Flexible Distributed Matrix Multiplication

TL;DR

This paper introduces a flexible distributed matrix multiplication method that efficiently handles unknown stragglers by utilizing entangled polynomial codes, reducing server load and adapting to available resources.

Contribution

It proposes a novel flexible coding scheme based on entangled polynomial codes that optimally balances computation across servers with unknown stragglers.

Findings

Achieves efficient matrix multiplication with fewer stragglers.

Reduces finite field size requirement to less than 2N.

Generalizes to batch and secure distributed matrix multiplication.

Abstract

The distributed matrix multiplication problem with an unknown number of stragglers is considered, where the goal is to efficiently and flexibly obtain the product of two massive matrices by distributing the computation across N servers. There are up to N - R stragglers but the exact number is not known a priori. Motivated by reducing the computation load of each server, a flexible solution is proposed to fully utilize the computation capability of available servers. The computing task for each server is separated into several subtasks, constructed based on Entangled Polynomial codes by Yu et al. The final results can be obtained from either a larger number of servers with a smaller amount of computation completed per server or a smaller number of servers with a larger amount of computation completed per server. The required finite field size of the proposed solution is less than 2N. Moreover, the optimal design parameters such as the partitioning of the input matrices is discussed. Our constructions can also be generalized to other settings such as batch distributed matrix multiplication and secure distributed matrix multiplication.