The Constrained Virtual Steiner Arborescence Problem: Formal Definition, Single-Commodity Integer Programming Formulation and Computational Evaluation

Abstract

As the Internet becomes more virtualized and software-defined, new functionality is introduced in the network core: the distributed resources available in ISP central offices, universal nodes, or datacenter middleboxes can be used to process (e.g., filter, aggregate or duplicate) data. Based on this new networking paradigm, we formulate the Constrained Virtual Steiner Arborescence Problem (CVSAP) which asks for optimal locations to perform in-network processing, in order to jointly minimize processing costs and network traffic while respecting link and node capacities. We prove that CVSAP cannot be approximated (unless P = NP ), and accordingly, develop the exact algorithm VirtuCast to compute (near) optimal solutions. VirtuCast consists of: (1) a compact single-commodity flow Integer Programming (IP) formulation; (2) a flow decomposition algorithm to reconstruct individual routes from the IP solution. The compactness of the IP formulation allows for computing lower bounds even on large instances quickly, speeding up the algorithm. We rigorously prove VirtuCast's correctness. To complement our theoretical findings, we have implemented VirtuCast and present an extensive computational evaluation, showing that, using VirtuCast, realistically sized instances can be solved (close to) optimality. We show that VirtuCast significantly improves upon naive multi-commodity formulations and also initiate the study of primal heuristics to generate feasible solutions during the branch-and-bound process.