Abstract
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( mod V mod /sup 2/ log mod V mod ) time and O( mod V/sup 2/ mod ) 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/sup -14/ for component reliabilities uniformly distributed between 0.99 and 1.00. Empirically, this difference is always less than 10/sup -17/. >
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