Optimal Communication-Computation Trade-Off in Heterogeneous Gradient Coding

Gradient coding allows a master node to derive the aggregate of partial gradients, calculated by some worker nodes over local data sets, with minimum communication cost, and in presence stragglers. In this paper, for gradient linear encoding, we characterize optimum cost heterogeneous distributed systems arbitrary placement, $s \in \mathbb {N}$ stragglers notation="LaTeX">$a adversarial nodes. particular, show that normalized size vectors, is equal notation="LaTeX">$(r-s-2a)^{-1}$ , where notation="LaTeX">$r number partition replicated. other words, determined replication, irrespective structure placement. The proposed achievable scheme also us target computation polynomial function aggregated matrix. It borrow ideas from approximation computing propose an approximate cases when repetition placement smaller than what needed meet restriction imposed on or appears be more presumed value system design.