A Short Note on Parameterized Computation of Network Reliability with respect to Treewidth
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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 appears in the network with its associated probability and the problem is to determine the probability of having at least one source-to-target path. This problem is known to be NP-hard for general networks and has been solved for several special families. In this work we present a fixed-parameter algorithm based on treewidth, which is a measure of tree-likeness of graphs. The problem was already known to be solvable in linear time for bounded treewidth, however the known methods used complicated structures and were not easy to implement. We provide a significantly simpler and more intuitive algorithm that while remaining linear, is much easier to implement.
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