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Independent Partitioning of Algorithms with Uniform Dependencies
February 1992 (vol. 41 no. 2)
pp. 190-206

Uniform dependence algorithms with arbitrary index sets are considered, and two computationally inexpensive methods to find their independent partitions are proposed. Each method has advantages over the other one for certain kinds of applications, and they both outperform previously proposed approaches in terms of computational complexity and/or optimality. Also, lower and upper bounds are given for the cardinality of maximal independent partitions. In multiple instruction multiple data (MIMD) systems, if different blocks of an independent partition are assigned to different processors, communications between processors will be minimized to zero. This is significant because the communications usually dominate the overhead in MIMD machines.

[1] U. Banerjee, S. C. Chen, D. J. Kuck, and R. A. Towle, "Time and parallel processor bounds for FORTRAN-like loops,"IEEE Trans. Comput., vol. C-28, pp. 660-670, Sept. 1979.
[2] R. Cytron, "Doacross: Beyond vectorization for multiprocessors," inProc. 1986 Int. Conf. Parallel Processing, pp. 836-844.
[3] J. A. B. Fortes, "Algorithm transformations for parallel processing and VLSI architecture design," Ph.D. dissertation, Univ. of Southern California, Los Angeles, Dec. 1983.
[4] D. D. Gajski and J.-K. Peir, "Essential issues in multiprocessor systems,"IEEE Comput. Mag., vol. 18, pp. 9-27, June 1985.
[5] K. Hwang and F. A. Briggs,Computer Architecture and Parallel Processing. New York: McGraw-Hill, 1984.
[6] R. Kannan and A. Bachem, "Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix,"SIAM J. Comput., vol. 8, no. 4, pp. 499-507, Nov. 1979.
[7] R. Karp, R. Miller, and S. Winograd, "The Organization of Computations for Uniform Recurrence Equations,"J. ACM, Vol. 14, No. 3, 1967, pp. 563-590.
[8] D. C. Kuck, A. H. Sameh, R. Cytron, A. V. Veidenbaum, C. D. Polychronopoulos, G. Lee, T. McDaniel, B. R. Leasure, C. Beckman, J. R. B. Davies, and C. Kruskal, "The effects of program restructuring, algorithm changes, and architecture choice on program performance," inProc. 1984 Int. Conf. Parallel Processing, pp. 129-138.
[9] D. Kuck, E. Davidson, D. Lawrie, and A. H. Sameh, "Parallel supercomputing today and the Cedar approach,"Science, vol. 231, pp. 967-974, Feb. 28, 1986.
[10] D. I. Moldovan and J. A. B. Fortes, "Partitioning and mapping algorithms into fixed size systolic arrays,"IEEE Trans. Comput., vol. C-35, pp. 1-12, Jan. 1986.
[11] D. I. Moldovan, "On the design of algorithms for VLSI systolic arrays,"Proc. IEEE, vol. 71, pp. 113-120, Jan. 1983.
[12] L. Mordell,Diophantine Equations. New York: Academic, 1969, p. 30.
[13] D. A. Padua, "Multiprocessors: Discussion of theoretical and practical problems," Ph.D. dissertation, Univ. of Illinois at Urbana-Champaign, Rep. UIUCDCS-R-79-990, Nov. 1979.
[14] D. A. Padua, D. J. Kuck, and D. L. Lawrie, "High speed multiprocessor and compilation techniques,"IEEE Trans. Comput., vol. C-29, pp. 763-776, Sept. 1980.
[15] J.-K. Peir and R. Cytron, "Minimum distance: A method for partitioning recurrences for multiprocessors," inProc. 1987 Int. Conf. Parallel Processing, pp. 217-225.
[16] J.-K. Peir and D. D. Gajski, "CAMP: A programming aid for multiprocessors," inProc. 1986 Int. Conf. Parallel Processing, pp. 475-482.
[17] J.-K. Peir, "Program partitioning and synchronization on multiprocessor systems," Ph.D dissertation, Rep. UIUCDCS-R-86-1259, Dep. Comput. Sci., Univ. of Illinois at Urbana-Champaign, Urbana, IL, Mar. 1986.
[18] C. D. Polychronopoulos, D. J. Kuck, and D. A. Padua, "Execution of parallel loops on parallel processor systems," inProc. 1986 Int. Conf. Parallel Processing, pp. 519-527.
[19] A. Schrijver,Theory of Linear and Integer Programming. New York: Wiley, 1986.
[20] W. Shang and J. A. B. Fortes, "Time optimal linear schedules for algorithms with uniform dependencies," inProc. Int. Conf. Systolic Arrays, May 1988, pp. 393-402.
[21] W. Shang and J. A. B. Fortes, "Partitioning of uniform dependency algorithms for parallel execution on MIMD/systolic systems," Tech. Rep. TR-EE 88-18, School of Electrical Engineering, Purdue Univ., W. Lafayette, IN 47907, Apr. 1988.
[22] W. Shang and J. A. B. Fortes, "Independent partitioning of algorithms with uniform dependencies," inProc. 1988 Int. Conf. Parallel Processing, Vol. 2, Software, pp. 26-33.
[23] G. Strang,Linear Algebra and its Applications, second ed. New York: Academic, 1980.
[24] O. Veblen and P. Franklin, "On matrices whose elements are integers,"Ann. of Mathematics, vol. 23 (1921-2), pp. 1-15.
[25] M. J. Wolfe, "Optimizing supercompilers for supercomputers," Ph.D. thesis, Ctr. Supercomput. Res. and Development, Univ. Illinois, Urbana-Champaign, 1980.

Index Terms:
uniform dependence algorithms; lower bounds; index sets; computational complexity; optimality; upper bounds; cardinality; maximal independent partitions; multiple instruction multiple data; MIMD machines; computational complexity; parallel algorithms.
Citation:
W. Shang, J.A.B. Fortes, "Independent Partitioning of Algorithms with Uniform Dependencies," IEEE Transactions on Computers, vol. 41, no. 2, pp. 190-206, Feb. 1992, doi:10.1109/12.123395
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