An optimal cardinality-constrained territory map on a network

The authors consider the problem of finding an optimal cardinality-constrained territory map, and propose an algorithm for the problem with the time and space complexities of O(n(m+k log k)) and O(n+m), respectively, where k,n, and m are the numbers of centers, vertices, and edges of a given network. It is noted that maps of this sort can be applied to an assignment problem, e.g., the problem of assigning an employer (vertex) to a project leader (center).<>