Approximation Algorithm for Multiple Strip Packing

Marin Bougeret 1 Pierre-Francois Dutot 2 Klaus Jansen 3 Christina Otte 3 Denis Trystram 2, 4
2 MOAIS - PrograMming and scheduling design fOr Applications in Interactive Simulation
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
3 Theory of Parallelism
Department of Computer Science, CAU - Christian-Albrechts-Universität zu Kiel
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, $r_1,\ldots,r_n$, with heights and widths $\le 1$, the goal is to find a non-overlapping orthogonal packing without rotations into $k\in\mathbb{N}$ strips $[0,1]\times[0,\infty)$, 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 $2+\EPS$. 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.
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Marin Bougeret, Pierre-Francois Dutot, Klaus Jansen, Christina Otte, Denis Trystram. Approximation Algorithm for Multiple Strip Packing. WAOA'2009: 7th Workshop on Approximation and Online Algorithms, Sep 2009, Copenhague, Denmark. pp.37-48, ⟨10.1007/978-3-642-12450-1_4⟩. ⟨hal-00738614⟩



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