Journal of Scheduling

, Volume 20, Issue 6, pp 601–621 | Cite as

Online bin stretching with three bins

  • Martin BöhmEmail author
  • Jiří Sgall
  • Rob van Stee
  • Pavel Veselý


Online bin stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for online bin stretching with a stretching factor of \(11/8 = 1.375\) for three bins. Additionally, we present a lower bound of \(45/33 = 1.\overline{36}\) for online bin stretching on three bins and a lower bound of 19/14 for four and five bins that were discovered using a computer search.


Online algorithms Semi-online algorithms Semi-online scheduling Bin stretching Bin packing Lower bounds for online algorithms Game tree search 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Martin Böhm
    • 1
    Email author
  • Jiří Sgall
    • 1
  • Rob van Stee
    • 2
  • Pavel Veselý
    • 1
  1. 1.Computer Science Institute of Charles UniversityPragueCzech Republic
  2. 2.Department of Computer ScienceUniversity of LeicesterLeicesterUK

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