More is Less: A Lightweight Model for SFC-Constrained Maximum Flow using Functions-Expanded Graph

Service Function Chain (SFC) is an architecture that can enable applications-driven networking. That is, as per an applications’ requirement, SFC ensures the data to be processed by an ordered set of service functions while delivering the data to its destination. SFC has been widely applied to remote sensing, blockchain, time-sensitive data delivery, 5G/6G network slicing. In this context, one fundamental problem is determining the maximum amount of flow that can be serviced (by the chained service functions) in a given network. Existing efforts model this as a linear programming problem with redundant variables and constraints, requiring high time complexity. To construct a lightweight model with a low time complexity, we introduce a functions-expanded graph (FEG) that gives a simple and intuitive representation of the SFC ordering requirements (where the data must be processed through a predefined sequence of service functions), while modeling both the computing and transmission resources. Additionally, this structure further allows us to prune useless edges and nodes, which allows for a more lightweight linear programming model with fewer variables and constraints. The complexity analysis shows the time complexity of solving the existing model(s) can be $1 /(1-\alpha)^{3.5}$-fold more than the time complexity of solving our proposed FEG-based model, where $\alpha$ is the ratio of the number of removed edges over the number of all the edges.