PARALLEL GEOMETRIC ALGORITHMS ON MESH-CONNECTED COMPUTERS.

It is shown that a number of geometric problems can be solved on a ROOT n ROOT multiplied by n mesh-connected computer (MCC) in O( ROOT n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires OMEGA ( ROOT n) time. The problems studied include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, and Voronoi diagrams. The O( ROOT n) algorithms for all of the above problems are based on the classical divide-and-conquer strategy.