The scheduling literature has traditionally focused on a single type of resource (e.g., computing nodes). However, scientific applications in modern High-Performance Computing (HPC) systems process large amounts of data, hence have diverse requirements on different types of resources (e.g., cores, cache, memory, I/O). All of these resources could potentially be exploited by the runtime scheduler to improve the application performance. In this paper, we study multi-resource scheduling to minimize the makespan of computational workflows comprised of parallel jobs subject to precedence constraints. The jobs are assumed to be moldable, allowing the scheduler to flexibly select a variable set of resources before execution. We propose a multi-resource, list-based scheduling algorithm, and prove that, on a system with $d$ types of schedulable resources, our algorithm achieves an approximation ratio of $1.619d+2.545\sqrt{d}+1$ for any $d$, and a ratio of $d+O(\sqrt[3]{d^2})$ for large $d$. We also present improved results for independent jobs and for jobs with special precedence constraints (e.g., series-parallel graphs and trees). Finally, we prove a lower bound of $d$ on the approximation ratio of any list scheduling scheme with local priority considerations. To the best of our knowledge, these are the first approximation results for moldable workflows with multiple resource requirements.

中文翻译：

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优先约束下可成型并行作业的多资源列表调度

调度文献传统上关注单一类型的资源（例如，计算节点）。然而，现代高性能计算 (HPC) 系统中的科学应用程序处理大量数据，因此对不同类型的资源（例如，内核、缓存、内存、I/O）有不同的要求。运行时调度程序可能会利用所有这些资源来提高应用程序性能。在本文中，我们研究了多资源调度以最小化由受优先级约束的并行作业组成的计算工作流的完工时间。假设作业是可塑的，允许调度程序在执行之前灵活地选择一组可变的资源。我们提出了一种多资源、基于列表的调度算法，并证明，在具有 $d$ 种可调度资源的系统上，我们的算法对任何 $d$ 实现了 $1.619d+2.545\sqrt{d}+1$ 的近似比率，对于大 $d 实现了 $d+O(\sqrt[3]{d^2})$ 的比率$. 我们还为独立作业和具有特殊优先约束的作业（例如，串并行图和树）提供了改进的结果。最后，我们证明了具有本地优先级考虑的任何列表调度方案的近似比率的下限 $d$。据我们所知，这些是具有多种资源需求的可塑工作流程的初步近似结果。我们证明了具有本地优先级考虑的任何列表调度方案的近似比率的下限 $d$。据我们所知，这些是具有多种资源需求的可塑工作流程的初步近似结果。我们证明了具有本地优先级考虑的任何列表调度方案的近似比率的下限 $d$。据我们所知，这些是具有多种资源需求的可塑工作流程的初步近似结果。