Erasure coding for distributed matrix multiplication for matrices with bounded entries

TL;DR

This paper introduces a new erasure coding strategy for distributed matrix multiplication that leverages bounds on matrix entries to optimize the recovery threshold, reducing the impact of stragglers in distributed computations.

Contribution

It proposes a novel coding approach that exploits bounds on matrix entries to improve straggler mitigation in distributed matrix multiplication.

Findings

Tradeoff between entry bounds and recovery threshold demonstrated.

Method achieves optimal recovery threshold under certain bounds.

Experimental validation on cloud clusters confirms effectiveness.

Abstract

Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has demonstrated that straggler mitigation can be viewed as a problem of designing erasure codes. For matrices $\mathbf A$ and $\mathbf B$, the technique essentially maps the computation of $\mathbf A^T \mathbf B$ into the multiplication of smaller (coded) submatrices. The stragglers are treated as erasures in this process. The computation can be completed as long as a certain number of workers (called the recovery threshold) complete their assigned tasks. We present a novel coding strategy for this problem when the absolute values of the matrix entries are sufficiently small. We demonstrate a tradeoff between the assumed absolute value bounds on the matrix entries and the recovery threshold. At one extreme, we are optimal with respect to the recovery threshold and on the other extreme, we match the threshold of prior work. Experimental results on cloud-based clusters validate the benefits of our method.