Distributed Matrix Multiplication with a Smaller Recovery Threshold through Modulo-based Approaches

TL;DR

This paper introduces a modulo-based technique to reduce the recovery threshold in distributed matrix multiplication, enhancing efficiency and resilience to stragglers in large-scale computations.

Contribution

It proposes a novel modulo approach that exploits interpolation point structures, improving recovery thresholds and applying to existing coded matrix designs.

Findings

Modulo technique reduces recovery threshold

Discrete Fourier transform code resists stragglers

Locally repairable code scheme enhances resilience

Abstract

This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication problems to reduce the recovery threshold. This technique exploits the special structure of interpolation points and can be applied to many existing coded matrix designs. Recently studied discrete Fourier transform based code achieves a smaller recovery threshold than the optimal MatDot code with the expense that it cannot resist stragglers. We also propose a distributed matrix multiplication scheme based on the idea of locally repairable code to reduce the recovery threshold of MatDot code and provide resilience to stragglers. We also apply our constructions to a type of matrix computing problems, where generalized linear models act as a special case.