Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous $4\sqrt{m/k}$4m/k-competitive online algorithm by Amaris et al. [1] , where $m$m is the number of CPUs and $k$k the number of GPUs ($m\geq k$m≥k). We prove that no online algorithm can have a competitive ratio smaller than $\sqrt{m/k}$m/k. We also study how adding flexibility on task processing, such as task migration or spoliation, or increasing the knowledge of the scheduler by providing it with information on the task graph, influences the lower bound. We provide a $(2\sqrt{m/k}+1)$(2m/k+1)-competitive algorithm as well as a tunable combination of a system-oriented heuristic and a competitive algorithm; this combination performs well in practice and has a competitive ratio in $\Theta (\sqrt{m/k})$Θ(m/k). We also adapt all our results to the case of multiple types of processors. Finally, simulations on different sets of task graphs illustrate how the instance properties impact the performance of the studied algorithms and show that our proposed tunable algorithm performs the best among the online algorithms in almost all cases and has even performance close to an offline algorithm.

中文翻译：

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异构平台上任务图的在线调度

现代计算平台通常包括加速器。我们的目标是在由两种类型的资源（例如 CPU 和 GPU）组成的混合平台上调度建模为任务图的应用程序的问题。我们认为任务图是动态发现的，并且调度程序仅具有有关可用任务的信息，即其前驱都已完成的任务。每个任务都可以由 CPU 或 GPU 处理，并且相应的处理时间是已知的。我们的研究扩展了以前的$4\sqrt{m/k}$4米/克-Amaris 等人的竞争性在线算法。 [1] ， 在哪里 百万美元米 是 CPU 的数量和 $千$克 GPU 的数量（$m\geq k$米≥克）。我们证明没有任何在线算法的竞争比小于$\sqrt{m/k}$米/克. 我们还研究了如何增加任务处理的灵活性，例如任务迁移或破坏，或通过向调度程序提供任务图上的信息来增加调度程序的知识，如何影响下限。我们提供一个$(2\sqrt{m/k}+1)$(2米/克+1)-竞争算法以及面向系统的启发式算法和竞争算法的可调组合；这种组合在实践中表现良好，并在$\Theta (\sqrt{m/k})$Θ(米/克). 我们还将所有结果调整到多种处理器的情况。最后，对不同任务图集的模拟说明了实例属性如何影响所研究算法的性能，并表明我们提出的可调算法在几乎所有情况下都在在线算法中表现最好，甚至具有接近离线算法的性能。