The terminal-pair reliabilities, between the root and a leaf, of the two-center binary tree, the X-tree, and the ring-tree are computed; the beheaded binary tree is used as a benchmark. A building block is identified in the two-center binary tree from which a decomposition method is formulated. Another building block is identified for the X-tree and ring-tree from which a truss-transformation method is obtained. Computation has been carried out using algorithms based on the analysis. Although the ring-tree is the most reliable at all practical ranges of link and mode reliabilities, the X-tree and two-center binary tree are also good candidates because link reliability over 0.95 is quite common, and node reliability can be kept very high. The X-tree in particular is quite desirable due to its lower connectivity at each node and hence a lower implementation complexity. Three computational methods are presented. The simplicity of the two-center binary-tree algorithm blends with the hierarchical structure of the network itself because the states directly show that the level of computation can be summarized by some reliability subcomponents.
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