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Uniform Approach for Solving some Classical Problems on a Linear Array
April 1991 (vol. 2 no. 2)
pp. 236-241

It is shown that a number of classical problems from linear algebra and graph theory,including instances of the algebraic path problem, matrix multiplication, matrix triangularization, and matrix transpose, can be solved using the same basic recurrence. Asimple mapping of the recurrence onto a unidirectional linear array is discussed. Qualitative advantages to programming linear arrays using this approach include uniformity of design, simplicity of programming, and scalability to larger problems. The major disadvantage is that the resulting algorithms are not necessarily optimal.

[1] S. Y. Kung, S. C. Lo, and P. S. Lewis, "Optimal systolic design for the transitive closure problem,"IEEE Trans. Comput., vol. C-36, no. 5, pp. 603-614, May 1987.
[2] P.S. Tseng, personal communication, 1987.
[3] H.T. Kung, "Why systolic architectures?,"IEEE Comput. Mag., pp. 37-46, Jan. 1982.
[4] S. Y. Kung, K. S. Arun, R. J. Gal-Ezer, and D.V. Bhaskar Rao, "Wavefront array architecture: Language, architecture, and applications,"IEEE Trans. Comput., vol. C-31, pp. 1054-1066, Nov. 1982.
[5] P. Quinton, "Automatic synthesis of systolic arrays from uniform recurrent equations," inProc. 11th Annu. Symp. Comput. Architecture, 1984, pp. 208-214.
[6] S. K. Rao, "Regular iterative algorithms and their implementations on processor arrays," Ph.D. dissertation, Stanford Univ., Stanford, CA, Oct. 1985.
[7] 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.
[8] P. Lee and Z. Kedem, "Synthesizing linear array algorithms from nested for loop algorithms,"IEEE Trans. Comput., vol. 37. pp. 1578-1598, Dec. 1588.
[9] P. Lee and Z. Kedem, "Mapping nested loop algorithms into multidimensional systolic arrays,"IEEE Trans. Parallel Distributed Syst., vol. 1. pp. 64-76, Jan. 1990.
[10] M. Annaraton, E. Arnould, T. Gross, H. Kung, M. Lam, O. Menzilcioglu, and J. Webb, "The Warp computer: Architecture, implementation, and performance,"IEEE Trans. Comput., vol. C-36, pp. 1523-1538, Dec. 1987.
[11] G. Rote, "A systolic array algorithm for the algebraic path problem,"Computing, vol. 34, pp. 191-219, 1985.
[12] R. Floyd, "Shortest path,"CACM, vol. 5, no. 6, 1962.
[13] B. M. Maggs and S. A. Plotkin, "Minimum-cost spanning tree as a path-finding problem,"Inform. Processing Lett., vol. 26, pp. 29-293, Jan. 1988.
[14] Y. Robert and D. Trystram, "Systolic solution of the algebraic path problem," inSystolic Arrays, W. Moore, A. McCabe, and R. Urquhart, Eds. Boston, MA: Hilger, 1986.
[15] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[16] J. M. Jover and T. Kailath, "A parallel architecture for Kalman filter measurement update and parameter estimation,"Automatica, vol. 22, no. 1, pp. 32-57, 1986.
[17] R. S. Baheti, D. R. O'Hallaron, and H. R. Itzkowitz, "Mapping extended Kalman filters onto linear arrays,"IEEE Trans. Automat. Contr., 1990.
[18] G. H. Golub and C. F. V. Loan,Matrix Computations.Baltimore, MD: Johns Hopkins University Press, 1983.

Index Terms:
Index Termslinear algebra; graph theory; algebraic path problem; matrix multiplication; matrixtriangularization; matrix transpose; unidirectional linear array; graph theory; linearalgebra; matrix algebra; parallel algorithms
D.R. O'Hallaron, "Uniform Approach for Solving some Classical Problems on a Linear Array," IEEE Transactions on Parallel and Distributed Systems, vol. 2, no. 2, pp. 236-241, April 1991, doi:10.1109/71.89068
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