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3/2-Dual Approximation for CPU/GPU Scheduling

Authors: Bernhard Sebastian Germann, Klaus Jansen, Felix Ohnesorge, and Malte Tutas

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)


Abstract
We present a fast and efficient 3/2 dual approximation algorithm for CPU/GPU scheduling under the objective of makespan minimization. In CPU/GPU scheduling tasks can be scheduled on two different architectures. When executed on the CPU, a task is moldable and can be assigned to multiple cores. The running time becomes a function in the assigned cores. On a GPU, the task is a classical job with a set processing time. Both settings have drawn recent independent scientific interest. For the moldable CPU scheduling, the current best known constant rate approximation is a 3/2 approximation algorithm [Wu et al. EJOR volume 306]. The best efficient algorithm for this setting is a 3/2+ε approximation [Mounie et al. SIAM '07] whereas GPU scheduling admits a 13/11 approximation [Coffman, Garey, Johnson SIAM'78]. We improve upon the current best known algorithms for CPU/GPU scheduling by Bleuse et al. by formulating a novel multidimensional multiple choice knapsack to allot tasks to either architecture and schedule them there with known algorithms. This yields an improved running time over the current state of the art. We complement our theoretical results with experimentation that shows a significant speedup by using practical optimizations and explore their efficacy.

Cite as

Bernhard Sebastian Germann, Klaus Jansen, Felix Ohnesorge, and Malte Tutas. 3/2-Dual Approximation for CPU/GPU Scheduling. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{germann_et_al:LIPIcs.SEA.2024.13,
  author =	{Germann, Bernhard Sebastian and Jansen, Klaus and Ohnesorge, Felix and Tutas, Malte},
  title =	{{3/2-Dual Approximation for CPU/GPU Scheduling}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.13},
  URN =		{urn:nbn:de:0030-drops-203782},
  doi =		{10.4230/LIPIcs.SEA.2024.13},
  annote =	{Keywords: computing, machine scheduling, moldable, CPU/GPU}
}
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