NDLI: A Heuristic of Scheduling Parallel Tasks and Its Analysis

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Cheng, Kam-Hoi Wang, Qingzhou
Copyright Year	1992
Abstract	This paper investigates the problem of nonreconfigurable, nonpreemptive scheduling of parallel tasks in a homogeneous system of processors. Given a task precedence graph where each task T may be executed on up to $\delta (T)$ processors, the problem is to find a schedule such that the makespan is minimized. A scheduling policy is nonreconfigurable if when more processors become available after a task T has been scheduled on p processors, $p < \delta (T)$, they cannot join the execution of task T. It is nonpreemptive if each task is executed without interruption until completion once the task has started execution. The problem of scheduling parallel tasks is NP-hard. The performance ratio of the makespan produced by the original list scheduling algorithm proposed by Graham [SIAM J. Appl. Math., 17 (1969), pp. 416429] to the optimal makespan is $\Delta + \frac{m - \Delta} {m}$ [Inform. Process. Lett., 37 (1991), pp. 291297], where m and $\Delta $ are the number of processors in the system and the maximum degree of parallelism in any task, respectively. To provide a performance improvement, the Earliest Completion Time (ECT) algorithm is proposed; it is also shown that its performance ratio is bounded by $3-\frac{2}{m}$. In addition, an example is presented to demonstrate that the bound is at least 2.5.
Starting Page	281
Ending Page	294
Page Count	14
File Format	PDF
ISSN	00975397
DOI	10.1137/0221021
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	2
Volume Number	21
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	NP-hard Analysis of algorithms and problem complexity task precedence graph scheduling heuristic Network models, deterministic parallel task
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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