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We consider an end-to-end approach of inferring network faults that manifest in multiple protocol layers, with an optimization goal of minimizing the expected cost of correcting all faulty nodes. Instead of first checking the most likely faulty nodes as in conventional fault localization problems, we prove that an optimal strategy should start with checking one of the candidate nodes, which are identified based on a potential function that we develop. We propose several efficient heuristics for inferring the best node to be checked in large-scale networks. By extensive simulation, we show that we can infer the best node in at least 95%, and that checking first the candidate nodes rather than the most likely faulty nodes can decrease the checking cost of correcting all faulty nodes by up to 25%.