.1187 for square packing and 2.6161 for cube packing.

Original languageEnglish
Pages (from-to)1415-1458
Number of pages44
Issue number5
StatePublished - May 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Bin packing
  • Competitive analysis
  • Cube packing
  • Square packing

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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