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Next-generation optical transport networks will automatically and dynamically provision end-to-end connections. In this paper, we study the problem of inter-domain dynamic routing under a multi-layer multi-domain network model, which allows the end-to-end connections to be set up not only across multiple routing domains but also through two transport layers: the optical layer and the digital layer. In this model, a connection can traverse the domain boundary either through optical bypass or through optical-electrical-optical (O/E/O) processing. We propose an inter-domain dynamic routing scheme with modest time complexity to address the problem from an algorithmic perspective.