Polling: A new randomized sampling technique for computational geometry
We introduce a new randomized sampling technique, called Polling which has applications to deriving efficient parallel algorithms. As an example of its use in computational geometry, we present an optimal parallel randomized algorithm for intersection of half-spaces in three dimensions. Because of well-known reductions, our methods also yield equally efficient algorithms for fundamental problems like the convex hull in three dimensions, Voronoi diagram of point sites on a plane and Euclidean minimal spanning tree. Our algorithms run in time T = O(log n) for worst-case inputs and uses P = O(n) processors in a CREW PRAM model where n is the input size.