Farthest-Polygon Voronoi Diagrams

Given a family of k disjoint connected polygonal sites of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k − 1 connected components, but if one component is bounded, then it is equal to the entire region.

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Otfried Cheong, Hazel Everett, Marc Glisse, Joachim Gudmundsson, Samuel Hornus, Sylvain Lazard, Mira Lee, Hyeon-Suk Na
• Keywords: ESA 2007, Farthest-site Voronoi Diagram, Polygonal Sites, Total Complexity