Provisioning a Virtual Private Network Under the Presence of Non-communicating Groups

the reservation of capacities in a weighted graph such that the
terminals in this network can communicate with one another. 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.