Tighter bounds for the harmonic bin packing algorithm

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The harmonic algorithm, defined for online bin packing, partitions items into a fixed number M of classes of similar items, and packs each class independently and greedily in constant time for every packed item. The positive integer M is a parameter of the algorithm. This algorithm had a major role in the development of the online bin packing problem. Tight bounds on its asymptotic approximation ratio were known for M≤7, and for values of M with specific properties. The parametric variant of this algorithm, where item sizes are bounded from above by a certain value, was studied as well. We find tight bounds for many additional cases that were known as open, including the case M=8 for the classic problem.

Original languageEnglish
JournalEuropean Journal of Operational Research
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.


  • Asymptotic approximation ratio
  • Bin packing
  • Bounded space algorithms

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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