Using the Decomposition-Tree of a Network in Reliability Computation

Available algorithms for measures of network reliability require computation time f(n) where f is at least exponential in n, the number of failure-prone elements in the system. Modularization is a familiar method of decomposing a network reliability problem into a set of subproblems. This decomposition reduces required computation time from f(n) to a sum of f(ni), ni < n, usually a considerable saving. For a 2-terminal communication network, the decomposition tree of a network provides the identity of the modules and an easily read map of the relations among them. The decomposition tree is derived by finding the triconnected components of the underlying graph. Reducing computation time by finding and analyzing the triconnected components of a network has been proposed for the reliability problems of 2-terminal communication, all-terminal communication, and feasible transportation flow. This paper introduces the use of the decomposition tree for reliability computation purposes, presents a general algorithm based on the tree, and demonstrates its application to the problems named above, as well as to the problem of feasible shortest path.