## Dynamic Critical-Path Scheduling: An Effective Technique for Allocating Task Graphs to Multiprocessors (1996)

Venue: | IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS |

Citations: | 121 - 17 self |

### BibTeX

@ARTICLE{Kwok96dynamiccritical-path,

author = {Yu-kwong Kwok and Ishfaq Ahmad},

title = {Dynamic Critical-Path Scheduling: An Effective Technique for Allocating Task Graphs to Multiprocessors},

journal = {IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS},

year = {1996},

volume = {7},

pages = {506--521}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper, we propose a static scheduling algorithm for allocating task graphs to fullyconnected multiprocessors. We discuss six recently reported scheduling algorithms and show that they possess one drawback or the other which can lead to poor performance. The proposed algorithm, which is called the Dynamic Critical-Path (DCP) scheduling algorithm, is different from the previously proposed algorithms in a number of ways. First, it determines the critical path of the task graph and selects the next node to be scheduled in a dynamic fashion. Second, it rearranges the schedule on each processor dynamically in the sense that the positions of the nodes in the partial schedules are not fixed until all nodes have been considered. Third, it selects a suitable processor for a node by looking ahead the potential start times of the remaining nodes on that processor, and schedules relatively less important nodes to the processors already in use. A global as well as a pair-wise comparison is c...

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258 |
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- Sarkar
- 1989
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- Hochbaum, Shmoys
- 1987
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Computer and Job-Shop Scheduling Theory
- Coffman
- 1976
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- Adam, Chandy, et al.
- 1974
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- Hu
- 1961
(Show Context)
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- 1979
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