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A fast and efficient algorithm for determining the connected orthogonal convex hulls

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  • Kieu Linh, Nguyen
  • Thanh An, Phan
  • Van Hoai, Tran

Abstract

The Quickhull algorithm for determining the convex hull of a finite set of points was independently conducted by Eddy in 1977 and Bykat in 1978. Inspired by the idea of this algorithm, we present a new efficient algorithm, for determining the connected orthogonal convex hull of a finite set of points through extreme points of the hull, that still keeps advantages of the Quickhull algorithm. Consequently, our algorithm runs faster than the others (the algorithms introduced by Montuno and Fournier in 1982 and by An, Huyen and Le in 2020). We also show that the expected complexity of the algorithm is O(nlogn), where n is the number of points.

Suggested Citation

  • Kieu Linh, Nguyen & Thanh An, Phan & Van Hoai, Tran, 2022. "A fast and efficient algorithm for determining the connected orthogonal convex hulls," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322002570
    DOI: 10.1016/j.amc.2022.127183
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    References listed on IDEAS

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    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.
    3. Carlos Alegría & David Orden & Carlos Seara & Jorge Urrutia, 2021. "Efficient computation of minimum-area rectilinear convex hull under rotation and generalizations," Journal of Global Optimization, Springer, vol. 79(3), pages 687-714, March.
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    2. 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).

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