Fast algorithms for the all nearest neighbors problem

The basic approach to algorithm ANNs, as well as to all of the algorithms presented here, is to use a cell technique ([BWY], [BFP]). The region containing the input points is partitioned into equal-sized cubic cells. 'rhe distance from a point to its nearest neighbors is bounded using the distance of the cell cont.aining the point to the nearest cell also occupied by a point. This bound is improved by refining the. cellular partition into smaller and smaBer cubic cells. Computational effort at each step is saved by storing, for each cell occupied by at least one point, a set of nearest neigh.bor occupied cells: those cells that contain points that might be nearest neighbors to the points in the cell.