Issue No. 06 - June (1982 vol. 31)
null Der-Tsai Lee , Department of Electrical Engineering and Computer Science, Northwestern University
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.
Voronoi diagram, Analysis of algorithm, computational complexity, divide and conquer technique, k-nearest neighbors, point location
n. Der-Tsai Lee, "On k-Nearest Neighbor Voronoi Diagrams in the Plane," in IEEE Transactions on Computers, vol. 31, no. , pp. 478-487, 1982.