We consider the two-dimensional bin packing and strip packing problem, where a list of rectangles has to be packed into a minimal number of rectangular bins or a strip of minimal height, respectively. All packings have to be non-overlapping and orthogonal, i.e., axis-parallel. Our algorithm for strip packing has an absolute approximation ratio of 1.9396 and is the first algorithm to break the approximation ratio of 2 which was established more than a decade ago. Moreover, we present a polynomial time approximation scheme (\(\mathcal{PTAS}\)) for strip packing where rotations by 90 degrees are permitted and an algorithm for two-dimensional bin packing with an absolute worst-case ratio of 2, which is optimal provided \(\mathcal{P} \not= \mathcal{NP}\).


two-dimensional bin packing strip packing rectangle packing approximation algorithm absolute worst-case ratio 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rolf Harren
    • 1
  • Rob van Stee
    • 1
  1. 1.Max-Planck-Institut für Informatik (MPII)SaarbrückenGermany

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