On the complexity of maintaining fault-tolerant distributed systems

The author considers the problem of maintaining a system that can be described as a graph with redundant vertices and edges in the case of failure of some vertice components. If one component fails, activation of this and may be some other components has to be switched from the default parts to redundant parts of the same type while retaining the structure of the graph. The author shows that even under severe restrictions the question whether the system can be maintained after a single vertice component failure is NP-complete