IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v429y2022ics0096300322002570.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322002570
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127183?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pablo Pérez-Lantero & Carlos Seara & Jorge Urrutia, 2024. "Rectilinear convex hull of points in 3D and applications," Journal of Global Optimization, Springer, vol. 90(2), pages 551-571, October.
    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).
    3. Carlos Alegría & David Orden & Carlos Seara & Jorge Urrutia, 2023. "Separating bichromatic point sets in the plane by restricted orientation convex hulls," Journal of Global Optimization, Springer, vol. 85(4), pages 1003-1036, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322002570. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.