Elsevier

Journal of Algorithms

Volume 4, Issue 2, June 1983, Pages 121-136
Journal of Algorithms

Efficient algorithms for computing the maximum distance between two finite planar sets

https://doi.org/10.1016/0196-6774(83)90040-8Get rights and content

Abstract

An 0(n log n) algorithm is presented for computing the maximum euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity can be reduced to 0(n). The algorithm is empirically compared to the brute-force method as well as an alternate 0(n2) algorithm. Both the 0(n log n) and 0(n2) algorithms run in 0(n) expected time for many underlying distributions of the points. An ϵ-approximate algorithm can be obtained that runs in 0(n + 1ϵ) worst-case time.

References (25)

  • A Renyi et al.

    Uber die konvexe Hülle von n zufällig gewählten Punkten, I

    Z. Wahrsch. Verw. Gebiete

    (1963)
  • A Renyi et al.

    Uber die konvexe Hülle von n zufällig gewählten Punkten, II

    Z. Wahrsch. Verw. Gebiete

    (1964)
  • Cited by (24)

    • α-Kernel problem with fuzzy visibility

      1995, Fuzzy Sets and Systems
    • Convexity problems on meshes with multiple broadcasting

      1995, Journal of Parallel and Distributed Computing
    • Editorial

      1993, Pattern Recognition Letters
    View all citing articles on Scopus
    View full text