Computing multidimensional Delaunay tessellations

We recall some properties of Voronoi and Delaunay tessellations in any numbers of dimensions. We then propose a solution to the following problem: Given the Delaunay tessellation of n d-dimensional data points X-1, ... , X-n, the problem is to insert a new data point X and to update the tessellation accordingly. The solution proposed achieves minimum space-complexity.