  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.
