A minimum length covering subgraph of a network

This paper concerns the problem of locating a central facility on a connected network N. The network, N, could be representative of a transport system, while the central facility takes the form of a connected subgraph of N. The problem is to locate a central facility of minimum length so that each of several demand points on N is covered by the central facility: a demand point at vi in N is covered by the central facility if the shortest path distance between vi and the closest point in the central facility does not exceed a parameter ri. This location problem is NP-hard, but for certain special cases, efficient solution methods are available.