Distributed Large Scale Network Utility Maximization

TL;DR

This paper introduces a novel distributed algorithm for network utility maximization that combines primal-dual interior-point methods with Gaussian belief propagation, outperforming previous centralized and distributed approaches in large-scale network settings.

Contribution

It presents the first distributed NUM algorithm combining primal-dual interior-point methods with Gaussian belief propagation, improving scalability and performance.

Findings

Outperforms previous methods like truncated Newton and dual-decomposition.

First evaluation comparing Gaussian belief propagation with preconditioned conjugate gradient for large-scale problems.

Demonstrates efficiency and scalability of the new distributed algorithm.

Abstract

Recent work by Zymnis et al. proposes an efficient primal-dual interior-point method, using a truncated Newton method, for solving the network utility maximization (NUM) problem. This method has shown superior performance relative to the traditional dual-decomposition approach. Other recent work by Bickson et al. shows how to compute efficiently and distributively the Newton step, which is the main computational bottleneck of the Newton method, utilizing the Gaussian belief propagation algorithm. In the current work, we combine both approaches to create an efficient distributed algorithm for solving the NUM problem. Unlike the work of Zymnis, which uses a centralized approach, our new algorithm is easily distributed. Using an empirical evaluation we show that our new method outperforms previous approaches, including the truncated Newton method and dual-decomposition methods. As an additional contribution, this is the first work that evaluates the performance of the Gaussian belief propagation algorithm vs. the preconditioned conjugate gradient method, for a large scale problem.