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Factorization and exact evaluation of the source‐terminal diameter‐constrained reliability

In classical network reliability, the system under study is a network with perfect nodes and imperfect links that fail randomly and independently. The probability that a given subset K of terminal nodes belongs to the same connected component is called classical or K ‐Terminal reliability. Although (and because) the classical reliability computation belongs to the class of N P ‐Hard problems, the literature offers many methods for this purpose, given the importance of the models. This article deals with diameter‐constrained reliability, where terminal nodes are further required to be connected by d hops or fewer ( d is a given strictly positive parameter of the metric called its diameter). This metric was defined in 2001, inspired by delay‐sensitive applications in telecommunications. Factorization theory is fundamental for the classical network reliability evaluation, and today it is a mature area. However, its extension to the diameter‐constrained context requires at least the recognition of irrelevant links, which is an open problem. In this article, irrelevant links are efficiently determined in the most used case, where |K|=2 , thus providing a first step toward a Factorization theory in diameter‐constrained reliability. We also analyze the metric in series‐parallel and composition graphs. The article closes with a Factoring algorithm and a discussion of trends for future work. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(4), 283–291 2017