Novel parallel algorithm for constructing Delaunay triangulation based on a twofold-divide-and-conquer scheme

To increase the efficiency when processing large data sets, a novel parallel algorithm is proposed for constructing the Delaunay triangulation of a planar point set based on a twofold-divide-and-conquer scheme. This algorithm automatically divides the planar point set into several non-overlapping subsets along the x-axis and y-axis directions alternately, according to the number of points and their spatial distribution. Next, the Guibas–Stolfi divide-and-conquer algorithm is applied to construct Delaunay sub-triangulations in each subset. Finally, the sub-triangulations are merged based on the binary tree. All three sequential steps are processed using multitasking parallel technology. Our results show that the proposed parallel algorithm is efficient for constructing the Delaunay triangulation with a good speed-up.