
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
AbdelElah AlAyyoub, Khaled Day, "Matrix Decomposition on the Star Graph," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 8, pp. 803812, August, 1997.  
BibTex  x  
@article{ 10.1109/71.605767, author = {AbdelElah AlAyyoub and Khaled Day}, title = {Matrix Decomposition on the Star Graph}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {8}, number = {8}, issn = {10459219}, year = {1997}, pages = {803812}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.605767}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Matrix Decomposition on the Star Graph IS  8 SN  10459219 SP803 EP812 EPD  803812 A1  AbdelElah AlAyyoub, A1  Khaled Day, PY  1997 KW  Interconnection networks KW  matrix decomposition KW  parallel processing KW  star graphs. VL  8 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of
[1] S.B. Akers, D. Harel, and B. Krishnamurthy, "The Star Graph: An Attractive Alternative to the nCubes," Proc. Int'l Conf. Parallel Processing, pp. 393400, 1987.
[2] S.G. Akl, K. Qiu, and I. Stojmenovic, "Data Communication and Computational Geometry on the Star and Pancake Interconnection Networks," Proc. Third IEEE Symp. Parallel and Distributed Systems, pp. 415422,Dallas, Dec. 1991.
[3] M. Angelacci and M. Colajanni, "Subcube Matrix Decomposition: A Unifying View of LU Factorization on Multicomputers," Parallel Computing, vol. 20, no. 2, pp. 257270, 1994.
[4] M. Angelacci and M. Colajanni, "Unifying and Optimizing Parallel Linear Algebra Algorithms," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 12, pp. 1,3821,397, Dec. 1993.
[5] N. Bagherzadeh, M. Dowd, and S. Latifi, "A WellBehaved Enumeration of Star Graphs," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 5, pp. 531535, May 1995.
[6] N. Bagherzadeh, N. Nassif, and S. Latifi, “A Routing and Broadcasting Scheme on Faulty Star Graphs,” IEEE Trans. Computers, vol. 42, no. 11, pp. 1,3981,403, Nov. 1993.
[7] Burden et al, Numerical Analysis, second edition. PWS Publishers, 1981.
[8] P.R. Cappelo, "Gaussian Elimination on Hypercube Automation," J. Parallel and Distributed Computing, no. 4, pp. 288308, 1987.
[9] P.R. Cappelo, "A Mesh Automation for Solving Dense Linear Systems," Proc. Int'l Conf. Parallel Processing, pp. 7986, 1985.
[10] K. Coolsaet and V. Fack, "Optimal Data Exchange Algorithms on Star Graphs," Computers and Mathematics with Applications, vol. 27, no. 3, pp. 2125, 1994.
[11] M. Cosnard, Y. Robert, and B. Tourancheau, "Evaluating Speedup on Distributed Memory Architectures," Parallel Computing, vol. 10, pp. 247253, 1989.
[12] K. Dackland et al., "Design and Evaluation of Parallel Block Algorithms: LU Factorization on the IBM 3090 VF/600J," Proc. Fifth SIAM Conf. Parallel Processing for Scientific Computing, pp. 310, 1992.
[13] K. Day and A. Tripathi, "A Comparative Study of Topological Properties of Hypercubes and Star Graphs," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 3138, Jan. 1994.
[14] P. Fragopoulou and S.G. Akl, "A Parallel Algorithm for Computing Fourier Transforms on the Star Graph," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 5, pp. 525531, May 1994.
[15] L. Gargano, U. Vaccaro, and A. Vozella, “FaultTolerant Routing in the Star and Pancake Interconnection Networks,” Information Processing Letters, vol. 45, pp. 315320, Apr. 1993.
[16] S.W. Graham and S.R. Seidel, "The Cost of Broadcasting on Star Graphs and Kary Hypercubes," IEEE Trans. Computers, vol. 42, no. 6, pp. 756759, June 1993.
[17] J.P. Sheu, C.T. Liaw, and T.S. Chen, “A Broadcasting Algorithm in Star Graph Interconnection Networks,” Information Processing Letters, vol. 48, pp. 237241, 1993.
[18] I.L. Jung and J.H. Chang, "Embedding Complete Binary Trees in Star Graphs," J. Korea Information Science Soc., vol. 21, no. 2, pp. 407415, 1994.
[19] J.S. Jwo, S. Lakshmivarahan, and S.K. Dhall, "Embedding of Cycles and Grids in Star Graphs," J. Circuits, Systems, and Computers, vol. 1, no. 1, pp. 4374, 1991.
[20] G. Laszewski et al., "On the Parallelization of Blocked LU Factorization Algorithms on Distributed Memory Architectures," Proc. Supercomputing '92, pp. 170179, 1992.
[21] S. Latifi and N. Bagherzadeh, "Incomplete Star: An Incrementally Scalable Network Based on the Star Graph," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 97102, Jan. 1994.
[22] W. Lichtenstein and S.L. Johnsson, “BlockCyclic Dense Linear Algebra,” SIAM J. Scientific and Statistical Computing, vol. 14, no. 6,pp. 1,259–1,288 1993.
[23] V.E. Mendia and D. Sarkar, “Optimal Broadcasting in the Star Graph,” IEEE Trans. Parallel and Distributed Systems, vol. 3, pp. 389396, July 1992.
[24] A. Menn and A.K. Somani, "An Efficient Sorting Algorithm for the Star Graph Interconnection Network," Proc. 1990 Int'l Conf. Parallel Processing, pp. III18, 1990.
[25] M. Nigam, S. Sahni, and B. Krishnamurthy, "Embedding Hamiltonians and Hypercubes in Star Interconnection Graphs," Proc. Int'l Conf. Parallel Processing, pp. 340343, 1990.
[26] B.V. Purushotham, A. Basu, and P.S. Kumar, "Performance Estimation of LU Factorization of Message Passing Multiprocessors," Parallel Processing Letters, vol. 2, no. 1, pp. 5160, 1992.
[27] K. Qiu and S.G. Akl, "Load Balancing and Selection on the Star and Pancake Interconnection Networks," Proc. 26th Hawaii Int'l Conf. System Sciences, vol. 2, pp. 235242, 1993.
[28] S. Rajasekaran and D.S.L. Wei, "Selection, Routing, and Sorting on the Star Graph," Proc. Seventh Int'l Parallel Processing Symp. pp. 661665, 1993.
[29] S. Ranka, J.C. Wang, and N. Yeh, "Embedding Meshes on the Star Graph," J. Parallel and Distributed Computing, vol. 19, no. 2, pp. 131135, Oct. 1993.
[30] Y. Saad, "Gaussian Elimination on Hypercubes," Parallel Algorithms and Architectures, M. Cosnard et al., eds., pp. 518. Elsevier Science, 1986.
[31] D. Saika and R.K. Sen, "Two Ranking Schemes for Efficient Computation on the Star Interconnection Network," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 4, pp. 321327, Apr. 1996.
[32] D. Saika and R.K. Sen, "Order Preserving Communication on a Star Network," Parallel Computing, vol. 21, pp. 771782, 1995.
[33] S. Starts and A.N. Beris, "LU Decomposition Optimized for Parallel Computer with a Hierarchical Distributed Memory," Parallel Computing, vol. 18, pp. 959971, 1992.
[34] B. Tourancheau, "LU Factorization on FPST Series Hypercube," Parallel and Distributed Computing, Elsevier Science, 1989.