Linear Algebra & Sequential Importance Sampling for Network Reliability
The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various sizes. Algorithms based on Sequential Importance Sampling (SIS) have been proposed to estimate a graph's reliability polynomial. The authors develop a new bottom-up SIS algorithm for estimating the reliability polynomial by choosing a spanning tree and adding edges.