We consider the expected number of Voronoi vertices (or number of Delaunay cells for the dual structure) for a set of n i.i.d. random point sites chosen uniformly from the unit d-hypercube [0, 1]. We show an upper bound for this number which is linear in n, the number of random point sites, where d is assumed to be a constant. This result matches the trivial lower bound of n. This is an open pr...
