Distributed Linearly Separable Computation problem under the cyclic assignment is studied in this paper. It is a problem widely existing in cooperated distributed gradient coding, real-time rendering, linear transformers, etc. In a distributed computing system, a master asks $N$ distributed workers to compute a linearly separable function from $K$ datasets. The task function can be expressed as $K_c$ linear combinations of $K$ messages, where each message is the output of one individual function of one dataset. Straggler effect is also considered, such that from the answers of each $N_r$ worker, the master should recover the task. The computation cost is defined as the number of datasets assigned to each worker, while the communication cost is defined as the number of (coded) messages which should be received. The objective is to characterize the optimal tradeoff between the computation and communication costs. Various distributed computing scheme were proposed in the literature with a well-known cyclic data assignment, but the (order) optimality of this problem remains open, even under the cyclic assignment. This paper proposes a new computing scheme with the cyclic assignment based on interference alignment, which is near optimal under the cyclic assignment.

翻译：本文研究了循环分配下的分布式线性可分计算问题。该问题广泛存在于协作分布式梯度编码、实时渲染、线性变换器等场景中。在分布式计算系统中，主节点要求$N$个分布式工作节点从$K$个数据集中计算一个线性可分函数。该任务函数可表示为$K$个消息的$K_c$个线性组合，其中每个消息是某个数据集上单个函数的输出。同时考虑滞后效应，即主节点需能从每个$N_r$个工作节点的应答中恢复任务。计算成本定义为分配给每个工作节点的数据集数量，而通信成本定义为需接收的（编码）消息数量。目标是刻画计算成本与通信成本之间的最优权衡。现有文献提出了多种基于经典循环数据分配的分布式计算方案，但该问题（在循环分配下）的最优性（阶次最优性）仍属未解。本文提出一种基于干扰对齐的循环分配新型计算方案，该方案在循环分配条件下达到近最优性能。