A decomposition algorithm for network reliability evaluation

This paper presents an algorithm for computing the K-terminal reliability of undirected networks, i.e. the probability that a given set of vertices in the network are connected, when edges and nodes fail independently with known probabilities. This algorithm is based on a decomposition method introduced by Rosenthal. It consists in numbering the vertices of the graph so that the successive boundary sets are as small as possible and in evaluating the probabilities of appropriate classes of boundary sets. We show that for the all terminal reliability problem these classes are the partitions of the boundary sets and we describe them for the general problem. Our computational results are so conclusive that networks much larger than those presented before can now be treated.