Computational geometry: an introduction
Computational geometry: an introduction
A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Computational geometry in C
The First Subquadratic Algorithm for Complete Linkage Clustering
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
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Let d(a,b) denote the Euclidean distance between two points a, b in the plane. For a cluster C of sites, and for a point p, define d (p, C) = max {d(p,x) | x &egr; C} as the distance between p and C. The Voronoi diagram of a set S of clusters C1,...,Cm is a partition of the plane into domains, one for each cluster, such that a point p belongs to the domain of Ci if and only if d(p,Ci) is leass than or equal to d(p, Cj), i does not equal j. In this note, we present an optimal time O(nlogn) algorithm for computing the Voronoi diagram of a set of convex-hull dijoint clusters, where n is the sum of cardinalities of all clusters. This improves upon the previous O(nsquaredx(n)) time bound, where x(n) is the inverse Ackermann function. OUr result is obtained by examining a new variant of the Voronoi diagram where each site is associated with a convex and unbounded region in which it is active.