# Erasure coding for distributed matrix multiplication for matrices with bounded entries

arXiv: https://arxiv.org/abs/1811.02144 · HTML: https://mlsanity.com/paper/1811.02144/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [Random Alloy Codes and the Fundamental Limits of Coded Distributed Tensors](https://mlsanity.com/paper/2202.03469/) (2022)

## Abstract (arXiv)

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 AT 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.