D-iteration: Evaluation of the Asynchronous Distributed Computation
For researchers and practitioners needing scalable solutions to large linear systems, this work demonstrates a promising asynchronous distributed approach with near-linear speedup.
D-iteration is a fluid diffusion based iterative method for solving linear systems that is natively distributive. Experiments show that distributing computation over K virtual machines reduces memory per machine linearly with K and increases computation speed almost linearly with K, with slope approaching 1 as the number of equations N increases.
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.