Multiplicative improvements in network reliability bounds

In the network design process, one goal is to select a network topology which is highly reliable. Although there is no universally accepted measure of reliability, the most widely used definition is a probabilistic one. The network is modelled as a probabilistic graph G = (V ,E) , in which V is a set of nodes representing sites in the network, and E is a collection of undirected edges representing bidirectional point-topoint communication links. Nodes are not susceptible to failure, but edges are. Each edge e operates with some known probability pe. In this setting, the reliability is the probability that the network can support some desired network operation, when edges fail independently according to the given probabilities. Three standard reliability measures arise in this way. An all-terminal operation requires that every pair of nodes has a path of operational edges connecting them, and all-terminal reliability is the probability that such an event occurs in the network. A two-terminal operation for specified nodes s and t requires that there be (at least) a path of operational edges connecting s with t; two-terminal reliability is then the probability of this event. Finally, a kterminal operation requires, for a specified set K of k target nodes, that every pair of target nodes has a path of operational edges connecting them. Numerous techniques have been developed for computing these three reliability