Traffic Engineering by Polynomially Solvable Link Metric Optimization

Open shortest path first (OSPF) is the most commonly used intra-domain Internet routing protocol. As the routes of paths are determined by basically only the link metrics, many paths may pass a link with small metric; therefore, there is high possibility that it causes the congestion of the link. It is essential that the number of the paths with large traffic in a link is limited to avoid a congestion; therefore, it is important to determine the link metrics so as to limit the number of the paths in a link. In this paper, we define this link metric decision problem, and we prove that it is NP-complete. In addition, when we restricted this problem to determine the metric of only a link, we show that it can be solved in polynomial time.