Network restoration is often done at the electronic layer by rerouting traffic along a redundant path. With Wavelength Division Multiplexing (WDM) as the underlying physical layer, it is possible that both the primary and backup paths traverse the same physical links and would fail simultaneously in the event of a link failure. It is therefore critical that lightpaths are routed in such a way that a single link failure would not disconnect the network. We call such a routing survivable and

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... op algorithms for survivable routing of a logical topology. First, we show that the survivable routing problem is NP-complete. We then prove necessary and sufficient conditions for a routing to be survivable and use these conditions to formulate the problem as an Integer Linear Program (ILP). Due to the excessive run-times of the ILP, we develop simple and effective relaxations for the ILP that significantly reduce the time required for finding survivable routings. We use our new formulation to route various logical topologies over a number of different physical topologies and show that this new approach offers a much greater degree of protection than alternative routing schemes such as shortest path routing and a greedy routing algorithm. Finally, we consider the special case of ring logical topologies for which we are able to find a significantly simplified formulation. We establish conditions on the physical topology for routing logical rings in a survivable manner.