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In this paper, we consider the problem of fault localization in all-optical networks. We introduce the concept of monitoring cycles (MCs) and monitoring paths (MPs) for unique identification of single-link failures. MCs and MPs are required to pass through one or more monitoring locations. They are constructed such that any single-link failure results in the failure of a unique combination of MCs and MPs that pass through the monitoring location(s). For a network with only one monitoring location, we prove that three-edge connectivity is a necessary and sufficient condition for constructing MCs that uniquely identify any single-link failure in the network. For this case, we formulate the problem of constructing MCs as an integer linear program (ILP). We also develop heuristic approaches for constructing MCs in the presence of one or more monitoring locations. For an arbitrary network (not necessarily three-edge connected), we describe a fault localization technique that uses both MPs and MCs and that employs multiple monitoring locations. We also provide a linear-time algorithm to compute the minimum number of required monitoring locations. Through extensive simulations, we demonstrate the effectiveness of the proposed monitoring technique.