Geodesic Fréchet distance inside a simple polygon

A.F. Cook IV, C. Wenk

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    16 Citations (Scopus)

    Abstract

    We unveil an alluring alternative to parametric search that applies to both the non-geodesic and geodesic Fréchet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its elegance and practical efficiency when compared to parametric search. We present the first algorithm for the geodesic Fréchet distance between two polygonal curves A and B inside a simple bounding polygon P. The geodesic Fréchet decision problem is solved almost as fast as its non-geodesic sibling and requires O(N2log k) time and O(k+N) space after O(k) preprocessing, where N is the larger of the complexities of A and B and k is the complexity of P. The geodesic Fréchet optimization problem is solved by a randomized approach in O(k+N2log kN log N) expected time and O(k+N2) space. This runtime is only a logarithmic factor larger than the standard non-geodesic Fréchet algorithm (Alt and Godau 1995). Results are also presented for the geodesic Fréchet distance in a polygonal domain with obstacles and the geodesic Hausdorff distance for sets of points or sets of line segments inside a simple polygon P.
    Original languageEnglish
    Title of host publicationProceedings 25th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2008, Bordeaux, France, February 21-23, 2008)
    EditorsS. Albers, P. Weil
    Place of PublicationSchloss Dagstuhl
    PublisherInternationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI)
    Pages193-204
    Publication statusPublished - 2008

    Publication series

    NameDagstuhl Seminar Proceedings
    Volume08001
    ISSN (Print)1862-4405

    Cite this