On the Tradeoff Between Computation and Communication Costs for Distributed Linearly Separable Computation

This paper studies the distributed linearly separable computation problem, which is a generalization of many existing computing problems such as gradient coding and linear transform. A master asks ${\mathsf {N}}$ workers to compute function {K}}$ datasets, set {K}}_{\mathrm{ c}}$ combinations equal-length messages (each message one dataset). We assign some datasets each worker in an uncoded manner, who then computes corresponding returns these messages, that from answers any {N}}_{\mathrm{ r}}$ out can recover task with high probability. In literature, specific case where c}}=1$ or cost minimum has been considered. this paper, we focus on general (i.e., c}} $ cost) aim find communication cost. first propose novel converse bound under constraint popular cyclic assignment (widely considered literature), assigns cyclic way. Motivated by observation strategies for fall short achieving bound, scheme system parameters. The proposed optimal assignment when large numbers are equal small. addition, it order within factor 2 remaining cases.