The distance-domination numbers of trees

The P-center problem is to locate P centers in a graph G so that the maximum distance between centers and non-centers is minimized. A related problem is to determine the maximum number of vertices that can be “covered” (within a distance of α) by a vertex set of cardinality P in G. In this paper we describe an O(n³P) algorithm which solves the maximum coverage problem on trees. We also apply the same idea to solve the P-median problem on trees.