The Virtual Network Embedding Problem lies at the heart of many network resource allocation problems. Typically, this problem is studied in a variant where both the mapping of nodes (e.g., the virtual machines) as well as the routing is flexible and hence subject to optimization. However, many networks today are based on control planes with fixed paths, which cannot easily be changed. This paper presents the first approximation algorithm for the embedding cost of a set of virtual networks which do not have to provide routing flexibilities. In particular, we analytically prove that our algorithm achieves an XP approximation: a constant approximation in a resource augmentation model for scenarios with and without routing flexibilities. Our extensive simulations further indicate that our algorithm is not only of theoretical interest but is a practical solution.

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