The Connected p-Center Problem with Extension

Let G(V, E, W) be a graph n vertices and m edges, where each edge e is associated with a positive distance W(e). The traditional p-Center problem is to locate some kind of facilities at p vertices of G to minimize the maximum distance between any vertex and its nearest facility. This paper proposes a practical constraint: the subgraph induced by the p facility vertices must be connected and the problem is called the Connected p-Center problem. We show that the problem on bipartite graphs is NP-Hard, but O(n)-time solvable on trees. After then, the algorithmic result on trees is extended to the situation that some vertices in V cannot be selected as facility vertices.