Dynamic Additively Weighted Voronoi Diagrams in 2D

摘要

In this paper we present a dynamic algorithm for the construction of the additively weighted Voronoi diagram of a set of weighted points in the plane. The novelty in our approach is that we use the dual of the additively weighted Voronoi diagram to represent it. This permits us to perform both insertions and deletions of sites easily. Given a set B of n sites, among which h sites have a non-empty cell, our algorithm constructs the additively weighted Voronoi diagram of B in O(nT(h) + h log h] expected time, where T(k) is the time to locate the nearest neighbor of a query site within a set of k sites. Deletions can be performed for all sites whether or not their cell is empty. The space requirements for the presented algorithm is O(n). Our algorithm is simple to implement and experimental results suggest an O(n log h) behavior.