Dual-Lagrange Encoding for Storage and Download in Elastic Computing for Resilience

TL;DR

This paper proposes a novel elastic computing scheme using Lagrange codes for encoding storage and download, reducing storage requirements and effectively handling stragglers in matrix computations.

Contribution

It introduces a new class of schemes that encode both storage and download with Lagrange codes, reducing storage size and improving resilience in elastic computing environments.

Findings

Reduced storage size to 1/L of previous methods.

Achieved efficient mitigation of elasticity and straggler effects.

Validated performance improvements on AWS EC2 with different task allocations.

Abstract

Coded elastic computing enables virtual machines to be preempted for high-priority tasks while allowing new virtual machines to join ongoing computation seamlessly. This paper addresses coded elastic computing for matrix-matrix multiplications with straggler tolerance by encoding both storage and download using Lagrange codes. In 2018, Yang et al. introduced the first coded elastic computing scheme for matrix-matrix multiplications, achieving a lower computational load requirement. However, this scheme lacks straggler tolerance and suffers from high upload cost. Zhong et al. (2023) later tackled these shortcomings by employing uncoded storage and Lagrange-coded download. However, their approach requires each machine to store the entire dataset. This paper introduces a new class of elastic computing schemes that utilize Lagrange codes to encode both storage and download, achieving a reduced storage size. The proposed schemes efficiently mitigate both elasticity and straggler effects, with a storage size reduced to a fraction $\frac{1}{L}$ of Zhong et al.'s approach, at the expense of doubling the download cost. Moreover, we evaluate the proposed schemes on AWS EC2 by measuring computation time under two different tasks allocations: heterogeneous and cyclic assignments. Both assignments minimize computation redundancy of the system while distributing varying computation loads across machines.