The scheduling of task graphs with communication delays has been extensively studied. Recently, new results for the common sub-case of fork-join shaped task graphs were published, including an EPTAS and polynomial algorithms for special cases. These new results modelled the target architecture to consist of homogeneous processors. However, forms of heterogeneity become more and more common in contemporary parallel systems, such as CPU--accelerator systems, with their two types of resources. In this work, we study the scheduling of fork-join task graphs with communication delays, which is representative of highly parallel workloads, onto heterogeneous systems of related processors. We present an EPAS, and some polynomial time algorithms for special cases, such as with equal processing costs or unlimited resources. Lastly, we briefly look at the above described case of two resource-types and its implications. It is interesting to note, that all results here also apply to scheduling independent tasks with release times and deadlines.

翻译：带有通信延迟的任务图调度问题已被广泛研究。最近，针对常见的fork-join形状任务图子类发布了一些新结果，包括一个EPTAS以及针对特殊情形的多项式算法。这些新结果将目标架构建模为同构处理器。然而，在当代并行系统中，异构形式变得越来越普遍，例如CPU-加速器系统及其两种资源类型。本文研究将带有通信延迟的fork-join任务图（代表高度并行工作负载）调度到相关处理器构成的异构系统上的问题。我们提出了一个EPAS，以及针对特殊情形（如处理成本相等或资源不受限）的多项式时间算法。最后，我们简要考察上述两种资源类型的情形及其影响。值得注意的是，本文所有结果同样适用于具有释放时间和截止时间的独立任务调度问题。