Local Re-Encoding for Coded Matrix Multiplication

Abstract

Matrix multiplication is a fundamental operation in various algorithms for big data analytics and machine learning. As the size of the dataset increases rapidly, it is now a common practice to distribute the computation on multiple servers. As straggling servers are inevitable in a distributed infrastructure, various coding schemes have been proposed to tolerate potential stragglers. However, as resources are shared with other jobs in a distributed infrastructure and their performance can change dynamically, the optimal way of encoding the input matrices is not static. So far, all existing coding schemes require encoding input matrices in advance, and cannot change the coding schemes or adjust their parameters flexibly. In this paper, we propose a framework that can change the coding schemes and/or their parameters by locally re-encoding the coded task on each server. We first present this framework for entangled polynomial codes, which changes the coding parameters with marginal overhead and saves job completion time. We then extend the framework for matrices with bounded entries, achieving a higher level of flexibility for local re-encoding while maintaining better numerical stability.

Keywords

• Big data infrastructure
• matrix multiplication
• re-encoding
• numerical stability