Fundamental Limits of Distributed Linearly Separable Computation under Cyclic Assignment

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.