We focus on the placement of Virtualized Network Functions (VNFs) chains in the Network Function Virtualization (NFV) context where NFV Infrastructures (NFVIs) are used to host the VNFs. The optimal placement of VNF (service) chains in hosting infrastructures is one of the key issues in the deployment of service functions in large-scale environments. The Virtualized Network Functions Chain Placement Problem VNF-CPP is NP-Hard and there is a need for placement approaches that can scale with problem size and find good solutions in acceptable times. We propose a matrix-based optimization and a multi-stage graph method that are cost efficient and improve scalability by finding solutions in polynomial times. These algorithms are compared with an exact formulation given by the Perfect 2-Matching leading to a polynomial variant of the VNF-CPP for VNF chains with 2 arcs. Simulation results for longer and more complex chains confirm the efficiency and scalability of the proposed methods and their ability to find good suboptimal solutions