Provisioning a virtual private network under the presence of non-communicating groups

Virtual private network design in the hose model deals with the reservation of capacities in a weighted graph such that the terminals in this network can communicate with one another. Each terminal is equipped with an upper bound on the amount of traffic that the terminal can send or receive. The task is to install capacities at minimum cost and to compute paths for each unordered terminal pair such that each valid traffic matrix can be routed along those paths. In this paper we consider a variant of the virtual private network design problem which generalizes the previously studied symmetric and asymmetric case. In our model the terminal set is partitioned into a number of groups, where terminals of each group do not communicate with each other. Our main result is a 4.74 approximation algorithm for this problem. © Springer-Verlag Berlin Heidelberg 2006.