An efficient algorithm for computing network reliability in small treewidth - Goharshady, Amir Kafshdar; Mohammadi, Fatemeh (Reliability engineering & system safety, 2020)
•We provide an efficient parameterized algorithm that is able to compute network reliability on graphs with small treewidth in linear time.•Small-treewidth graphs are the most general family of graphs for which efficient algorithms for computing network reliability are known (to date).•Our algorithm is extremely scalable and can handle graphs with 100,000 vertices in less than 5 min. In contrast, previous methods could only handle graphs with up to 10 vertices.•We show that our algorithm is able to compute the reliability of subway networks in several major cities. To the best of our knowledge, this is the first algorithm for network reliability that can handle real-world instances of the problem. We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard. We provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.