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Improved Algorithms for Partitioning Problems in Parallel, Pipelined, and Distributed Computing
June 1992 (vol. 41 no. 6)
pp. 769-771

S.H. Bokhari has studied the assignment of the modules of a parallel program to the processors of a multiple-computer system. He proposed algorithms to solve optimally the following problems: (1) partition chain-structured parallel or pipelined programs over chain-connected systems; (2) partition multiple chain-structured parallel or pipelined programs over single-host multiple satellite systems; (3) partition multiple arbitrarily structured serial programs over single-host multiple-satellite systems; (4) partition single-tree structured parallel or pipelined programs over single-host multiple identical satellite systems. The authors solve here problem 1 by dynamic programming and problem 2 by sorting and using bisection search for the bottleneck value. They also note that Bokhari's algorithms for problems 3 and 4 can be improved by using recent results of G. Gallo et al. (1989), and by implementing E.W. Dijkstra's (1959) algorithm, which is used as a subroutine, with a heap structure. The time complexity of all algorithms is thus reduced.

[1] S. H. Bokhari,Assignment Problems in Parallel and Distributed Computing. Boston, MA: Kluwer Academic, 1987.
[2] S. H. Bokhari, "Partitioning problems in parallel, pipelined, and distributed computing,"IEEE Trans. Comput., vol. C-37, pp. 48-57, Jan. 1988.
[3] E. W. Dijkstra, "A note on two problems in connexion with graphs,"Numerische Mathematik, vol. 1, pp. 269-271, 1959.
[4] M. J. Eisner and D. G. Severance, "Mathematical techniques for efficient record segmentation in large shared databases,"J. ACM, vol. 23, pp. 619-635, Oct. 1976.
[5] G. Gallo, M. D. Grigoriadis, and R. E. Tarjan, "A fast parametric maximum flow algorithm,"SIAM J. Comput., vol. 18, no. 1, pp. 30-55, 1989.
[6] H. S. Stone, "Critical load factors in two-processor distributed systems,"IEEE Trans. Software Eng., vol. SE-4, pp. 254-258, May 1978.

Index Terms:
partitioning problems; parallel; pipelined; distributed computing; parallel program; bottleneck value; time complexity; computational complexity; parallel programming.
Citation:
P. Hansen, K.W. Lih, "Improved Algorithms for Partitioning Problems in Parallel, Pipelined, and Distributed Computing," IEEE Transactions on Computers, vol. 41, no. 6, pp. 769-771, June 1992, doi:10.1109/12.144628
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