On k-Nearest Neighbor Voronoi Diagrams in the Plane

The notion of Voronoi diagram for a set of N points in the Euclidean plane is generalized to the Voronoi diagram of order k and an iterative algorithm to construct the generalized diagram in 0(k2N log N) time using 0(k2(N − k)) space is presented. It is shown that the k-nearest neighbor problem and other seemingly unrelated problems can be solved efficiently with the diagram.