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Complexity of Scheduling Parallel Task Systems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Du, Jianzhong Leung, Joseph Y.-T.
Copyright Year	1989
Abstract	One of the assumptions made in classical scheduling theory is that a task is always executed by one processor at a time. With the advances in parallel algorithms, this assumption may not be valid for future task systems. In this paper, a new model of task systems is studied, the so-called Parallel Task System, in which a task can be executed by one or more processors at the same time. The complexity of scheduling Parallel Task Systems to minimize the schedule length is examined. For nonpreemptive scheduling, it is shown that the problem is strongly NP-hard even for two processors when the precedence constraints consist of a set of chains. For independent tasks, the problem is strongly NP-hard for five processors, but solvable in pseudo-polynomial time for two and three processors. For preemptive scheduling, it is shown that the problem is strongly NP-hard for arbitrary number of processors for a set of independent tasks. Furthermore, it is shown that it is NP-hard, but solvable in pseudo-polynomial time, for a fixed number of processors.
Starting Page	473
Ending Page	487
Page Count	15
File Format	PDF
ISSN	08954801
DOI	10.1137/0402042
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	2
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-08
Access Restriction	Subscribed
Subject Keyword	pseudo-polynomial time preemptive scheduling NP-hard nonpreemptive scheduling Production models schedule length parallel task system Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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