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Uncoded Download in Lagrange-Coded Elastic Computing with Straggler Tolerance

Xi Zhong, Samuel Lu, Joerg Kliewer, Mingyue Ji

TL;DR

This work tackles elastic cloud computing for matrix-matrix multiplications by introducing Lagrange-coded storage with uncoded download (LCSUD), a paradigm that reduces storage size and upload/encoding burdens while preserving straggler tolerance. It replaces prior uncoded-storage plus coded-download approaches with uncoded download and a family of Lagrange-encoded storage schemes, yielding three concrete schemes that trade off storage size, download cost, and upload/decoding complexity. The authors provide a detailed system model, fixed-availability and generalized constructions, and a comprehensive complexity discussion, showing that LCSUD achieves lower storage and upload costs compared with existing methods while maintaining recovery from up to $S$ stragglers. The proposed framework supports both fixed and variable availability scenarios, enabling practical deployment in heterogeneous and dynamic cloud environments with tunable performance–cost profiles. Overall, LCSUD offers a versatile, scalable path to efficient coded elastic computing for matrix-matrix multiplications, with clear guidance on when to deploy each scheme based on resource constraints.

Abstract

Coded elastic computing, introduced by Yang et al. in 2018, is a technique designed to mitigate the impact of elasticity in cloud computing systems, where machines can be preempted or be added during computing rounds. This approach utilizes maximum distance separable (MDS) coding for both storage and download in matrix-matrix multiplications. The proposed scheme is unable to tolerate stragglers and has high encoding complexity and upload cost. In 2023, we addressed these limitations by employing uncoded storage and Lagrange-coded download. However, it results in a large storage size. To address the challenges of storage size and upload cost, in this paper, we focus on Lagrange-coded elastic computing based on uncoded download. We propose a new class of elastic computing schemes, using Lagrange-coded storage with uncoded download (LCSUD). Our proposed schemes address both elasticity and straggler challenges while achieving lower storage size, reduced encoding complexity, and upload cost compared to existing methods.

Uncoded Download in Lagrange-Coded Elastic Computing with Straggler Tolerance

TL;DR

This work tackles elastic cloud computing for matrix-matrix multiplications by introducing Lagrange-coded storage with uncoded download (LCSUD), a paradigm that reduces storage size and upload/encoding burdens while preserving straggler tolerance. It replaces prior uncoded-storage plus coded-download approaches with uncoded download and a family of Lagrange-encoded storage schemes, yielding three concrete schemes that trade off storage size, download cost, and upload/decoding complexity. The authors provide a detailed system model, fixed-availability and generalized constructions, and a comprehensive complexity discussion, showing that LCSUD achieves lower storage and upload costs compared with existing methods while maintaining recovery from up to stragglers. The proposed framework supports both fixed and variable availability scenarios, enabling practical deployment in heterogeneous and dynamic cloud environments with tunable performance–cost profiles. Overall, LCSUD offers a versatile, scalable path to efficient coded elastic computing for matrix-matrix multiplications, with clear guidance on when to deploy each scheme based on resource constraints.

Abstract

Coded elastic computing, introduced by Yang et al. in 2018, is a technique designed to mitigate the impact of elasticity in cloud computing systems, where machines can be preempted or be added during computing rounds. This approach utilizes maximum distance separable (MDS) coding for both storage and download in matrix-matrix multiplications. The proposed scheme is unable to tolerate stragglers and has high encoding complexity and upload cost. In 2023, we addressed these limitations by employing uncoded storage and Lagrange-coded download. However, it results in a large storage size. To address the challenges of storage size and upload cost, in this paper, we focus on Lagrange-coded elastic computing based on uncoded download. We propose a new class of elastic computing schemes, using Lagrange-coded storage with uncoded download (LCSUD). Our proposed schemes address both elasticity and straggler challenges while achieving lower storage size, reduced encoding complexity, and upload cost compared to existing methods.

Paper Structure

This paper contains 16 sections, 13 equations, 2 figures, 1 table.

Table of Contents

  1. introduction
  2. System Model
  3. Three Examples with A Fixed $\mathcal{N}^{(t)}$
  4. Example for LCSUD Scheme $1$: Reduce Download Cost
  5. Example for LCSUD Scheme $2$: Reduce Storage Size
  6. Example for LCSUD Scheme $3$: Reduce both Storage Size and Download Cost with Higher Upload Cost
  7. Difference Among Three Schemes
  8. Proposed General LCSUD Systems
  9. General LCSUD Schemes for A Fixed $\mathcal{N}^{(t)}$
  10. LSCUD Scheme $1$
  11. Scheme $2$
  12. LCSUD Scheme $3$
  13. General LCSUD Schemes Given $\boldsymbol{\mathcal{N}}_{U}$
  14. Discussion
  15. Storage Size
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Downloads in Example \ref{['ex-low-commu']}, where the yellow shaded area represents the download data for the available machines.
  • Figure 2: Storage Size of System when $N =20$, $L = 5$, and $S = 0$. The $x$-axis and $y$-axis represent $U$ and the storage size of the system normalized by the size of $\boldsymbol{A}$, respectively.

Theorems & Definitions (4)

  • Definition 1
  • Example 1
  • Example 2
  • Example 3