A practical implementation of the factoring theorem for network reliability

The factoring theorem is a simple tool for determining the K-terminal reliability of a network, i.e. the probability that a given set K of terminals in the network are connected to each other by a path of working edges. An implementation of an algorithm which uses the factoring theorem, in conjunction with degree-1 and degree-2 vertex reductions, to determine the reliability of a network is presented. Networks treated have completely reliable nodes and have edges which fail statistically and independently with known probabilities. The reliability problem is to determine the probability that all nodes in a designated set of nodes can communicate with each other. Such an implementation of the factoring theorem can be incorporated in a small, stand-alone program of about 500 lines of code. A program of this type requires little computer memory and is ideally suited for microcomputer use.>