The Farthest-Point Geodesic Voronoi Diagram of Points on the Boundary of a Simple Polygon

Authors Eunjin Oh, Luis Barba, Hee-Kap Ahn

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Eunjin Oh
Luis Barba
Hee-Kap Ahn

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Eunjin Oh, Luis Barba, and Hee-Kap Ahn. The Farthest-Point Geodesic Voronoi Diagram of Points on the Boundary of a Simple Polygon. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 56:1-56:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


Given a set of sites (points) in a simple polygon, the farthest-point geodesic Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O((n+m)loglogn)-time algorithm to compute the farthest-point geodesic Voronoi diagram for m sites lying on the boundary of a simple n-gon.
  • Geodesic distance
  • simple polygons
  • farthest-point Voronoi diagram


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