Network design with a discrete set of traffic matrices

In this paper, we deal with network design problems in which we are given a finite set of possible traffic matrices. We settle some questions about the computational complexity of this problem. We also show that, unless P=NP, there is no polynomial-time approximation scheme even on ring networks, a special case that has received considerable attention for a variety of related problems. However, for such networks, we provide a 43-approximation algorithm, and an exact polynomial-time algorithm for the single source case.