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Theory of Computing Systems

, Volume 63, Issue 8, pp 1757–1780 | Cite as

Lower Bounds for Several Online Variants of Bin Packing

  • János BaloghEmail author
  • József Békési
  • György Dósa
  • Leah Epstein
  • Asaf Levin
Article
Part of the following topical collections:
  1. Special Issue on Approximation and Online Algorithms (2017)

Abstract

We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.

Keywords

Bin packing Online algorithms Lower bounds Competitive ratio 

Notes

Acknowledgments

An extended abstract version appears in the Proceedings of WAOA2017. J. Balogh was supported by the project “Integrated program for training new generation of scientists in the fields of computer science”, no. EFOP-3.6.3-VEKOP-16-2017-0002. J. Békési was supported by the EU-funded Hungarian grant EFOP-3.6.2-16-2017-00015. Gy. Dósa was supported by Szechenyi 2020 under the EFOP-3.6.1-16-2016-00015 and by National Research, Development and Innovation Office NKFIH under the grant SNN 116095. L. Epstein and A. Levin were partially supported by a grant from GIF - the German-Israeli Foundation for Scientific Research and Development (grant number I-1366-407.6/2016).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • János Balogh
    • 1
    Email author
  • József Békési
    • 1
  • György Dósa
    • 2
  • Leah Epstein
    • 3
  • Asaf Levin
    • 4
  1. 1.Department of Applied Informatics, Gyula Juhász Faculty of EducationUniversity of SzegedSzegedHungary
  2. 2.Department of MathematicsUniversity of PannoniaVeszprémHungary
  3. 3.Department of MathematicsUniversity of HaifaHaifaIsrael
  4. 4.Faculty of Industrial Engineering and Management, The TechnionHaifaIsrael

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