Computing external farthest neighbors for a simple polygon

Pankaj K. Agarwal, Alok Aggarwal, Boris Aronov, S. Rao Kosaraju, Baruch Schieber, Subhash Suri

    Research output: Contribution to journalArticlepeer-review


    Let P be (the boundary of) a simple polygon with n vertices. For a vertex p of P, let φ{symbol}(p) be the set of points on P that are farthest from p, where the distance between two points is the length of the (Euclidean) shortest path that connects them without intersecting the interior of P. In this paper, we present an O(n log n) algorithm to compute a member of φ{symbol}(p) for every vertex p of P. As a corollary, the external diameter of P can also be computed in the same time.

    Original languageEnglish (US)
    Pages (from-to)97-111
    Number of pages15
    JournalDiscrete Applied Mathematics
    Issue number2
    StatePublished - Apr 15 1991

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics


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