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Algorithmica

pp 1–40 | Cite as

The Geodesic Farthest-Point Voronoi Diagram in a Simple Polygon

  • Eunjin Oh
  • Luis Barba
  • Hee-Kap AhnEmail author
Article
  • 14 Downloads

Abstract

Given a set of point sites in a simple polygon, the geodesic farthest-point 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 \(O(n\log \log n+ m\log m)\)-time algorithm to compute the geodesic farthest-point Voronoi diagram of m point sites in a simple n-gon. This improves the previously best known algorithm by Aronov et al. (Discrete Comput Geom 9(3):217–255, 1993). In the case that all point sites are on the boundary of the simple polygon, we can compute the geodesic farthest-point Voronoi diagram in \(O((n+m) \log \log n)\) time.

Keywords

Farthest-point Voronoi diagram Simple polygon Geodesic metric 

Notes

Acknowledgements

Funding was provided by Ministry of Science and ICT (KR) (Grant No. IITP-2017-0-00905).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Pohang University of Science and TechnologyPohangKorea
  2. 2.Department of Computer ScienceETH ZürichZurichSwitzerland

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