Coding theoretic approaches have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade computation resources to reduce the communication load in MapReduce like computing systems. For the more general cascaded CDC, Map computations are repeated at $r$ nodes to significantly reduce the communication load among nodes tasked with computing $Q$ Reduce functions $s$ times. In this paper, we propose a novel low-complexity combinatorial design for cascaded CDC which 1) determines both input file and output function assignments, 2) requires significantly less number of input files and output functions, and 3) operates on heterogeneous networks where nodes have varying storage and computing capabilities. We provide an analytical characterization of the computation-communication tradeoff, from which we show the proposed scheme can outperform the state-of-the-art scheme proposed by Li et al. for the homogeneous networks. Further, when the network is heterogeneous, we show that the performance of the proposed scheme can be better than its homogeneous counterpart. In addition, the proposed scheme is optimal within a constant factor of the information theoretic converse bound while fixing the input file and the output function assignments.

中文翻译：

---

通用网络级联编码分布式计算的组合设计

已经开发了编码理论方法来显着减少现代分布式计算系统中的通信负载。特别是Li介绍的编码分布式计算（CDC）等。可以有效地交易计算资源以减少 MapReduce 等计算系统中的通信负载。对于更一般的级联 CDC，Map 计算在 $r$ 节点以显着减少负责计算的节点之间的通信负载 $Q$ 减少功能 $s$ 次。在本文中，我们为级联 CDC 提出了一种新颖的低复杂度组合设计，它 1) 确定输入文件和输出函数的分配，2) 需要的输入文件和输出函数的数量要少得多，以及 3) 在节点的异构网络上运行具有不同的存储和计算能力。我们提供了计算-通信权衡的分析表征，从中我们表明所提出的方案可以胜过 Li 提出的最新方案等。对于同构网络。此外，当网络是异构的时，我们表明所提出的方案的性能可以优于其同类方案。此外，在固定输入文件和输出函数分配的同时，所提出的方案在信息论逆界的常数因子内是最优的。