English

Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon

Computational Geometry 2018-01-09 v1

Abstract

Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones for m <= n/ polylog n. Moreover, the algorithms for the geodesic nearest-point and farthest-point Voronoi diagrams are optimal for m <= n/ polylog n. This partially answers a question posed by Mitchell in the Handbook of Computational Geometry.

Keywords

Cite

@article{arxiv.1801.02292,
  title  = {Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon},
  author = {Eunjin Oh and Hee-Kap Ahn},
  journal= {arXiv preprint arXiv:1801.02292},
  year   = {2018}
}