International audiencen 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 P=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 NP -hard, an FPTAS is ruled out and an AFPTAS is also the best possible result in the sense of approximation theory
In the context of grid scheduling we consider a scheduling scenario, where parallel jobs have to be scheduled non-preemptively on heterogeneous computational platforms of processors. The speed of the processors may differ among the platforms and the jobs are submitted simultaneously or over the time and cannot run across multiple platforms. We focus on the target of minimizing the total makespan, i.e. the global latest finishing time of a job. In this paper we present an AFPTAS for the problem without release times and show how to generalize our result to malleable jobs and jobs with release times.
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