Exact Methods to compute Network Reliability

In this paper, we present and compare some exact methods to resolve the network reliability problems. These problems concern all kinds of networks, such as computer, communication or power networks. When components of the network are subject to random failures, the network may or may not continue functioning after the failures of some components. The probability that the network will function is its reliability. Networks are modeled by a graph G = (V,E) composed of elements that fail independently of each other with known probabilities. The K-terminal reliability problem has been studied extensively. It consists in evaluating the probability that a given subset of vertices, denoted K, is connected. This problem is NP-hard. We propose here to expose the main methods, developed since the 1970’s. We first consider the enumeration methods using elementary states, paths or cuts. Then we explain the factoring method performed by the reductions. These allow to treat series-parallel graph in linear time. At last, we present the decomposition method implemented as a table-based reduction algorithm and that allows us to resolve the reliability problem in linear time for graphs with bounded treewidth.