Distributed Least-Squares Iterative Methods in Networks: A Survey

TL;DR

This survey reviews distributed iterative methods for solving large sparse least-squares problems in networked systems, emphasizing their efficiency, modifications for distribution, and communication costs, filling a gap in existing literature.

Contribution

It is the first comprehensive survey of distributed least-squares iterative methods, analyzing their algorithms, modifications, and performance metrics in networked systems.

Findings

Distributed iterative methods are effective for large sparse systems in networks.

Modifications to existing algorithms improve their suitability for distributed environments.

Analysis of time-to-completion and communication costs guides practical implementation.

Abstract

Many science and engineering applications involve solving a linear least-squares system formed from some field measurements. In the distributed cyber-physical systems (CPS), often each sensor node used for measurement only knows partial independent rows of the least-squares system. To compute the least-squares solution they need to gather all these measurement at a centralized location and then compute the solution. These data collection and computation are inefficient because of bandwidth and time constraints and sometimes are infeasible because of data privacy concerns. Thus distributed computations are strongly preferred or demanded in many of the real world applications e.g.: smart-grid, target tracking etc. To compute least squares for the large sparse system of linear equation iterative methods are natural candidates and there are a lot of studies regarding this, however, most of them are related to the efficiency of centralized/parallel computations while and only a few are explicitly about distributed computation or have the potential to apply in distributed networks. This paper surveys the representative iterative methods from several research communities. Some of them were not originally designed for this need, so we slightly modified them to suit our requirement and maintain the consistency. In this survey, we sketch the skeleton of the algorithm first and then analyze its time-to-completion and communication cost. To our best knowledge, this is the first survey of distributed least-squares in distributed networks.