Date of Original Version
20th Fall Workshop on Computational and Combinatorial Geometry, Tufts, November 2009.
Abstract or Table of Contents
The tremendous usefulness of Voronoi diagrams is tempered by their worst-case O(n⌈d/2⌉) size blowup. This makes them an obvious target for approximation, and indeed, several methods have been proposed that produce linear size approximations to the Voronoi diagram supporting logarithmic-time approximate nearest neighbor queries. All such methods use quadtrees to approximate the Voronoi cells. But what if the input does not have a “bad” Voronoi diagram? There is a huge gap between the best-case and the worst case complexity. Sometimes, the exact solution is both simpler and more precise than an approximation