In 2018, Yang et al. introduced a novel and effective approach, using maximum distance separable (MDS) codes, to mitigate the impact of elasticity in cloud computing systems. This approach is referred to as coded elastic computing. Some limitations of this approach include that it assumes all virtual machines have the same computing speeds and storage capacities, and it cannot tolerate stragglers for matrix-matrix multiplications. In order to resolve these limitations, in this paper, we introduce a new combinatorial optimization framework, named uncoded storage coded transmission elastic computing (USCTEC), for heterogeneous speeds and storage constraints, aiming to minimize the expected computation time for matrix-matrix multiplications, under the consideration of straggler tolerance. Within this framework, we propose optimal solutions with straggler tolerance under relaxed storage constraints. Moreover, we propose a heuristic algorithm that considers the heterogeneous storage constraints. Our results demonstrate that the proposed algorithm outperforms baseline solutions utilizing cyclic storage placements, in terms of both expected computation time and storage size.

翻译：2018年，Yang等人引入了一种新颖且有效的方法，利用最大距离可分（MDS）编码来减轻云计算系统中弹性带来的影响。该方法被称为编码弹性计算。其局限性包括假定所有虚拟机具有相同的计算速度和存储容量，且无法容忍矩阵-矩阵乘法中的拖后腿现象。为解决这些局限，本文提出了一种名为无编码存储编码传输弹性计算（USCTEC）的新型组合优化框架，适用于异构速度和存储约束场景，旨在最小化矩阵-矩阵乘法的预期计算时间，同时考虑拖后腿容忍性。在此框架内，我们提出了在放宽存储约束下具有拖后腿容忍性的最优解。此外，我们提出了一种考虑异构存储约束的启发式算法。结果表明，与采用循环存储放置的基线解决方案相比，所提算法在预期计算时间和存储大小方面均表现更优。