Separating point sets in polygonal environments

Erik D. Demaine, Jeff Erickson, Ferran Hurtado, John Iacono, Stefan Langerman, Henk Meijer, Mark Overmars, Sue Whitesides

    Research output: Contribution to journalArticle

    Abstract

    We consider the separability of two point sets inside a polygon by means of chords or geodesic lines. Specifically, given a set of red points and a set of blue points in the interior of a polygon, we provide necessary and sufficient conditions for the existence of a chord and for the existence of a geodesic path that separate the two sets; when they exist we also derive efficient algorithms for their obtention. We also study the separation of the two sets using the minimum number of pairwise non-crossing chords.

    Original languageEnglish (US)
    Pages (from-to)403-419
    Number of pages17
    JournalInternational Journal of Computational Geometry and Applications
    Volume15
    Issue number4
    DOIs
    StatePublished - Aug 2005

    Fingerprint

    Point Sets
    Chord or secant line
    Polygon
    Geodesic
    Separability
    Pairwise
    Interior
    Efficient Algorithms
    Necessary Conditions
    Path
    Line
    Sufficient Conditions

    Keywords

    • Chord
    • Geodesic
    • Separation
    • Simple polygon

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Applied Mathematics
    • Geometry and Topology
    • Computational Mathematics

    Cite this

    Demaine, E. D., Erickson, J., Hurtado, F., Iacono, J., Langerman, S., Meijer, H., ... Whitesides, S. (2005). Separating point sets in polygonal environments. International Journal of Computational Geometry and Applications, 15(4), 403-419. https://doi.org/10.1142/S0218195905001762

    Separating point sets in polygonal environments. / Demaine, Erik D.; Erickson, Jeff; Hurtado, Ferran; Iacono, John; Langerman, Stefan; Meijer, Henk; Overmars, Mark; Whitesides, Sue.

    In: International Journal of Computational Geometry and Applications, Vol. 15, No. 4, 08.2005, p. 403-419.

    Research output: Contribution to journalArticle

    Demaine, ED, Erickson, J, Hurtado, F, Iacono, J, Langerman, S, Meijer, H, Overmars, M & Whitesides, S 2005, 'Separating point sets in polygonal environments', International Journal of Computational Geometry and Applications, vol. 15, no. 4, pp. 403-419. https://doi.org/10.1142/S0218195905001762
    Demaine ED, Erickson J, Hurtado F, Iacono J, Langerman S, Meijer H et al. Separating point sets in polygonal environments. International Journal of Computational Geometry and Applications. 2005 Aug;15(4):403-419. https://doi.org/10.1142/S0218195905001762
    Demaine, Erik D. ; Erickson, Jeff ; Hurtado, Ferran ; Iacono, John ; Langerman, Stefan ; Meijer, Henk ; Overmars, Mark ; Whitesides, Sue. / Separating point sets in polygonal environments. In: International Journal of Computational Geometry and Applications. 2005 ; Vol. 15, No. 4. pp. 403-419.
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