Service chain placement in SDNs

We study the allocation problem of a compound request for a service chain in a software defined network that supports network function virtualization. Given a network that contains servers with limited processing power and links with limited bandwidth, a service chain is a sequence of virtual network functions (VNFs) that serve a certain flow request in the network. The allocation of a service chain consists of routing and VNF placement, namely each VNF from the sequence is placed in a server along a path. It is feasible if each server can handle the VNFs that are assigned to it, and if each link on the path can carry the flow that is assigned to it. A request for service is composed of a source and a destination in the network, an upper bound on the total latency, and a specification in the form of a directed acyclic graph (DAG) of VNFs that provides all service chains that are considered valid for this request. In addition, each pair of server and VNF is associated with a cost for placing the VNF in the server. Given a request, the goal is to find a valid service chain of minimum total cost that respects the latency constraint or to identify that such a service chain does not exist. We show that even the feasibility problem is NP-hard in general graphs. Hence we focus on DAGs. We show that the problem is still NP-hard in DAGs even for a very simple network, and even if the VNF specification consists of only one option (i.e., the virtual DAG is a path). On the other hand, we present an FPTAS for the case where the network is a DAG. In addition, based on our FPTAS, we provide algorithms for general instances in which the service chain passes through a bounded number of vertices whose degree is larger than two. Finally, we provide an FPTAS for a fault-tolerant version of the problem.