Partial factoring: an efficient algorithm for approximating two-terminal reliability on complete graphs

An efficient network reliability approximation algorithm for two-terminal undirected complete graphs is presented. The method recursively applies a factoring theorem of network reliability in conjunction with series-parallel reliability-preserving reductions. After each pivot, one of the resulting subproblems is further factored, while the other is approximated. The final approximate solution is given in terms of an upper and a lower bound. In the worse case, the algorithm requires O(|V|² log |V|) time and O(|V²|) space. For 128-node complete graphs, the method requires less than 16 s on an IBM AT personal computer. The algorithm´s mean error bound is both theoretically and empirically analyzed. The mean difference between the upper and lower bounds is guaranteed to be less than 10^-14 for component reliabilities uniformly distributed between 0.99 and 1.00. Empirically, this difference is always less than 10^-17