In a WDM network, a single component failure may lead to multiple failures in the logical topology. Protection switching schemes that adopt traditional edge-disjoint or node-disjoint path-selection algorithms may not be able to protect the active connections properly. In this paper, we generalize the disjoint path problem by providing a framework that can model arbitrary types of failures, so that a solution to the problem can be applied to protection switching in WDM networks. We prove the necessary and sufficient condition for the existence of disjoint paths that are free from simultaneous disruption by a single failure. The necessary and sufficient condition suggests a way to find such disjoint paths. Based on the result, we formulate an integer linear program (ILP) that finds the disjoint paths.
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