Efficient Algorithms for Scheduling Moldable Tasks

Xiaohu Wu, Patrick Loiseau, Esa Hyytia

Moldable tasks allow schedulers to determine the number of processors assigned to a task, enabling efficient use of large-scale parallel processing systems. A generic assumption is that every task is monotonic, i.e., its workload increases but its execution time decreases as the number of assigned processors increases. In this paper, we study the problem of scheduling moldable tasks on processors. Motivated by many benchmark studies, we introduce a new speedup model: it is linear when the number of assigned processors is small, up to some threshold; then, it possibly declines and even become negative as the number increases. 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 similar works have been done for other types of parallel tasks.

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