A TIME-OPTIMAL MULTIPLE-QUERY NEAREST-NEIGHBOR ALGORITHM ON MESHES WITH MULTIPLE BROADCASTING

The multiple-query nearest-neighbour (MQNN) problem is stated as follows: given a set S of n points in plane and a set Q of m(1 less than or equal to m less than or equal to n) query points, determine for every point in Q its closest neighbor in S. Besides the pure theoretical interest, this problem has many practical applications in various areas such as: computer graphics, pattern recognition and image processing. First, this paper proposes a new time-optimal algorithm to solve the all nearest-neighbor (ANN) problem in O(root n) time on a mesh-connected computer of size root n x root n. Next, using this result in conjunction with the generalized multiple search (GMS) paradigm of Bokka et al.(3,5) we devise a time-optimal algorithm that solves the MQNN problem in O(n(1/6) m(1/3)) time on a mesh with multiple broadcasting (MMB) of size root n x root n.