Algorithms to evaluate the reliability of a network

We consider problems of network reliability: the two-terminal network reliability consists, given an undirected graph G≡(V, E), and a series of independent edge failure events, in computing the probability that two nodes remain connected. The all-terminal network reliability is the probability that the whole network remains connected. We present in the following two different approaches to compute two-terminal and all-terminal reliability, with various characteristics on the precision level of the result. We give an exact algorithm to compute the reliability in O([V]f(w)² + [E]f(w)) with f(x)≡ and w is the tree-width of G. We also present polynomial methods to give bounds on the reliability. We discuss methods to optimize the mean time to repair of the components.