Combination of conditional Monte Carlo and approximate zero-variance importance sampling for network reliability estimation

We study the combination of two efficient rare event Monte Carlo simulation techniques for the estimation of the connectivity probability of a given set of nodes in a graph when links can fail: approximate zero-variance importance sampling and a conditional Monte Carlo method which conditions on the event that a prespecified set of disjoint minpaths linking the set of nodes fails. Those two methods have been applied separately. Here we show how their combination can be defined and implemented, we derive asymptotic robustness properties of the resulting estimator when reliabilities of individual links go arbitrarily close to one, and we illustrate numerically the efficiency gain that can be obtained.