Abstract
Scheduling interdependent tasks on parallel/distributed architectures is a hard problem. We consider jobs consisting of tasks whose interdependency relationships form a tree, such as QuickSort, Brute-Force Search, and other Divide-and-Conquer jobs. Tree nodes (tasks) have a scale which satisfies an “additive condition”: a leaf's scale is 1 and a non-leaf's is the sum of its children's. The execution time L of a task is a function of its scale S, like aS α+b for some known constants a, b, α. The task set and the shape of the tree, however, may or may not be known in advance. We provide a general algorithm that assigns these tasks to processors in a large set of architectures (including meshes, linear arrays, and rings). We also discuss the relationship between certain complexity parameters and the tree shape. We show that for almost all cases considered, the scheduling achieves optimal or nearly optimal time.
Partially supported by NSF grant CCR-93-16209 and CISE Institutional Infrastructure Grant CDA-90-24735
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© 1995 Springer-Verlag Berlin Heidelberg
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Yu, X., Yung, M. (1995). Scheduling task-tree with additive scales on parallel/distributed machines. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030883
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DOI: https://doi.org/10.1007/BFb0030883
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