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：带通信延迟的任务图调度问题已被广泛研究。近期，针对分叉-合并任务图这一常见子情况，学者们发表了包括EPTAS（高效参数化近似方案）及特殊情形下的多项式算法在内的新成果。这些新成果将目标架构建模为同构处理器。然而，在现代并行系统（如CPU-加速器系统）中，异构性（包含两种资源类型）正日益普遍。本研究探讨了将带通信延迟的分叉-合并任务图（代表高度并行工作负载）调度到相关处理器异构系统的问题。我们提出了EPAS算法，并针对处理成本相等或资源无限等特殊情形给出了多项式时间算法。最后，我们简要探讨了上述描述的双资源类型情况及其影响。值得注意的是，本文所有结果同样适用于带释放时间和截止时间的独立任务调度场景。