English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

Optimal Communication-Computation Trade-Off in Heterogeneous Gradient Coding