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A Novel Computational Model for GPUs with Applications to Efficient Algorithms

Atsushi Koike, Kunihiko Sadakane
Information Systems Architecture Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan
International Journal of Networking and Computing, Vol 5, No 1, 2015

@article{koike2015novel,

   title={A Novel Computational Model for GPUs with Applications to Efficient Algorithms},

   author={Koike, Atsushi and Sadakane, Kunihiko},

   journal={International Journal of Networking and Computing},

   volume={5},

   number={1},

   pages={26–60},

   year={2015}

}

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We propose a novel computational model for GPUs. Known parallel computational models such as the PRAM model are not appropriate for evaluating GPU-based algorithms. Our model, called AGPU, abstracts the essence of current GPU architectures such as global and shared memory, memory coalescing and bank conflicts. Using our model, we can evaluate asymptotic behavior of GPU algorithms more efficiently than the known models and we can develop algorithms that run fast on real GPU devices. As a showcase, we analyze the asymptotic behavior of basic existing algorithms including reduction, prefix scan, and comparison sorting. We further develop new algorithms by detecting and resolving performance bottlenecks of the existing algorithms. Our reduction algorithm has the optimal time and I/O complexities and works with non-commutative operators. Our comparison sorting algorithm has the optimal I/O complexity. Additionally, we show our algorithms run faster than the existing algorithms not only in theory but also in practice.
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