Farthest-polygon Voronoi diagrams

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Abstract

Given a family of k disjoint connected polygonal sites in general position and 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(nlog3n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k1 connected components, but if one component is bounded, then it is equal to the entire region.

Keywords

Voronoi diagram

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This research was supported by the INRIA équipe associée KI, the Brain Korea 21 Project, the School of Information Technology, KAIST, and the Korea Science and Engineering Foundation Grant R01-2008-000-11607-0 funded by the Korean government.

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National ICT Australia is funded through the Australian Government's Backing Australia's Ability initiative, in part through the Australian Research Council.