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

TL;DR

This paper introduces the CVSAP, a new problem in network optimization for in-network processing, providing a formal definition, an exact solution algorithm VirtuCast, and extensive computational evaluation demonstrating near-optimal solutions.

Contribution

It formulates the CVSAP, proves its computational hardness, and develops VirtuCast, a novel exact algorithm with a compact IP formulation and flow decomposition, validated through extensive experiments.

Findings

VirtuCast efficiently computes near-optimal solutions for large instances.

The compact IP formulation speeds up lower bound calculations.

VirtuCast outperforms naive multi-commodity approaches.

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.