Straggler Mitigation in Distributed Matrix Multiplication: Fundamental Limits and Optimal Coding

TL;DR

This paper introduces an optimal coding strategy called entangled polynomial code to mitigate stragglers in distributed matrix multiplication, significantly reducing the number of worker nodes needed for computation.

Contribution

It proposes a novel entangled polynomial coding scheme that achieves orderwise optimal recovery thresholds and extends to other distributed computing problems.

Findings

Entangled polynomial code minimizes recovery threshold in distributed matrix multiplication.

The scheme is orderwise optimal within a factor of 2 among linear codes.

Extensions to coded convolution and fault-tolerant computing are demonstrated.

Abstract

We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which is due to the unpredictable latency in waiting for slowest nodes (or stragglers) to finish their tasks. We propose a novel coding strategy, named \emph{entangled polynomial code}, for designing the intermediate computations at the worker nodes in order to minimize the recovery threshold (i.e., the number of workers that we need to wait for in order to compute the final output). We demonstrate the optimality of entangled polynomial code in several cases, and show that it provides orderwise improvement over the conventional schemes for straggler mitigation. Furthermore, we characterize the optimal recovery threshold among all linear coding strategies within a factor of $2$ using \emph{bilinear complexity}, by developing an improved version of the entangled polynomial code. In particular, while evaluating bilinear complexity is a well-known challenging problem, we show that optimal recovery threshold for linear coding strategies can be approximated within a factor of $2$ of this fundamental quantity. On the other hand, the improved version of the entangled polynomial code enables further and orderwise reduction in the recovery threshold, compared to its basic version. Finally, we show that the techniques developed in this paper can also be extended to several other problems such as coded convolution and fault-tolerant computing, leading to tight characterizations.