Abstract
Row-wise and column-wise prefix-sum computation of a matrix has many applications in the area of image processing such as computation of the summed area table and the Euclidean distance map. It is known that the prefix-sums of a one-dimensional array can be computed efficiently on the GPU. Hence, row-wise prefix-sums of a matrix can also be computed efficiently on the GPU by executing this prefix-sum algorithm for every row in parallel. However, the same approach does not work well for computing column-wise prefix-sums due to inefficient stride memory access to the global memory is performed. The main contribution of this paper is to present an almost optimal column-wise prefix-sum algorithm on the GPU. Quite surprisingly, experimental results using NVIDIA TITAN X show that our column-wise prefix-sum algorithm runs only 2–6% slower than matrix duplication. Thus, our column-wise prefix-sum algorithm is almost optimal.
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Tokura, H., Fujita, T., Nakano, K. et al. Almost optimal column-wise prefix-sum computation on the GPU. J Supercomput 74, 1510–1521 (2018). https://doi.org/10.1007/s11227-018-2242-8
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DOI: https://doi.org/10.1007/s11227-018-2242-8