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

  • Kohei Yamashita
  • Yasuaki ItoEmail author
  • Koji Nakano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10777)


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.


GPGPU CUDA Triangulation Dynamic programming Parallel algorithms Bulk execution 


  1. 1.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms, 1st edn. MIT Press, Cambridge (1990)zbMATHGoogle Scholar
  2. 2.
    Gilbert, P.D.: New results on planar triangulations. M.Sc. thesis, pp. Report R-850, July 1979Google Scholar
  3. 3.
    Huang, S.H.S., Liu, H., Viswanathan, V.: Parallel dynamic programming. IEEE Trans. Parallel Distrib. Syst. 5(3), 326–328 (1994)CrossRefGoogle Scholar
  4. 4.
    Hwu, W.W.: GPU Computing Gems Emerald Edition. Morgan Kaufmann, Burlington (2011)Google Scholar
  5. 5.
    Ito, Y., Nakano, K.: A GPU implementation of dynamic programming for the optimal polygon triangulation. IEICE Trans. Inf. Syst. E96–D(12), 2596–2603 (2013)CrossRefGoogle Scholar
  6. 6.
    Ito, Y., Ogawa, K., Nakano, K.: Fast ellipse detection algorithm using Hough transform on the GPU. In: Proceedings of International Conference on Networking and Computing, pp. 313–319, December 2011Google Scholar
  7. 7.
    Klincsek, G.T.: Minimal triangulations of polygonal domains. Ann. Disc. Math. 9, 121–123 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Luebke, D., Reddy, M., Cohen, J.D., Varshney, A., Watson, B., Huebner, R.: Level of Detail for 3D Graphics. Morgan Kaufmann, Burlington (2003)Google Scholar
  9. 9.
    Man, D., Uda, K., Ito, Y., Nakano, K.: A GPU implementation of computing Euclidean distance map with efficient memory access. In: Proceedings of International Conference on Networking and Computing, pp. 68–76, December 2011Google Scholar
  10. 10.
    Man, D., Uda, K., Ueyama, H., Ito, Y., Nakano, K.: Implementations of a parallel algorithm for computing Euclidean distance map in multicore processors and GPUs. Int. J. Netw. Comput. 1(2), 260–276 (2011)CrossRefGoogle Scholar
  11. 11.
    Nishida, K., Ito, Y., Nakano, K.: Accelerating the dynamic programming for the matrix chain product on the GPU. In: Proceedings of International Conference on Networking and Computing, pp. 320–326, December 2011Google Scholar
  12. 12.
    NVIDIA Corp.: CUDA C Best Practice Guide Version 8.0 (2017)Google Scholar
  13. 13.
    NVIDIA Corp.: NVIDIA CUDA C Programming Guide Version 8.0 (2017)Google Scholar
  14. 14.
    Pólya, G.: On picture-writing. Amer. Math. Monthly 63, 689–697 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Tani, K., Takafuji, D., Nakano, K., Ito, Y.: Bulk execution of oblivious algorithms on the unified memory machine, with GPU implementation. In: Proceedings of International Parallel and Distributed Processing Symposium Workshops, pp. 586–595 (2014)Google Scholar
  16. 16.
    Uchida, A., Ito, Y., Nakano, K.: Fast and accurate template matching using pixel rearrangement on the GPU. In: Proceedings of International Conference on Networking and Computing, pp. 153–159, December 2011Google Scholar
  17. 17.
    Vaidyanathan, R., Trahan, J.L.: Dynamic Reconfiguration: Architectures and Algorithms. Kluwer Academic/Plenum Publishers, London (2004)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Information EngineeringHiroshima UniversityHigashi HiroshimaJapan

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