Moldable tasks allow schedulers to determine the number of processors assigned to each task, enabling efficient use of large-scale parallel processing systems. A common assumption is that every task is monotonic, i.e., its workload increases but its execution time decreases as the number of assigned processors increases. Motivated by many benchmark studies, we introduce a new speedup model: the speedup is linear when the number of assigned processors is small, up to some threshold; afterwards, like monotonic tasks, the speedup declines as the number becomes larger. Given any threshold value achievable, we propose a generic approximation algorithm to minimize the makespan, which is simpler and achieves a better performance guarantee than the existing ones under the monotonic assumption. As a by-product, we also propose an approximation algorithm to maximize the sum of values of tasks completed by a deadline; this scheduling objective is considered for moldable tasks for the first time, while it has been addressed for other types of parallel tasks in literature of scheduling theory.

中文翻译：

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调度可塑任务的高效算法

可模制任务允许调度程序确定分配给每个任务的处理器数量，从而有效使用大规模并行处理系统。一个常见的假设是每个任务都是单调的，即随着分配的处理器数量的增加，其工作量增加，但其执行时间减少。受许多基准研究的启发，我们引入了一个新的加速模型：当分配的处理器数量很少时，加速是线性的，达到某个阈值；之后，就像单调任务一样，随着数字变大，加速比下降。给定任何可达到的阈值，我们提出了一种通用的近似算法来最小化完工时间，它比单调假设下的现有算法更简单并获得更好的性能保证。作为副产品，我们还提出了一种近似算法，以最大化在截止日期前完成的任务值的总和；该调度目标首次被考虑用于可塑任务，而在调度理论文献中已针对其他类型的并行任务进行了处理。