Triangulation in a plane and 3D convex hull on mesh-connected arrays and hypercubes

The authors present four new parallel algorithms for triangulation of points in a plane. The first two, for one-way iterative arrays and two-way cellular arrays, requiring O(n) time and O (n) processors. Next they give an algorithm for d-dimensional mesh arrays which requires O(n ^1/d) time and a hypercube algorithm with a worst case running time of O(log³ n) and an expected running time of O(log² n), both using O( n) processors. The linear array algorithms are the first known of for these architectures which compute Delaunay and greedy triangulations. The mesh array and hypercube algorithms appear to be the first which directly compute a triangulation on these architectures. These algorithms can be modified to compute the Voronoi diagram of points in the plane and the convex hull of points in 3-space