Delete point from Voronoi diagram efficiently

I have a point set and create a Delaunay triangulation and a Voronoi diagram. Then I would like to delete a point and calculate the Delaunay triangulation and Voronoi diagram again. It is easy to delete the point from the Delaunay trianglation: If I have a triangulation DT (DT = delaunayTriangulation(x,y)), I can delete a point using DT.Points(index,:) = [];. The question is how can I then create the new Voronoi diagram efficiently? I know that only the cells adjacent to the deleted point will change, so I would like to avoid computing the whole Voronoi diagram again.