Abstract
AbstractCut set inclusion and exclusion is a well known reliability evaluation procedure. However, many of the cut set intersection terms cancel so it can be laborious to use. In directed graphs it is shown that the number of noncancelling terms cannot exceed the number of possible ordered partitions of the set of nodes. The resulting node partition formula will still contain cancelling terms when applied to incomplete graphs. An algorithm is developed to determine the set of noncancelling terms and its application illustrated on some special classes of graphs: acyclic graphs and graphs admitting a modular decomposition.
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