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 journalArticle

    Abstract

    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
    Volume31
    Issue number2
    DOIs
    StatePublished - Apr 15 1991

    Fingerprint

    Simple Polygon
    Computing
    Vertex of a graph
    Shortest path
    Set of points
    Euclidean
    Corollary
    Interior

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Applied Mathematics
    • Discrete Mathematics and Combinatorics
    • Theoretical Computer Science

    Cite this

    Agarwal, P. K., Aggarwal, A., Aronov, B., Kosaraju, S. R., Schieber, B., & Suri, S. (1991). Computing external farthest neighbors for a simple polygon. Discrete Applied Mathematics, 31(2), 97-111. https://doi.org/10.1016/0166-218X(91)90063-3

    Computing external farthest neighbors for a simple polygon. / Agarwal, Pankaj K.; Aggarwal, Alok; Aronov, Boris; Kosaraju, S. Rao; Schieber, Baruch; Suri, Subhash.

    In: Discrete Applied Mathematics, Vol. 31, No. 2, 15.04.1991, p. 97-111.

    Research output: Contribution to journalArticle

    Agarwal, PK, Aggarwal, A, Aronov, B, Kosaraju, SR, Schieber, B & Suri, S 1991, 'Computing external farthest neighbors for a simple polygon', Discrete Applied Mathematics, vol. 31, no. 2, pp. 97-111. https://doi.org/10.1016/0166-218X(91)90063-3
    Agarwal PK, Aggarwal A, Aronov B, Kosaraju SR, Schieber B, Suri S. Computing external farthest neighbors for a simple polygon. Discrete Applied Mathematics. 1991 Apr 15;31(2):97-111. https://doi.org/10.1016/0166-218X(91)90063-3
    Agarwal, Pankaj K. ; Aggarwal, Alok ; Aronov, Boris ; Kosaraju, S. Rao ; Schieber, Baruch ; Suri, Subhash. / Computing external farthest neighbors for a simple polygon. In: Discrete Applied Mathematics. 1991 ; Vol. 31, No. 2. pp. 97-111.
    @article{c18568c3e73b4c70855845fdfdd716ac,
    title = "Computing external farthest neighbors for a simple polygon",
    abstract = "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.",
    author = "Agarwal, {Pankaj K.} and Alok Aggarwal and Boris Aronov and Kosaraju, {S. Rao} and Baruch Schieber and Subhash Suri",
    year = "1991",
    month = "4",
    day = "15",
    doi = "10.1016/0166-218X(91)90063-3",
    language = "English (US)",
    volume = "31",
    pages = "97--111",
    journal = "Discrete Applied Mathematics",
    issn = "0166-218X",
    publisher = "Elsevier",
    number = "2",

    }

    TY - JOUR

    T1 - Computing external farthest neighbors for a simple polygon

    AU - Agarwal, Pankaj K.

    AU - Aggarwal, Alok

    AU - Aronov, Boris

    AU - Kosaraju, S. Rao

    AU - Schieber, Baruch

    AU - Suri, Subhash

    PY - 1991/4/15

    Y1 - 1991/4/15

    N2 - 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.

    AB - 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.

    UR - http://www.scopus.com/inward/record.url?scp=4043153839&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=4043153839&partnerID=8YFLogxK

    U2 - 10.1016/0166-218X(91)90063-3

    DO - 10.1016/0166-218X(91)90063-3

    M3 - Article

    AN - SCOPUS:4043153839

    VL - 31

    SP - 97

    EP - 111

    JO - Discrete Applied Mathematics

    JF - Discrete Applied Mathematics

    SN - 0166-218X

    IS - 2

    ER -