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.
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Bougeret, M., Dutot, P.F., Jansen, K., Otte, C., Trystram, D. (2010). Approximation Algorithms for Multiple Strip Packing. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_4
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DOI: https://doi.org/10.1007/978-3-642-12450-1_4
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