On Computing All North-East Nearest Neighbors in the L1 Metric

Abstract Given a collection of n points in the plane, we exhibit an algorithm that computes the nearest neighbor in the north-east (first quadrant) of each point, in the L1 metric. By applying a suitable transformation to the input points, the same procedure can be used to compute the L1 nearest neighbor in any given octant of each point. This is the basis of an algorithm for computing the minimum spanning tree of the n points in the L1 metric. All three algorithms run in O(n lg n) total time and O(n) space.