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An Approximation Algorithm for Scheduling Tasks on Varying Partition Sizes in Partitionable Multiprocessor Systems
December 1992 (vol. 41 no. 12)
pp. 1572-1579

A partitionable multiprocessor system can form multiple partitions, each consisting of a controller and a varying number of processors. Given such a system and a set of tasks, each of which can be executed on partitions of varying sizes, the authors study the problem of choosing the partition sizes and a minimum completion time schedule for the execution of these tasks. They assume that the number of tasks to be scheduled on the system is no more than the maximum number of partitions that can be formed simultaneously by the system, and that parallelization of the tasks can achieve at most perfect speedup. They show this scheduling problem to be NP-hard, and present a polynomial time approximation algorithm for this problem. The authors derive a parameter dependent, asymptotically tight worst-case performance bound for the algorithm, and evaluate its average performance through simulation.

[1] G. H. Barnes, R. M. Brown, M. Kato, D. J. Kuck, D. L. Slotnick, and R. A. Stokes, "The ILLIAC IV computer,"IEEE Trans. Comput., vol. C-17, pp. 746-757, Aug. 1968.
[2] B. S. Baker, E. G. Coffman, Jr., and R. L. Rivest, "Orthogonal packings in two dimensions,"SIAM J. Comput., vol. 9, no. 4, pp. 846-855, Nov. 1980.
[3] G. Baudet and D. Stevenson, "Optimal sorting algorithms for parallel computers,"IEEE Trans. Comput., vol. C-27, pp. 84-87, Jan. 1978.
[4] B. S. Baker and J. S. Schwarz, "Shelf algorithms for two-dimensional packing problems,"SIAM J. Comput., vol. 12, no. 3, pp. 508-525, Aug. 1983.
[5] M.-S. Chen and K. G. Shin, "Processor allocation in anN-cube multiprocessorusing Gray codes,"IEEE Trans. Comput., vol. C-36, no. 12, pp. 1396-1407, Dec. 1987.
[6] J. Du and J. Y-T. Leung, "Complexity of scheduling parallel task systems,"SIAM J. Disc. Math., vol. 2, no. 4, pp. 473-487, Nov. 1989.
[7] M. R. Garey and D. S. Johnson, "Bounds for multiprocessor scheduling with resource constraints.SIAM J. Comput., vol. 4, no. 2, pp. 187-200, June 1975.
[8] M. R. Garey and D. S. Johnson, "Complexity results for multiprocessor scheduling under resource constraints,"SIAM J. Comput., vol. 4, no. 4, pp. 397-411, Dec. 1975.
[9] R. Krishnamurti and E. Ma, "The processor partitioning problem in special-purpose partitionable systems," inProc. Int. Conf. Parallel Processing, vol. 1, Aug. 1988, pp. 434-443.
[10] R. Krishnamurti and E. Ma, "An approximation algorithm for scheduling tasks on varying partition sizes in partitionable multiprocessor systems," IBM Research Report RC 15900 (#70682), July 1990.
[11] J. T. Kuehn and H. J. Siegel, "Simulation studies of a parallel histogramming algorithm for PASM," inProc. Seventh Int. Conf. Pattern Recognition, 1984, pp. 646-649.
[12] K. Li and K. H. Cheng, "Job scheduling in partitionable mesh connected systems," inProc. Int. Conf. Parallel Processing, vol. 2, Aug. 1989, pp. 65-72.
[13] W. H. Lee and M. Malek, "MOPAC - A partitionable and reconfigurable multicomputer array," inProc. Int. Conf. Parallel Processing, 1983, pp. 506-510.
[14] W. Lin and C-L. Wu, "A distributed resource management mechanism for a partitionable multiprocessor system,"IEEE Trans. Comput., vol. C-37, no. 2, pp. 201-210, Feb. 1988.
[15] G. J. Nutt, "Multiprocessor implementation of a parallel processor," inProc. Fourth Annu. Symp. Comput. Architecture, 1977, pp. 147-152.
[16] H. J. Siegel, L. J. Siegel, F. C. Kemmerer, P. T. Mueller Jr., H. E. Smalley Jr., and S. D. Smith, "PASM: A partitionable SIMD/MIMD system for image processing and pattern recognition,"IEEE Trans. Comput., vol. C-30, pp. 934-947, Dec. 1981.
[17] D. L. Tuomenoksa and H. J. Siegel, "Application of two-dimensional bin packing algorithms for task scheduling in the PASM multimicrocomputer system," inProc. Nineteenth Allerton Conf. Commun., Contr., and Comput., Oct. 1981, p. 542.
[18] D. L. Tuomenoksa and H. J. Siegel, "Task scheduling on the PASM parallel processing system,"IEEE Trans. Software Eng., vol. SE-11, pp. 145-157, Feb. 1985.
[19] W. Wilcke, D. G. Shea, R. C. Booth, D. H. Brown, M. E. Giampapa, L. Huisman, G. R. Irwin, E. Ma, T. T. Murakami, F. T. Tong, P. R. Varker, and D. J. Zukowski, "The IBM Victor multiprocessor project," inProc. Fourth Int. Conf. Hypercubes, vol. 1, Apr. 1989, pp. 201-207.

Index Terms:
task scheduling; polynomial time algorithm; parameter dependent bound; asymptotically tight bound; approximation algorithm; partition sizes; partitionable multiprocessor systems; multiple partitions; controller; processors; minimum completion time schedule; parallelization; NP-hard; worst-case performance bound; computational complexity; multiprocessing programs; multiprocessing systems; parallel algorithms; scheduling.
Citation:
R. Krishnamurti, E. Ma, "An Approximation Algorithm for Scheduling Tasks on Varying Partition Sizes in Partitionable Multiprocessor Systems," IEEE Transactions on Computers, vol. 41, no. 12, pp. 1572-1579, Dec. 1992, doi:10.1109/12.214665
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