An optimal algorithm for the angle-restricted all nearest neighbor problem on the reconfigurable mesh

Given a set S of n points in the plane and two directions r/sub 1/ and r/sub 2/, the angle-restricted all nearest neighbor problem (ARANN) asks to compute for every point p in S the nearest point in S lying in the planar region bounded by two rays in the directions r/sub 1/ and r/sub 2/ emanating from p. The ARANN problem generalizes the well-known ANN problem and finds applications to pattern recognition, image processing, and computational morphology. Our main contribution is to present an algorithm that solves an arbitrary instance of size n of the ARANN problem in O(1) time on a reconfigurable mesh of size n/spl times/n. Our algorithm is optimal in the sense that /spl Omega/(n/sup 2/) processors are necessary to solve the ARANN problem in O(1) time.