Lower bounds on two-terminal network reliability

Abstract

Computing the probability that two nodes in a probabilistic network are connected is a well-known computationally difficult problem. Two strategies are devised for obtaining lower bounds on the connection probability for two terminals. The first improves on the Kruskal-Katona bound by using efficient computations of small pathsets. The second strategy employs efficient algorithms for finding edge-disjoint paths. The resulting bounds are compared; while the edge-disjoint path bounds typically outperform the Kruskal-Katona bounds, they do not always do so. Finally, a method is outlined for developing a uniform bound which combines both strategies.