Optimality of HLF for scheduling divide-and-conquer UET task graphs on identical parallel processors

The problem of scheduling a set of n unit execution time (UET) tasks subject to precedence constraints on m identical parallel processors is known to be N P -hard in the strong sense. However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class...

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Veröffentlicht in:Discrete optimization Jg. 6; H. 1; S. 79 - 91
Hauptverfasser: Kubiak, Wieslaw, Rebaine, Djamal, Potts, Chris
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.02.2009
Schlagworte:
Complexity
Divide-and-conquer graph
HLF
Identical parallel processors
Makespan
Divide-and-conquer graph
Makespan
HLF
Complexity
Identical parallel processors
ISSN:1572-5286, 1873-636X
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Zusammenfassung:The problem of scheduling a set of n unit execution time (UET) tasks subject to precedence constraints on m identical parallel processors is known to be N P -hard in the strong sense. However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class of divide-and-conquer graphs that naturally models the execution of the recursive control abstraction of divide-and-conquer algorithms. We prove that the Highest Level First (HLF) strategy minimizes the schedule length for this class, thus settling a conjecture of Rayward-Smith and Clark.
ISSN:1572-5286
1873-636X
DOI:10.1016/j.disopt.2008.09.001