Coded Elastic Computing on Machines with Heterogeneous Storage and Computation Speed

TL;DR

This paper develops an optimal computation assignment strategy for heterogeneous Coded Elastic Computing networks, improving efficiency by accounting for varying machine speeds and storage capacities.

Contribution

It introduces a novel combinatorial optimization framework and a low-complexity filling algorithm for heterogeneous CEC, extending prior homogeneous network designs.

Findings

Optimal computation time minimized for heterogeneous networks

Exact solutions obtained via convex and filling problem decomposition

Algorithm complexity is manageable with iteration bounds

Abstract

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.