Efficient Parallel Solutions to Some Geometric Problems

This paper presents new algorithms for solving some geometric problems on a shared memory parallel computer j where concurrent reads are allowed but no two processors can simultaneously attempt to write in the same memory location. The algorithms are quite different from known sequential algorithms, and are based on the use of a new parallel divide-and-conquer technique. One of our results is an O(logn) time, O(n) processor algorithm for the convex hull problem. Another result is an O(Iogn log log n) time, O(n) processor algorithm for the problem of selecting a closest pair of points among n input points.