Placement and Allocation of VNF Nodes Under Budget and Capacity Constraints Revisited

Network function virtualization (NFV) enables cost reduction and optimized service deployment. By means of virtualization, network functions which used to be executed on specialized hardware are being replaced with software called Virtual Network Functions (VNFs) that can run on commodity hardware. These VNFs are applied to data flows passing through network nodes with VNFs hosted on them. To fully realize the benefits of NFV, each flow must be fully processed on VNF nodes. Given the budget constraints, only a finite number of nodes can be selected to host VNFs, and these nodes also have limited capacity to process the flows passing through them. In this paper, we consider the problem of VNF node placement and capacity allocation in a network graph $G=(V,E)$, i.e., selecting the best subset of VNF nodes and optimally distributing their bandwidth to maximize the total volume of fully processed traffic flows F. We propose a simpler algorithm for solving this problem than the previously proposed version, representing it as an integer linear programming problem with an approximation ratio of ${\displaystyle \frac{1}{2}}(1-1/e)$, and time complexity $O\left(\right|V{|}^{2.5}·\left|F{|}^{2.5}·L\right)$, where L is the number of bits of input data.