Network reliability analysis using 2-connected digraph reductions

The problem of computing the SKT reliability, the probability that a source s can send communication to a specified set of terminals K ⊂ V in a probabilistic digraph D = (V,E) is considered. For general digraphs, this problem is known to be NP-hard and it is helpful to consider schemes that can decompose the problem into a number of smaller problems. A non-separable digraph is 2-connected if it contains a separation pair, a pair of nodes whose removal disconnects the digraph. Such a digraph can be partitioned into two or more segments. It is shown that at least one of these segments can be replaced by a simpler structure; this replacement results in an exact reliability preserving reduction. The proposed reduction scheme is general and is applicable to all digraphs containing a separation pair; earlier methods could only handle special cases. For a class of digraphs, called BSP digraphs, such a reduction is always admissible and the SKT reliability can be computed in time O(∣E∣). A digraph is a BSP digraph if its underlying undirected graph is series-parallel. A BSP digraph can be cyclic or acyclic. No polynomial-time algorithms were previously known for this class of digraphs.