A Technique to Identify Nearest Neighbors

A nonarithmetic procedure is described for discovering among a set of points in a d-dimensional space, the k neighbors nearest a given point, according to the Minkowski "max metric." It is shown that this procedure may be used to eliminate distance calculations when finding nearest neighbors according to any Minkowski p-metric. When used with a set of uniformly distributed sample points, the expected number of distance calculations n required by this technique is given by E[n] ≃ kCp,d where Cp,d is a constant determined by p and d. In the case of the Euclidean metric used in two dimensions with 1000 uniformly distributed sample points, the effective number of distance calculations required to find the nearest neighbor is approximately five.