Speeding Up Private Distributed Matrix Multiplication via Bivariate Polynomial Codes

TL;DR

This paper introduces bivariate polynomial codes to enhance private distributed matrix multiplication, reducing computation time and communication costs by leveraging partial work from stragglers, thus improving efficiency.

Contribution

It proposes a novel use of bivariate polynomial codes to speed up private distributed matrix multiplication by utilizing partial straggler work, outperforming existing methods.

Findings

Reduces average computation time compared to previous methods.

Improves upload communication cost.

Enhances workers' storage efficiency.

Abstract

We consider the problem of private distributed matrix multiplication under limited resources. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against the workers and boosting the computation speed by efficiently mitigating stragglers. In this work, we propose the use of recently-introduced bivariate polynomial codes to further speed up private distributed matrix multiplication by exploiting the partial work done by the stragglers rather than completely ignoring them. We show that the proposed approach reduces the average computation time of private distributed matrix multiplication compared to its competitors in the literature while improving the upload communication cost and the workers' storage efficiency.