  We study the optimal design of heterogeneous Coded Elastic Computing (CEC)
where machines have varying computation speeds and storage. CEC introduced by
Yang et al. in 2018 is a framework that mitigates the impact of elastic events,
where machines can join and leave at arbitrary times. In CEC, data is
distributed among machines using a Maximum Distance Separable (MDS) code such
that subsets of machines can perform the desired computations. However,
state-of-the-art CEC designs only operate on homogeneous networks where
machines have the same speeds and storage. This may not be practical. In this
work, based on an MDS storage assignment, we develop a novel computation
assignment approach for heterogeneous CEC networks to minimize the overall
computation time. We first consider the scenario where machines have
heterogeneous computing speeds but same storage and then the scenario where
both heterogeneities are present. We propose a novel combinatorial optimization
formulation and solve it exactly by decomposing it into a convex optimization
problem for finding the optimal computation load and a "filling problem" for
finding the exact computation assignment. A low-complexity "filling algorithm"
is adapted and can be completed within a number of iterations equals at most
the number of available machines.
