To reduce the cost of fault management in all-optical networks, it is a promising approach to detect the degradation of optical signal quality solely at the terminal points of all-optical monitoring paths. The all-optical monitoring paths must be routed so that all single-link failures can be localized using route information of monitoring paths where signal quality degradation is detected. However, route computation for the all-optical monitoring paths that satisfy the above condition is time consuming. This paper proposes a procedure for deriving the lower bounds of the required number of monitoring paths to localize all single-link failures, and proposes an efficient monitoring path computation method based on the derived lower bounds. The proposed method repeats the route computation for the monitoring paths until feasible routes can be found, while the assumed number of monitoring paths increases, starting from the lower bounds. With the proposed method, the minimum number of monitoring paths with the overall shortest routes can be obtained quickly by solving several small-scale integer linear programming problems when the possible terminal nodes of monitoring paths are arbitrarily given. Thus, the proposed method can minimize the required number of monitors for detecting the degradation of signal quality and the total overhead traffic volume transferred through the monitoring paths.