An efficient parallel solution for Euclidean shortest path in three dimensions

We describe an efficient parallel solution for the problem of finding the shortest Euclidean path between two points in three dimensional space in the presence of polyhedral obstacles. We consider the important case where the order in which the obstacles are encountered in this shortest path is known. In particular for this case we describe an efficient parallel numerical iterative method on a concurrent-read exclusive-write synchronous shared-memory model. The iterations are essentially convergent non-linear block Gauss-Seidel. For special relative orientations of the, say n, polyhedral obstacles, we further describe a direct method that gives the exact solution in O(log n) time using n processors.