More on online bin packing with two item sizes

  • Authors:

  • Leah Epstein;Asaf Levin

  • Affiliations:

  • Department of Mathematics, University of Haifa, 31905 Haifa, Israel;Department of Statistics, The Hebrew University, Jerusalem, Israel

  • Venue:
  • Discrete Optimization
  • Year:
  • 2008

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Abstract

We follow the work of [G. Gutin, T. Jensen, A. Yeo, On-line bin packing with two item sizes, Algorithmic Operations Research 1 (2) (2006)] and study the online bin packing problem, where every item has one of two possible sizes which are known in advance. We focus on the parametric case, where both item sizes are bounded from above by 1k for some natural number k=1. We show that for every possible pair of item sizes, there is an algorithm with competitive ratio of at most (k+1)^2k^2+k+1. We prove that this bound is tight for every k and, moreover, that it cannot be achieved if the two item sizes are not known in advance.