Coded distributed computing (CDC) can alleviate the communication load in distributed computing systems by leveraging coding opportunities via redundant computation. While the optimal computation-communication tradeoff has been well studied for homogeneous systems, it remains largely unknown for heterogeneous systems where workers have different computation capabilities. This paper characterizes the upper and lower bounds of the optimal communication load as two linear programming problems for a general heterogeneous CDC system using the MapReduce framework. Our achievable scheme first designs a parametric data shuffling strategy for any given mapping strategy, and then jointly optimizes the mapping strategy and the data shuffling strategy to obtain the upper bound. The parametric data shuffling strategy allows adjusting the size of the multicast message intended for each worker set, so that it can largely decrease the number of unicast messages and hence increase the communication efficiency. Numerical results show that our achievable communication load is lower than those achieved in existing works. Our lower bound is established by unifying an improved cut-set bound and a peeling method. The obtained upper and lower bounds degenerate to the existing result in homogeneous systems, and coincide with each other when the system is approximately homogeneous or grouped homogeneous.

中文翻译：

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异构编码分布式计算的计算-通信权衡的新结果

编码的分布式计算（CDC）可以通过冗余计算利用编码机会来减轻分布式计算系统中的通信负载。尽管已经对同类系统进行了最佳的计算-通信折衷研究，但对于工人具有不同计算能力的异构系统，它仍然是未知之数。本文将最佳通信负载的上限和下限表征为使用MapReduce框架的通用异构CDC系统的两个线性编程问题。我们可实现的方案首先针对任何给定的映射策略设计参数数据改组策略，然后共同优化映射策略和数据改组策略以获得上限。参数数据改组策略允许调整针对每个工作集的多播消息的大小，从而可以大大减少单播消息的数量，从而提高通信效率。数值结果表明，我们可以实现的通信负载低于现有工作中实现的通信负载。我们的下限是通过统一改进的剪切定界和剥离方法来确定的。所获得的上限和下限退化为均质系统中的现有结果，并且当系统近似均质或成组均质时彼此重合。数值结果表明，我们可以实现的通信负载低于现有工作中实现的通信负载。我们的下限是通过统一改进的剪切定界和剥离方法来确定的。所获得的上限和下限退化为均质系统中的现有结果，并且当系统近似均质或成组均质时彼此重合。数值结果表明，我们可以实现的通信负载低于现有工作中实现的通信负载。我们的下限是通过统一改进的剪切定界和剥离方法来确定的。所获得的上限和下限退化为均质系统中的现有结果，并且当系统近似均质或成组均质时彼此重合。