Lower Bound for the Online Bin Packing Problem with Restricted Repacking

  • Authors:

  • János Balogh;József Békési;Gábor Galambos;Gerhard Reinelt

  • Affiliations:

  • balogh@jgypk.u-szeged.hu and bekesi@jgypk.u-szeged.hu and galambos@jgypk.u-szeged.hu;-;-;gerhard.reinelt@informatik.uni-heidelberg.de

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2008

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Abstract

In 1996 Ivkovič and Lloyd [A fundamental restriction onfully dynamic maintenance of bin packing, Inform. Process.Lett., 59 (1996), pp. 229-232] gave the lower bound $\frac{4}{3}$on the asymptotic worst-case ratio for so-called fully dynamic binpacking algorithms, where the number of repackable items in eachstep is restricted by a constant. In this paper we improve thisresult to about $1.3871$. We present our proof for a semionlinecase of the classical bin packing, but it works for fully dynamicbin packing as well. We prove the lower bound by analyzing andsolving a specific optimization problem. The bound can be expressedexactly using the Lambert $W$ function.