The Wheatstone Bridge Reduction in Network Reliability Computations

The subgraph configuration known as the Wheatstone bridge of s-independent elements can be replaced by a single edge in a reliabilit-preserving network transformation. The formulas for calculating the good and bad probabilities of this edge are presented. This reduction technique reduces by more than half the complexity of some backtrack algorithms that solve network reliability problems. Computational experience indicates that the benefits are worth the extra efforts it takes to perform this reduction. For problems of moderate size, use of the Wheatstone bridge reduction typically led to computational savings of between 20% and 40%.