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Detecting degraded optical signal quality solely at the terminal nodes of monitoring trails is a promising approach for reducing the fault management cost in all-optical mesh networks. However, this approach requires that monitoring trails are routed so that all failures can be localized using route information for the monitoring trails where degraded signal quality is detected. Thus, this paper proposes a novel heuristic method to compute the least number of monitoring trails required to localize all link failures in an arbitrary failure scenario. In particular, the proposed method can compute the monitoring trails terminating only at specified nodes to which monitors can be attached. This paper verifies the effectiveness of the proposed method by comparison with the optimum method based on an integer programming model and an existing heuristic method. Using the proposed method, an accurate estimate of the least number of monitoring trails and their routes can be computed quickly, even for practical large-scale networks.