Online Bin Packing of Squares and Cubes

Leah Epstein, Loay Mualem

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In the d-dimensional online bin packing problem, hyper-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 the analysis, where the claimed bounds were 2.1187 for square packing and 2.6161 for cube packing.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings
EditorsAnna Lubiw, Mohammad Salavatipour
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages14
ISBN (Print)9783030835071
StatePublished - 2021
Event17th International Symposium on Algorithms and Data Structures, WADS 2021 - Virtual, Online
Duration: 9 Aug 202111 Aug 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12808 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Symposium on Algorithms and Data Structures, WADS 2021
CityVirtual, Online

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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