An Improved Algorithm for Constructing kth-Order Voronoi Diagrams

The kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E
²
subdivides E
²
into 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(n
²
log n + k(n - k) log
²
n) time, O(k(n - k)) storage, and in O(n
²
+ k(n - k) log
²
n) time, O(n
²
) storage, respectively.