An efficient VLSI architecture with applications to geometric problems

Abstract We present a parallel organization with a reduced number of processors and special communication features for efficient solutions to problems in computational geometry. The organization has n processors operating in synchronous mode with row and column access to an n × n array of memory modules. The organization has simple regular structure and can be implemented in VLSI on a single chip or using a limited chip set. We develop fast parallel algorithms for computing several geometric properties of a set of n 2 points in the plane. We present O( n log n ) time parallel algorithms to compute the convex hull of n 2 points in the plane, to compute the intersection of two convex polygons each having n 2 edges, and to compute the diameter and a smallest enclosing box of a set of n 2 points. All these problems require O( n 2 log n ) sequential time. Thus, all our solutions are optimal in the sense that their processor-time product is equal to the sequential complexity of these problems. We also consider the problem of computing nearest neighbors when the n 2 points belong to an n × n digitized image. We show that this problem can be solved on the proposed parallel organization in O( n ) time using n PEs, which is the same time taken by a two-dimensional mesh-connected computer with n 2 processors to solve the same problem.