Efficient approximation algorithms for scheduling moldable tasks

Moldable tasks allow schedulers to determine the number of processors assigned to each task, thus enabling efficient use of large-scale parallel processing systems. We consider the problem of scheduling independent moldable tasks on processors and propose a new perspective of the existing speedup models: as the number pof processors assigned to a task increases, the speedup is linear if pis small and becomes sublinear after pexceeds a threshold. Based on this, we propose an efficient approximation algorithm to minimize the makespan. 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. (C) 2023 Elsevier B.V. All rights reserved.