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We consider the problem of routing the lightpaths of a logical topology of a WDM network on an arbitrary physical topology, such that the logical topology remains,connected even after the failure of a physical link. We focus our attention on the ring interconnection as the logical topology because it is widely used in many protection schemes. We first establish the necessary and sufficient condition for a ring logical topology to withstand failure of a single physical link. Next we show that the testing of this necessary and sufficient condition is an NP-complete problem. Finally, we give an algorithm for testing the necessary and sufficient condition and demonstrate the execution of the algorithm with the help of an example.