D-iteration: Evaluation of the Asynchronous Distributed Computation

TL;DR

This paper evaluates the D-iteration method, a fluid diffusion-based asynchronous distributed computation approach, demonstrating its efficiency and scalability in solving large linear systems across multiple virtual machines.

Contribution

It provides the first experimental assessment of D-iteration's potential for improving distributed linear algebra computations.

Findings

Memory per machine decreases linearly with number of virtual machines

Computation speed increases almost linearly with number of virtual machines

Efficiency improves as the size of the linear system increases

Abstract

The aim of this paper is to present a first evaluation of the potential of an asynchronous distributed computation associated to the recently proposed approach, D-iteration: the D-iteration is a fluid diffusion based iterative method, which has the advantage of being natively distributive. It exploits a simple intuitive decomposition of the matrix-vector product as elementary operations of fluid diffusion associated to a new algebraic representation. We show through experiments on real datasets how much this approach can improve the computation efficiency when the parallelism is applied: with the proposed solution, when the computation is distributed over $K$ virtual machines (PIDs), the memory size to be handled by each virtual machine decreases linearly with $K$ and the computation speed increases almost linearly with $K$ with a slope becoming closer to one when the number $N$ of linear equations to be solved increases.