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Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model

Authors Leah Epstein , Asaf Levin

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Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • Bin packing
  • Best Fit
  • Random order
  • Bounded space algorithms

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Abstract

We consider the performance of standard bin packing algorithms in the random order model. We provide an improved lower bound of 1.15582656 on the asymptotic approximation ratio of Best Fit (BF) for randomly ordered inputs. We also show lower bounds on the asymptotic approximation ratio for two bounded space bin packing algorithms in this model, namely for 2-BF and 2-FF. These are well-studied bounded space algorithms and the first one has the same asymptotic worst-case performance as BF. However, the resulting lower bounds on their performances in the random order model are much higher than that of BF.

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Leah Epstein and Asaf Levin. Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.26

Author Details

Leah Epstein
  • Department of Mathematics, Faculty of Natural Sciences, University of Haifa, Israel
Asaf Levin
  • Faculty of Data and Decisions Science, The Technion, Haifa, Israel

Funding

  • Levin, Asaf: Partially supported by ISF - Israel Science Foundation grant number 1467/22.

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