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Approximation Algorithms for Multiple Strip Packing

  • Marin Bougeret
  • Pierre Francois Dutot
  • Klaus Jansen
  • Christina Otte
  • Denis Trystram
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5893)

Abstract

In this paper we study the Multiple Strip Packing (MSP) problem, a generalization of the well-known Strip Packing problem. For a given set of rectangles, r 1,...,r n , with heights and widths ≤ 1, the goal is to find a non-overlapping orthogonal packing without rotations into k ∈ ℕ strips [0,1]×[0, ∞ ), minimizing the maximum of the heights. We present an approximation algorithm with absolute ratio 2, which is the best possible, unless \({\cal P}={\cal NP}\), and an improvement of the previous best result with ratio 2 + ε. Furthermore we present simple shelf-based algorithms with short running-time and an AFPTAS for MSP. Since MSP is strongly \({\cal NP}\)-hard, an FPTAS is ruled out and an AFPTAS is also the best possible result in the sense of approximation theory.

Keywords

Strip Packing Scheduling in grids 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marin Bougeret
    • 1
  • Pierre Francois Dutot
    • 1
  • Klaus Jansen
    • 2
  • Christina Otte
    • 2
  • Denis Trystram
    • 1
  1. 1.LIGGrenoble UniversityFrance
  2. 2.Department of Computer ScienceChristian-Albrechts-University KielKielGermany

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