I know that delaunay triangulation can be extended into arbitrary dimensions by solving the convex hull problem in $(p+1)$ dimensions and projecting the lower hull into dimension $p$ to obtain a mesh in dimension $p$.  However, this approach is asymptotically $\Omega({n}^{{p}/{2}})$.  I was wondering if there are any other algorithms to produce arbitrary dimensional meshes that can be implemented faster. If so, what are they, how do they work and what is their asymptotic runtime (in terms of the number of mesh points)?
What efficient algorithms are there to generate arbitrary dimensional meshes of simplices?
algorithms;mesh generation;computational geometry;delaunay triangulation
How about;Watson, D.F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput J 24, 167172 (1981).http://comjnl.oxfordjournals.org/content/24/2/167.abstractIf I understood it, it should be $\mathcal{O}\left(n^{\frac{2p-1}{n}}\right)$, isn't that better then $\left(n^{p/2}\right)$?