Static Network Reliability Estimation via Generalized Splitting

We propose a novel simulation-based method that exploits a generalized splitting (GS) algorithm to estimate the reliability of a graph (or network), defined here as the probability that a given set of nodes are connected, when each link of the graph fails with a given (small) probability. For large graphs, in general, computing the exact reliability is an intractable problem and estimating it by standard Monte Carlo methods poses serious difficulties, because the unreliability (one minus the reliability) is often a rare-event probability. We show that the proposed GS algorithm can accurately estimate extremely small unreliabilities and we exhibit large examples where it performs much better than existing approaches. It is also flexible enough to dispense with the frequently made assumption of independent edge failures.