Optimal Parallel Hypercube Algorithms for Polygon Problems

We present parallel techniques on hypercubes for solving optimally a class of polygon problems. We thus obtain optimal O(logn)-lime, n-processor hypercube algorithms for the problems of computing the portions of an n-vertex simple polygonal chain C that are visible from a given source point, computing the convex hull of C, testing an n-verlex simple polygon P for monotonicity, and other related problems as well. Previously it was not known how to achieve these complexity bounds on hypercubes, one of the main difficulties being that there is no known optimal sorting hypercube algorithm that achieves these bounds. In fad these are the first optimal geometric hypercube algorithIIl5 that do not assume that the input is given already sorted by x or y coordinates. The hypercube model we use is the standard one, with 0(1) local memory per processor, and with one-port communication.