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Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5687))

Abstract

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 \(\mathcal{P} \not= \mathcal{NP}\).

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik (MPII), Campus E1 4, 66123, Saarbrücken, Germany

    Rolf Harren & Rob van Stee

Authors
  1. Rolf Harren
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  2. Rob van Stee
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Editor information

Editors and Affiliations

  1. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Irit Dinur

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Technion, Computer Science Department, 32000, Haifa, Israel

    Joseph Naor

  4. University of Geneva, Centre Universitaire d’Informatique, Battelle Bat. A, 7 rte de Drize, 1227, Carouge, Switzerland

    José Rolim

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© 2009 Springer-Verlag Berlin Heidelberg

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Harren, R., van Stee, R. (2009). Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_14

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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