Software Defined Networking and Network Function Virtualization are two paradigms that offer flexible software-based network management. Service providers are instantiating Virtualized Network Functions - e.g., firewalls, DPIs, gateways - to highly facilitate the deployment and reconfiguration of network services with reduced time-to-value. They employ Service Function Chaining technologies to dynamically reconfigure network paths traversing physical and virtual network functions. Providing a cost-efficient virtual function deployment over the network for a set of service chains is a key technical challenge for service providers, and this problem has recently caught much attention from both Industry and Academia. In this paper, we propose a formulation of this problem as an Integer Linear Program that allows one to find the best feasible paths and virtual function placement for a set of services with respect to a total financial cost, while taking into account the (total or partial) order constraints for Service Function Chains of each service and other constraints such as end-to-end latency, anti-affinity rules between network functions on the same physical node and resource limitations in terms of network and processing capacities. Furthermore, we propose a heuristic algorithm based on a linear relaxation of the problem that performs close to optimum for large scale instances.
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