Facility location on terrains

Boris Aronov, Marc Van Kreveld, René Van Oostrum, Kasturirangan Varadarajan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the optimum placement, we compute the furthest-site Voronoi diagram of the sites on the polyhedron. The diagram has maximum combinatorial complexity θ(mn 2), and the algorithm runs in O(mn 2 log 2 m(logm + logn)) time.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings
    Pages19-29
    Number of pages11
    Volume1533 LNCS
    StatePublished - 1998
    Event9th Annual International Symposium on Algorithms and Computation, ISAAC'98 - Taejon, Korea, Republic of
    Duration: Dec 14 1998Dec 16 1998

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume1533 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other9th Annual International Symposium on Algorithms and Computation, ISAAC'98
    CountryKorea, Republic of
    CityTaejon
    Period12/14/9812/16/98

    Fingerprint

    Facility Location
    Polyhedron
    Combinatorial Complexity
    Piecewise Linear Function
    Voronoi Diagram
    Shortest path
    Placement
    Triangle
    Euclidean
    Simplify
    Diagram
    Minimise

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Aronov, B., Van Kreveld, M., Van Oostrum, R., & Varadarajan, K. (1998). Facility location on terrains. In Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings (Vol. 1533 LNCS, pp. 19-29). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1533 LNCS).

    Facility location on terrains. / Aronov, Boris; Van Kreveld, Marc; Van Oostrum, René; Varadarajan, Kasturirangan.

    Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings. Vol. 1533 LNCS 1998. p. 19-29 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1533 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Aronov, B, Van Kreveld, M, Van Oostrum, R & Varadarajan, K 1998, Facility location on terrains. in Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings. vol. 1533 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1533 LNCS, pp. 19-29, 9th Annual International Symposium on Algorithms and Computation, ISAAC'98, Taejon, Korea, Republic of, 12/14/98.
    Aronov B, Van Kreveld M, Van Oostrum R, Varadarajan K. Facility location on terrains. In Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings. Vol. 1533 LNCS. 1998. p. 19-29. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Aronov, Boris ; Van Kreveld, Marc ; Van Oostrum, René ; Varadarajan, Kasturirangan. / Facility location on terrains. Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings. Vol. 1533 LNCS 1998. pp. 19-29 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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