An Improved Algorithm for Constructing kth-Order Voronoi Diagrams
Bernard Chazelle, Herbert Edelsbrunner · IEEE Transactions on Computers · 1987
The kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E2subdivides E2into maximal regions such that all points within a given region have the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in O(n2log n + k(n - k) log2n) time, O(k(n - k)) storage, and in O(n2+ k(n - k) log2n) time, O(n2) storage, respectively.