A locality-based lens for coded computation

Coded computation is an emerging paradigm for robustness in large-scale distributed computing, which applies principles from coding theory to provide robustness against slow or otherwise unavailable workers. We propose a new approach to view coded computation via the lens of locality of codes. We do so by defining a new notion of locality, called computational locality, via the locality properties of an appropriately defined code for the function being computed. This notion of locality incorporates the unique aspects of locality arising in the context of coded computation. Using this new approach, (1) We demonstrate how to design a coded computation scheme for a function using the local decoding scheme of an appropriately defined code. This rederives the best-known coded computation scheme for multivariate polynomial functions via the viewpoint of locality of the Reed Muller code. (2) We show that the proposed locality-based approach enables coded computation schemes with significantly lower resource overhead than existing schemes. Specifically, matrix multiplication over complex numbers, a common workload in high performance computing, is achieved with 33.3% fewer workers than state-of-the-art coded computation schemes.