Cascading divide-and-conquer: A technique for designing parallel algorithms

Abstract

We present techniques for parallel divide-and-conquer, resulting in improved parallel algorithms for a number of problems. The problems for which we give improved algorithms include intersection detection, trapezoidal decomposition (hence, polygon triangulation), and planar point location (hence, Voronoi diagram construction). We also give efficient parallel algorithms for fractional cascading, 3-dimensional maxima, 2-set dominance counting, and visibility from a point. All of our algorithms run in O(log n) time with either a linear or sub-linear number of processors in the CREW PRAM model.