Optimal location of high-speed facility in heterogeneous networks

This paper discuss a problem of locating a facility on tree networks. The facility takes the form of a path- or a tree-shaped subgraph on the network To construct efficient network, we must set the facility to optimal location. In this paper, we propose new evaluation function, all-pair distancesum, which is the sum of distance of all pairs of nodes on the network. Then we show some characteristics of it, which lead to the following relations. In case of continuous tree-shaped version, minimum all-pair distance sum facility is same to minimum distancesum facility. In case of path-shaped or discrete tree-shaped versions, these facilities may be different. Furthermore, we show how to locate minimum all-pair distancesum facility