Online bin packing with cardinality constraints resolved

János Balogh, József Békési, György Dósa, Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


Bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k≥2, items having sizes in (0,1] associated with them are presented one by one to be packed into unit capacity bins, such that the capacities of bins are not exceeded, and no bin receives more than k items. We resolve the online problem and prove a lower bound of 2 on the overall asymptotic competitive ratio. Additionally, we significantly improve the known lower bounds on the asymptotic competitive ratio for every specific value of k. The novelty of our constructions is based on full adaptivity that creates large gaps between item sizes. Last, we show a lower bound strictly larger than 2 on the asymptotic competitive ratio of the online 2-dimensional vector packing problem, where no such lower bound was known even for fixed high dimensions.

Original languageEnglish
Pages (from-to)34-49
Number of pages16
JournalJournal of Computer and System Sciences
StatePublished - Sep 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.


  • Bin packing
  • Cardinality constraints
  • Competitive ratio

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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