Complexity of Scheduling Parallel Task Systems

Du, Jianzhong; Leung, Joseph Y.-T.

doi:10.1137/0402042

Cited by 277 publications

(121 citation statements)

References 4 publications

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“…Malleable Scheduling Quite some research has been dedicated to malleable scheduling for independent tasks,see [2,6,15,16,23,25,26,30]. Notably, Turek et al [30] were the first to describe a general method to employ algorithms for independent parallel tasks to obtain similar results for the malleable case.…”

Section: Related Workmentioning

confidence: 96%

Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width

2012

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We study the problems of non-preemptively scheduling and packing malleable and parallel tasks with precedence constraints to minimize the makespan. In the scheduling variant, we allow the free choice of processors; in packing, each task must be assigned to a contiguous subset. Malleable tasks can be processed on different numbers of processors with varying processing times, while parallel tasks require a fixed number of processors.For precedence constraints of bounded width, we resolve the complexity status of the problem with any number of processors and any width bound. We present an FPTAS based on Dilworth's decomposition theorem for the NP-hard problem variants, and exact efficient algorithms for all remaining special cases. For our positive results, we do not require the otherwise common monotonous penalty assumption on the processing times of malleable tasks, whereas our hardness results hold even when assuming this restriction. We complement our results by showing that these problems are all strongly NP-hard under precedence constraints which form a tree.

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Section: Related Workmentioning

confidence: 96%

Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width

2012

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“…Du and Leung [4] proved this problem to be NP-hard. However, some special cases are polynomially solvable, see Bianco et al [5] and Błażewicz et al [6].…”

Section: Problem Formulation and Literature Reviewmentioning

confidence: 99%

Scheduling arbitrary number of malleable tasks on multiprocessor systems

Barketau¹,

Kovalyov²,

Węglarz³

et al. 2014

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The problem of scheduling n tasks in a multiprocessor system with m processors to minimize the makespan is studied. Tasks are malleable, which means that a task can be executed by several processors at a time, its processing speed depends on the number of allocated processors, and a set of processors allocated to the same task can change over time. The processing speed of a task is a strictly increasing function of the number of processors allocated to this task. The earlier studies considered the case n ≤ m. This paper presents results for arbitrary n and m including characterizations of a feasible domain and an optimal solution, polynomial time algorithms for strictly increasing convex and concave processing speed functions, and a combinatorial exponential algorithm for arbitrary strictly increasing functions.

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“…An application that has a fixed number of processors is called rigid. In 1989, Du and Leung [8] developed a model called the Parallel Task System, where an application is executed by one or more processors at the same time, but the number of processors assigned to one application cannot exceed a certain threshold. Contrarily to the B lażewicz's model, the number of processors is not fixed in advance, but once it is determined (between one and the threshold), it remains fixed during the execution.…”

Section: Related Workmentioning

confidence: 99%

Resilient co-scheduling of malleable applications

Benoît

Pottier

Robert

2017

The International Journal of High Performance Computing Applica

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Recently, the benefits of co-scheduling several applications have been demonstrated in a fault-free context, both in terms of performance and energy savings. However, large-scale computer systems are confronted by frequent failures, and resilience techniques must be employed for large applications to execute efficiently. Indeed, failures may create severe imbalance between applications, and significantly degrade performance. In this paper, we aim at minimizing the expected completion time of a set of co-scheduled applications. We propose to redistribute the resources assigned to each application upon the occurrence of failures, and upon the completion of some applications, in order to achieve this goal. First, we introduce a formal model and establish complexity results. The problem is NP-complete for malleable applications, even in a faultfree context. Therefore, we design polynomial-time heuristics that perform redistributions and account for processor failures. A fault simulator is used to perform extensive simulations that demonstrate the usefulness of redistribution and the performance of the proposed heuristics.

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Complexity of Scheduling Parallel Task Systems

Cited by 277 publications

References 4 publications

Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width

Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width

Scheduling arbitrary number of malleable tasks on multiprocessor systems

Resilient co-scheduling of malleable applications

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