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Tighter bounds for the harmonic bin packing algorithm

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  • Epstein, Leah

Abstract

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.

Suggested Citation

  • Epstein, Leah, 2024. "Tighter bounds for the harmonic bin packing algorithm," European Journal of Operational Research, Elsevier, vol. 316(1), pages 72-84.
    • Handle: RePEc:eee:ejores:v:316:y:2024:i:1:p:72-84
    DOI: 10.1016/j.ejor.2024.01.051
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