## 2 Related Works  
The problem of VNF placement has been the subject of research during the last few years. Different works have formulated the VNF placement problem in an NFV environment as an optimization problem and solved it exactly considering Integer Linear Programming (ILP) models, Mixed Integer Linear Programming (MILP) models, or Mixed Integer Quadratically Constraint Programming (MIQCP). The exact solution of these models is an NP-hard problem, requiring an execution time that grows non-linearly with the network size. As an alternative, the proposal of heuristics to solve the VNF placement is a widely used method to obtain near-optimal solutions in reduced execution time. Optimization targets also vary when defining the optimization problem: the number of used physical machines, the total resource consumption, the total service delay, the energy cost, and the bandwidth consumption are some of the parameters that have been considered, individually or jointly, in the literature. The problem of placing VNFs in edge computing scenarios is different from placing VNFs in a traditional centralized data center network. It is necessary to consider the placement of VNFs in both edge cloud servers (with limited resource capacity and low latency) and core cloud servers (with relatively sufficient resource capacity and high latency) so as to satisfy some strict service-specific requirements. The variety of edge computing scenarios is translated into the definition of different physical and logical network topologies that would affect the proposed solutions. In this work, the edge computing scenario defines three types of nodes (SARs, MDCs, and CDCs), creating a hierarchical and geo-distributed network substrate that should be considered in the mathematical formulation of the optimization problem and the proposed heuristic. [PERSON] et al. [14] studied the VNF-Forwarding Graph (VNF-FG) design and VNF placement problem in 5G mobile networks. Before the VNF placement, this solution defines a first step composed of flow designing and flow combining to generate a VNF-FG according to network service requests. Then, the VNF mapping is solved with the aim of minimizing bandwidth consumption. Defining an MECas a cloud data center located at the edge of the mobile network, the authors of [15] proposed a cross-domain service function placement solution for 5G applications. This work considers a hierarchical network consisting in a top-domain network (containing several cloud data centers) and sub-domain networks (the detailed description of the cloud data center network). In the top-domain network, the requested service chain is divided into subchains by the service chain partition mechanism, and then, the required resources are allocated for these sub-chains in the sub-domain networks by the service subchain mapping solution. The optimization objective of the service chain partitioning is to minimize the end-to-end delay, and the optimization goal of the service sub-chain mapping is to minimize the sub-chain service cost. [PERSON] et al. [16] studied the Cross-Slice Communication (CSC) in 5G network slicing in the context of edge computing. The work proposes the use of a shared CSC slice as a solution to facilitate interactions between services deployed in slices co-located in edge cloud infrastructures. The intermediate slice provides connectivity between the two communicating slices, and it also provides management, monitoring, and security functions (implemented by VNFs in the form of a service chain) to the interconnected slices. The pre-configuration and instantiation of VNFs in the shared CSC slice lead to resource and service time savings. Network softwarization was also identified as an important factor in network slicing in [17].