Geometric problems on two-dimensional array processors

Abstract

Parallel algorithms for solving geometric problems on two array processor models—the mesh-connected computer (MCC) and a two-dimensional systolic array—are presented. We illustrate a recursive divide- and-conquer paradigm for MCC algorithms by presenting a time-optimal solution for the problem of finding thenearest neighbors of a set of planar points represented by their Cartesian coordinates. The algorithm executes on a√n×√n MCC, and requires an optimalO(√n) time. An algorithm for constructing theconvex hull of a set of planar points and anupdate algorithm for thedisk placement problem on ann 2/3×n 2/3 two-dimensional systolic array are presented. Both these algorithms requireO(n 2/3) time steps. The advantage of the systolic solutions lies in their suitability for direct hardware implementation.