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Network Service Providers (NSPs) envisage to support the divergent and stringent requirements of future services by instantiating these services as service chains, commonly referred to as Service Function Chains (SFCs), that are customized and configured to meet specific service requirements. However, due to the limited footprint of the Infrastructure Providers (InPs), these SFCs may have to transcend multiple InPs/domains. In this regard, determining the optimal set of InPs in which to embed the SFC request emerges as a complex problem for several reasons. First, the large number of possible combinations for selecting the InPs to embed the different sub-chains of the request makes this problem computationally complex, rendering optimal solutions only after long computations, especially in large scale networks, which is unfeasible for delay sensitive applications. Second, the unwillingness of InPs to disclose …