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To support multiple on-demand services over fixed communication networks, network operators must allow flexible customization and fast provision of their network resources. One effective approach to this end is network virtualization, whereby each service is mapped to a virtual subnetwork providing dedicated on-demand support to network users. In practice, each service consists of a prespecified sequence of functions, called a service function chain (SFC), while each service function in a SFC can only be provided by some given network nodes. Thus, to support a given service, we must select network function nodes according to the SFC and determine the routing strategy through the function nodes in a specified order. A crucial network slicing problem that needs to be addressed is how to optimally localize the service functions in a physical network as specified by the SFCs, subject to link and node capacity constraints. In this paper, we formulate the network slicing problem as a mixed binary linear program and establish its strong NP-hardness. Furthermore, we propose efficient penalty successive upper bound minimization (PSUM) and PSUM-R(ounding) algorithms, and two heuristic algorithms to solve the problem. Simulation results are shown to demonstrate the effectiveness of the proposed algorithms.

Network Slicing for Service-Oriented Networks Under Resource Constraints