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Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity

Author

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  • Hoang, Nam-Dũng
  • Linh, Nguyen Kieu
  • Phu, Hoang Xuan

Abstract

This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R2, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of n points distributed bleast-bmost-boundedly in some rectangle can be determined with the complexity O(n). Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.

Suggested Citation

  • Hoang, Nam-Dũng & Linh, Nguyen Kieu & Phu, Hoang Xuan, 2024. "Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324003928
    DOI: 10.1016/j.amc.2024.128931
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    References listed on IDEAS

    as
    1. An, Phan Thanh & Huyen, Phong Thi Thu & Le, Nguyen Thi, 2021. "A modified Graham’s convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    2. Nguyen, Linh Kieu & Song, Chanyoung & Ryu, Joonghyun & An, Phan Thanh & Hoang, Nam-Dũng & Kim, Deok-Soo, 2019. "QuickhullDisk: A faster convex hull algorithm for disks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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