Network virtualization has become a fundamental technology to deliver services for emerging data-intensive applications in fields such as bioinformatics and retail analytics hosted at multi-data center scales. To create and maintain a successful virtual network service, the problem of generating a constrained path manifests both in the management plane with a physical path creation (chains of virtual network functions or virtual link embedding) and in the data plane with on-demand path

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... n (traffic steering with Service Level Objective (SLO) guarantees). In this paper, we define the virtual path embedding problem to subsume the virtual link embedding and the constrained traffic steering problems, and propose a new scheme to solve it optimally. Specifically, we introduce a novel algorithm viz., "Neighborhood Method" (NM) which provides an on-demand path with SLO guarantees while reducing expensive over provisioning. We show that by solving the Virtual Path Embedding problem in a set of diverse topology scenarios we gain up to 20% in network utilization, and up to 150% in energy efficiency, compared to the existing path embedding solutions.