Distributed Matrix Computations with Low-weight Encodings

TL;DR

This paper introduces a distributed matrix computation method using low-weight random linear combinations that is efficient for sparse matrices, resilient to stragglers, and improves overall computation speed and encoding efficiency.

Contribution

The authors propose a novel low-weight encoding scheme for distributed matrix computations that enhances efficiency for sparse matrices and maintains straggler resilience.

Findings

Up to 30% reduction in per worker computation time

100x faster encoding compared to existing methods

Effective utilization of partial computations in heterogeneous systems

Abstract

Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum distance separable) codes into the framework; this can achieve resilience against an optimal number of stragglers. However, these codes assign dense linear combinations of submatrices to the worker nodes. When the input matrices are sparse, these approaches increase the number of non-zero entries in the encoded matrices, which in turn adversely affects the worker computation time. In this work, we develop a distributed matrix computation approach where the assigned encoded submatrices are random linear combinations of a small number of submatrices. In addition to being well suited for sparse input matrices, our approach continues have the optimal straggler resilience in a certain range of problem parameters. Moreover, compared to recent sparse matrix computation approaches, the search for a "good" set of random coefficients to promote numerical stability in our method is much more computationally efficient. We show that our approach can efficiently utilize partial computations done by slower worker nodes in a heterogeneous system which can enhance the overall computation speed. Numerical experiments conducted through Amazon Web Services (AWS) demonstrate up to 30% reduction in per worker node computation time and 100x faster encoding compared to the available methods.