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A GPU Implementation of Bulk Execution of the Dynamic Programming for the Optimal Polygon Triangulation

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10777))

Abstract

The optimal polygon triangulation problem for a convex polygon is an optimization problem to find a triangulation with minimum total weight. It is known that this problem can be solved using the dynamic programming technique in \(O(n^3)\) time. The main contribution of this paper is to present an efficient parallel implementation of this \(O(n^3)\)-time algorithm for a lot of instances on the GPU (Graphics Processing Unit). In our proposed GPU implementation, we focused on the computation for a lot of instances and considered programming issues of the GPU architecture such as coalesced access of the global memory, warp divergence. Our implementation solves the optimal polygon triangulation problem for 1024 convex 1024-gons in 4.77 s on the NVIDIA TITAN X, while a conventional CPU implementation runs in 241.53 s. Thus, our GPU implementation attains a speedup factor of 50.6.

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Author information

Authors and Affiliations

  1. Department of Information Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi Hiroshima, 739-8527, Japan

    Kohei Yamashita, Yasuaki Ito & Koji Nakano

Authors
  1. Kohei Yamashita
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  2. Yasuaki Ito
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  3. Koji Nakano
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Corresponding author

Correspondence to Yasuaki Ito .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Yamashita, K., Ito, Y., Nakano, K. (2018). A GPU Implementation of Bulk Execution of the Dynamic Programming for the Optimal Polygon Triangulation. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10777. Springer, Cham. https://doi.org/10.1007/978-3-319-78024-5_28

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  • DOI: https://doi.org/10.1007/978-3-319-78024-5_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78023-8

  • Online ISBN: 978-3-319-78024-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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