Efficient approximation algorithms for scheduling moldable tasks

•We study scheduling independent moldable tasks under the proposed (δj,kj)-monotonic model, whose generality is between the classic monotonic and linear-speedup models.•An efficient algorithm for makespan minimization is proposed, achieving an approximation ratio close to 1.333 under mild assumption...

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Vydáno v:European journal of operational research Ročník 310; číslo 1; s. 71 - 83
Hlavní autoři: Wu, Xiaohu, Loiseau, Patrick
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.10.2023
Elsevier
Témata:
Approximation algorithms
Computer Science
Moldable tasks
Operations Research
Scheduling
Moldable tasks
Approximation algorithms
Scheduling
Scheduling; approximation algorithms; moldable tasks
ISSN:0377-2217, 1872-6860
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Shrnutí:•We study scheduling independent moldable tasks under the proposed (δj,kj)-monotonic model, whose generality is between the classic monotonic and linear-speedup models.•An efficient algorithm for makespan minimization is proposed, achieving an approximation ratio close to 1.333 under mild assumptions.•Additionally, an efficient algorithm for throughput maximization with a deadline is proposed, achieving an approximation ratio close to 0.75 under mild assumptions. 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 p of processors assigned to a task increases, the speedup is linear if p is small and becomes sublinear after p exceeds 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2023.02.044