Location of speed-up subnetworks

Let a network with edge weights, a set of point-to-point transportation requests and a factor $$\alpha $$α be given. Our goal is to design a subnetwork of given length along which transportation costs are reduced by $$\alpha $$α. This reduces the costs of the network traffic which will choose to use edges of the new subnetwork if this is the more efficient option. Our goal is to design the subnetwork in such a way that the worst-case cost of all routing requests is minimized. The problem occurs in many applications, among others in transportation networks, in backbone, information, communication, or electricity networks. We classify the problem according to the types of the given network and of the network to be established. We are able to clarify the complexity status in all considered cases. It turns out that finding an optimal subtree in a tree already is NP-hard. We therefore further investigate this case and propose results and a solution approach.