Complexity of Delaunay triangulation for points on lower-dimensional~polyhedra

Abstract : We show that the Delaunay triangulation of a set of points distributed nearly uniformly on a polyhedron (not necessarily convex) of dimension p in d-dimensional space is of order n to the power (d-1)/p for p between 2 and d-1. This improves on the well-known worst-case bound of n to the power ceiling of d/2.