
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
PenYuang Chang, JongChuang Tsay, "A Family of Efficient Regular Arrays for Algebraic Path Problem," IEEE Transactions on Computers, vol. 43, no. 7, pp. 769777, July, 1994.  
BibTex  x  
@article{ 10.1109/12.293256, author = {PenYuang Chang and JongChuang Tsay}, title = {A Family of Efficient Regular Arrays for Algebraic Path Problem}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {7}, issn = {00189340}, year = {1994}, pages = {769777}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.293256}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A Family of Efficient Regular Arrays for Algebraic Path Problem IS  7 SN  00189340 SP769 EP777 EPD  769777 A1  PenYuang Chang, A1  JongChuang Tsay, PY  1994 KW  parallel algorithms; computational complexity; systolic arrays; graph theory; matrix algebra; efficient regular arrays; algebraic path problem; dependence graph decomposition; multiple phases; mphase schedule function; matrix multiplication; transitive closure; parallel algorithms; execution times; cylindrical array; orthogonal array; spherical array; systolic array; VLSI architecture. VL  43 JA  IEEE Transactions on Computers ER   
The method of decomposing a dependence graph into multiple phases with an appropriate mphase schedule function is useful for designing faster regular arrays for matrix multiplication and transitive closure. In this paper, we further apply this method to design several parallel algorithms for the algebraic path problem and derive N/spl times/N 2D regular arrays with execution times [9N/2]2 (for the cylindrical array and the orthogonal one) and 4N2 (for the spherical one).
[1] H. T. Kung and C. E. Leiserson, "Systolic arrays for VLSI," inProc. 1978 Society for Indust. Appl. Math., 1979, pp. 256282.
[2] S.K. Rao and T. Kailath, "Regular Iterative Algorithms and Their Implementation on Processor Arrays,"IEEE Proc., Vol. 76, No. 3, Mar. 1988, pp. 259269.
[3] S. K. Rao and T. Kailath, "What is a systolic algorithm,"? inProc. SPIE Highly Parallel Signal Processing Architectures, 1986, pp. 3448.
[4] S. K. Rao, "Regular iterative algorithms and their implementations on processor arrays," Ph.D. dissertation, Stanford Univ., Stanford, CA, Oct. 1985.
[5] V. P. Roychowdhury and T. Kailath, "Subspace scheduling and parallel implementation of nonsystolic regular iterative algorithms,"J. VLSI Signal Processing, vol. 1, pp. 127142, 1989.
[6] J. C. Tsay and P. Y. Chang, "Some new designs of 2D array for matrix multiplication and transitive closure,"IEEE Trans. Parallel Distrib. Syst., June 1991, submitted.
[7] M. Gondran and M. Minoux,Graphs and Algorithms. Chichester, UK: Wiley, 1984.
[8] G. Rote, "A systolic array algorithm for the algebraic path problem,"Computing, vol. 34, pp. 191219, 1985.
[9] Y. Robert and D. Trystram, "Systolic solution of the algebraic path problem," inProc. Int. Workshop on Systolic Arrays, 1986, pp. 171180.
[10] F. J. Nunez and M. Valero, "A block algorithm for the algebraic path problem and its execution on a systolic array," inProc. Int. Conf. on Systolic Arrays, 1988, pp. 265274.
[11] A. Benaini and Y. Robert, "Spacetimeminimal systolic architectures for gaussian elimination and the algebraic path problem," inProc. Int. Conf. on Applicat. Specific Array Processors, 1990, pp. 747757.
[12] P. S. Lewis and S. Y. Kung, "An optimal systolic array for the algebraic path problem,"IEEE Trans. Comput., vol. 40, pp. 100105, Jan. 1991.
[13] S. Rajopadhye, "An improved systolic algorithm for the algebraic path problem,"Integration, the VLSI J., vol. 14, pp. 279296, Feb. 1993.
[14] D. I. Moldovan and J. A. B. Fortes, "Partitioning and mapping algorithms into fixed size systolic arrays,"IEEE Trans. Comput., vol. C35, pp. 112, Jan. 1986.
[15] S. Y. Kung, S. C. Lo, and P. S. Lewis, "Optimal systolic design for the transitive closure problem,"IEEE Trans. Comput., vol. C36, no. 5, pp. 603614, May 1987.