Design Method of Smallest Robust Networks Against Performance Deterioration During Failures

A telecommunication network should be reliable. However, in many actual networks, there exists the risk that the quality of service drastically deteriorates when the length of paths increases due to a link failure. To get rid of this risk, it is necessary to design a stable network that the maximum increasing ratio of the length of all paths in case of a link failure is small. We proposed the approximation algorithm for the network design problem that constructs such a network by adding some links to a network before. On the other hand, a network design method to construct a network from scratch is also needed. For that purpose, in this paper, we deal with the network design problem that determines a graph with the limited degree, diameter, and maximum increasing ratio of the lengths of all paths in case of an edge deletion. First, we prove that this problem is NP-complete. Next, we propose a heuristic algorithm for this problem and evaluate its performance by the comparison with some actual ISP backbone networks. Our experimental results show that the proposed algorithm worked well on a set of network structures.