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We consider the classic problem of Network Reliability. A network is giventogether with a source vertex, one or more target vertices, and probabilitiesassigned to each of the edges. Each edge appears in the network with itsassociated probability and the problem is to determine the probability ofhaving at least one source-to-target path. This problem is known to be NP-hard.  We present a linear-time fixed-parameter algorithm based on a parametercalled treewidth, which is a measure of tree-likeness of graphs. NetworkReliability was already known to be solvable in polynomial time for boundedtreewidth, but there were no concrete algorithms and the known methods usedcomplicated structures and were not easy to implement. We provide asignificantly simpler and more intuitive algorithm that is much easier toimplement.  We also report on an implementation of our algorithm and establish theapplicability of our approach by providing experimental results on the graphsof subway and transit systems of several major cities, such as London andTokyo. To the best of our knowledge, this is the first exact algorithm forNetwork Reliability that can scale to handle real-world instances of theproblem.

An Efficient Algorithm for Computing Network Reliability in Small Treewidth