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Constant Time Inner Product and Matrix Computations on Permutation Network Processors
December 1994 (vol. 43 no. 12)
pp. 1429-1434

Inner product and matrix operations find extensive use in algebraic computations. In this brief contribution, we introduce a new parallel computation model, called a permutation network processor, to carry out these computations efficiently. Unlike the traditional parallel computer architectures, computations on this model are carried out by composing permutations on permutation networks. We show that the sum of N algebraic numbers on this model can be computed in O(1) time using N processors. We further show that the inner product and matrix multiplication can both be computed on this model in O(1) time at the cost of O(N) and O(N/sup 3/), respectively, for N element vectors, and N/spl times/N matrices. These results compare well with the time and cost complexities of other high level parallel computer models such as PRAM and CRCW PRAM.

[1] Selim G. Akl,The Design and Analysis of Parallel Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[2] D. M. Champion and J. Rothstein, "Immediate parallel solution of the longest common subsequence problem," inIEEE Int. Conf. Parallel Processing, 1987, pp. 70-77.
[3] K. M. Elleithy, M. A. Bayoumi, and K. P. Lee, "θ(lgN) architecture for RNS arithmetic decoding," inIEEE 9th Comput. Arith. Symp., 1989, pp. 202-209.
[4] K. Hwang,Computer Arithmetic: Principles, Architecture, and Design. New York: Wiley, 1979.
[5] S. Lakshmivarahan and Sudarshan K. Dhall,Analysis and Design of Parallel Algorithms, McGraw-Hill Pub., 1990.
[6] M.-B. Lin and A. Yavuz Oruç, "The design of a network-based arithmetic processor," Tech. Rep. UMIACS-TR-91-141, Univ. of Maryland, College Park, MD, Oct. 1991.
[7] M.-B. Lin, "Unified algebraic computations on permutation networks," Ph.D. dissertation, EE Dept., Univ. of Maryland, College Park, 1992.
[8] M. Maresca and H. Li, "Connection autonomy in SIMD computers: A VLSI implementation,"J. Parallel Distrib. Computing, vol. 7, pp. 302-320, 1989.
[9] R. Miller, V. K. Prasanna Kumar, D. Reisis, and Q. F. Stout, "Data movement operations and applications on reconfigurable VLSI arrays," inInt. Conf. Parallel Processing, St. Charles, IL, vol. I, Aug. 1988, pp. 205-208.
[10] A. Yavuz Oruç, V. G. J. Peris, and M. Yaman Oruç, "Parallel modular arithmetic on a permutation network," inInt. Conf. Parallel Processing, St. Charles, IL, vol. 1, Aug. 1991, pp. 706-707.
[11] S. J. Piestrak, "Design of residue generators and multi-operand modular adders using carry-save adders," inIEEE 10th Comput. Arith. Symp., 1991. pp. 100-107.
[12] W. Shen and A. Yavuz Oruç, "Mapping algebraic formulas onto mesh connected processor networks,"Inform. Sci. Syst. Conf., Princeton Univ., NJ, pp. 535-538, 1986.
[13] S. P. Smith and H. C. Torng, "Design of a fast inner product processor," inProc. IEEE 7th Comput. Arith. Symp., 1985, pp. 38-43.
[14] E. E. Swartzlander, Jr., B. K. Gilbert and I. S. Reed, "Inner product computers,"IEEE Trans. Comput., vol. C-27, pp. 21-31, Jan. 1978.
[15] B. F. Wang, G. H. Chen, and F. C. Lin, "Constant time sorting on a processor array with a reconfigurable bus systems,"Info. Processing Letts., pp. 187-192, 1990.
[16] B. F. Wang and G. H. Chen, "Constant time algorithms for the transitive closure and some related graph problems on processor arrays with reconfigurable bus systems,"IEEE Trans. Parallel Distrib. Syst., vol. 1, pp. 500-507, Oct. 1990.

Index Terms:
computational complexity; parallel architectures; matrix algebra; constant time inner product; matrix computations; permutation network processors; algebraic computations; parallel computation model; cost complexities; time complexities; PRAM; CRCW PRAM.
Citation:
Ming-Bo Lin, A. Yavuz Oruc, "Constant Time Inner Product and Matrix Computations on Permutation Network Processors," IEEE Transactions on Computers, vol. 43, no. 12, pp. 1429-1434, Dec. 1994, doi:10.1109/12.338104
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