Method for Finding Protected Nodes for Robust Network against Node Failures

The reliability of a communication network is important, as the Internet is an important social infrastructure. However, especially in a large network, it is difficult to avoid the failures due to various factors. It is necessary to design a network that keeps communication among nodes even during failures. However, in many actual networks, there exists the risk of telecommunication blackout by a node failure or attack. To get rid of this risk, it is necessary to design a network so that many nodes can communicate mutually even if nodes fail. It is desirable that all nodes have their backup facility, but it needs much cost; therefore, at least critical nodes whose failures fragment a network to many small connected components must be protected by backup facility. We addressed a problem to determine protected nodes such that, even if non-protected nodes fail, the minimum size of the connected components of a remaining network is not less than a threshold. In this paper, we propose an approximation algorithm with the approximation ratio of two for the problem restricted to the case that at most two nodes simultaneously fail. Moreover, we evaluate the performance of the approximation algorithm by using actual network topologies.