The reliability problem of the quickest path deals with the transmission of a message of size σ from a source to a destination with both the minimum end-to-end delay and the reliability of the path over a network with bandwidth, delay, and probability of fault free on the links. For any value of message size σ, we propose O(n~2m) time algorithm for all-pairs quickest most reliable path problem, where n and m are the number of nodes and the number of arcs or links in the network, respectively.
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