Improving reliability bounds in computer networks

The probability that a computer network is operational in an environment of statistically independent link failures has been widely studied. Three natural problems arise, when all nodes are to be connected (all-terminal reliability), when two nodes are to communicate (2-terminal reliability), and when k specified nodes are to communicate (k-terminal reliability); the latter case includes the first two. Each of these reliability measures is NPhard to compute, and thus efficiently computable reliability bounds are of significant interest. To date, the all-terminal and 2-terminal cases have been treated separately, and few results apply to the k-terminal case. In this paper, we develop a simple strategy to obtain k-terminal reliability bounds. In the process, we demonstrate improvements on the previous best bounds for all-terminal, k-terminal, and 2-terminal reliability. Computational experience with these new bounds is reported, by comparing the new lower bounds to existing lower bounds.