Dependability Analysis for Networks Via Longest Paths Trees
Firstly, for a given network topology graph ( or digraph) all langest acyclic paths from a given node to any other node are constructed using a special rooted tree, the Longest Paths Tree. Then it is shown how fault trees can be found systematically for numerous unconstrained and constrained network connectivity and flow problems by using this tree. Wherever feasible not only point-to-point connections problems are solved but also obvious generalizations including the problems of intersecting and concurring information flows. It is shown that neither the existence of directed and/or non-directed links nor the fallibility of nodes and/or links pose any real problems with this very general approach. Severe computational complexity problems are pointed at to warn practitioners but several helpful algorithms, useful at least with smallsize systems, are included.
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