A simple universal generating function method to search for all minimal paths in networks
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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In this paper,we propose an algorithm to construct theOrdered Binary Decision Diagram (OBDD) representingthe cut function of a terminal-pair network. The algorithmrecognizes isomorphic sub-problems and thus avoids redundant computations. The system reliability could be efficiently computed by the OBDD. Finally, we propose anapproach to compute the importance measures for multiplecomponents by traversing the OBDD only once. The correctness and the effectiveness of our approach are demonstrated by experiments on 30 benchmark networks. Theexperimental results on a 2-by-100 lattice network, whichhas 299paths or 10,000 cuts,show an impressive improvement compared to the previous works using the sum ofdisjoint products method that have exponential complexity.The CPU time of our method, including the calculation ofnot only the reliability but also the importance measures,for a 100-stage lattice network is only about 0.24 seconds.Thus, this approach is very helpful for the reliability andsensitivity analysis of large networks.