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This paper investigates the problem of dynamic survivable lightpath provisioning in optical mesh networks employing wavelength-division multiplexing (WDM). In particular, we focus on shared-path protection because it is resource efficient due to the fact that backup paths can share wavelength links when their corresponding working paths are mutually diverse. Our main contributions are as follows. 1) First, we prove that the problem of finding an eligible pair of working and backup paths for a new lightpath request requiring shared-path protection under the current network state is NP-complete. 2) Then, we develop a heuristic, called CAFES, to compute a feasible solution with high probability. 3) Finally, we design another heuristic, called OPT, to optimize resource consumption for a given solution. The merits of our approaches are that they capture the essence of shared-path protection and approach to optimal solutions without enumerating paths. We evaluate the effectiveness of our heuristics and the results are found to be promising.