An efficient algorithm for the three-dimensional diameter problem

Abstract

We explore a new approach for computing the diameter of n points in ?3 that is based on the restriction of the furthest-point Voronoi diagram to the convex hull. We show that the restricted Voronoi diagram has linear complexity. We present a deterministic algorithm with O(n log2n) running time. The algorithm is quite simple and is a good candidate to be implemented in practice. Using our approach the chromatic diameter and all-furthest neighbors in ?3 can be found in the same running time.