Efficient Geometric Algorithms on the EREW PRAM

We present a technique that can be used to obtain efficient parallel algorithms in the EREW-PRAM computational model. This technique enables us to optimally solve a number of geometric problems in O(logn) time using O(n/logn) EREW-PRAM processors, where n is the input size. These problerns include: computing the convex hull oCa sorted point set in the plane, computing the convex hull oCa simple polygon, finding the kernel of a simple polygon, triangulating a sorted point set in the plane, triangulating monotone polygons and star-shaped polygons, computing the all dominating neighbors, etc. PRAM algorithms for these problems were previously known to be optimal (i.e., O(log n) time and O(n{logn) processors) only in the CREW-PRAM, which is a stronger model than the EREW-PRAM.