Exact graph-reduction algorithms for network reliability analysis

Consideration is given to the problem of analyzing the reliability of a network, specifically, the probability that a given set of critical nodes within the network can communicate, given the failure probabilities for component nodes and links. An exact graph-reduction algorithm is presented for solving the k-terminal reliability problem with node failures on an arbitrary network. k-terminal reliability means that a specific set of k target nodes must be able to communicate with one another. The authors model the network by an undirected probabilistic graph whose vertices represent the nodes and whose edges represent the links