A tight bound for the Delaunay triangulation of points on a polyhedron
Abstract
We show that the Delaunay triangulation of a set of $n$ points distributed nearly uniformly on a $p$-dimensional polyhedron (not necessarily convex) in $d$-dimensional Euclidean space is $O(n^{\frac{d-k+1}{p}})$, where $k = \lceil \frac{d+1}{p+1} \rceil$. This bound is tight in the worst case, and improves on the prior upper bound for most values of $p$.
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