Two dimensional maximum weight matching using Manhattan topology

Let V be a finite set of points embedded in a plane. Consider a complete graph on the points in V and use Manhattan topology to measure the weight of all edges. A maximum weight perfect matching finds disjoint edges that cover all points, such that the sum of the weights of the edges is maximized. This paper presents an algorithm that finds a maximum weight perfect matching for points embedded in a plane in O(|V|log⁡(|V|) time complexity.