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We study the optimal design of heterogeneous Coded Elastic Computing (CEC)where machines have varying computation speeds and storage. CEC introduced byYang 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 isdistributed among machines using a Maximum Distance Separable (MDS) code suchthat subsets of machines can perform the desired computations. However,state-of-the-art CEC designs only operate on homogeneous networks wheremachines have the same speeds and storage. This may not be practical. In thiswork, based on an MDS storage assignment, we develop a novel computationassignment approach for heterogeneous CEC networks to minimize the overallcomputation time. We first consider the scenario where machines haveheterogeneous computing speeds but same storage and then the scenario whereboth heterogeneities are present. We propose a novel combinatorial optimizationformulation and solve it exactly by decomposing it into a convex optimizationproblem for finding the optimal computation load and a "filling problem" forfinding the exact computation assignment. A low-complexity "filling algorithm"is adapted and can be completed within a number of iterations equals at mostthe number of available machines.

Coded Elastic Computing on Machines with Heterogeneous Storage and Computation Speed