
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
R.K. Das, K. Mukhopadhyaya, B.P. Sinha, "A New Family of Bridged and Twisted Hypercubes," IEEE Transactions on Computers, vol. 43, no. 10, pp. 12401247, October, 1994.  
BibTex  x  
@article{ 10.1109/12.324555, author = {R.K. Das and K. Mukhopadhyaya and B.P. Sinha}, title = {A New Family of Bridged and Twisted Hypercubes}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {10}, issn = {00189340}, year = {1994}, pages = {12401247}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.324555}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A New Family of Bridged and Twisted Hypercubes IS  10 SN  00189340 SP1240 EP1247 EPD  12401247 A1  R.K. Das, A1  K. Mukhopadhyaya, A1  B.P. Sinha, PY  1994 KW  hypercube networks; hypercubes; bridged; routing; twisting; interconnection. VL  43 JA  IEEE Transactions on Computers ER   
We show that by adding eight extra edges, referred to as bridges, to an ncube (n/spl ges/4) its diameter can be reduced by 2, and by adding sixteen bridges to an ncube (n/spl ges/6) its diameter can be reduced by 3. We also show that by adding (/sub m+1sup 4m/)+1(m/spl ges/2) bridges to an ncube (n/spl ges/4m and n/spl ges/8) its diameter can be reduced by 2m and by adding 2(/sub msup 4m3/)+1, (m<2) to an ncube (n/spl ges/4m2 and n/spl ges/10) its diameter can be reduced by 2m1. We also consider the reduction of diameter of an ncube by exchanging some independent edges (twisting), where two edges are called independent if they are not incident on a common node. We have shown that by exchanging four pairs of independent edges in a dcube (d/spl ges/5), we can reduce its diameter by 2. By exchanging sixteen pairs of independent edges, the diameter of a dcube (d/spl ges/7) can be reduced by 3. By exchanging 57 pairs of independent edges, the diameter can be reduced by 4 for d/spl ges/9. To reduce the diameter by lower bound [d/2], (d/spl ges/10) we need to exchange (/sub r+1sup d1/) pairs of independent edges, where r=lower bound [d/4]+1.
[1] R. Armstrong and F. G. Gray, "Fault diagnosis in a Boolean cube of microprocessors,"IEEE Trans. Comput., vol. C30, no. 8, pp. 587590, Aug. 1981.
[2] S. Abraham and K. Padmanabhan, "Performance of direct binaryncube network for multiprocessors,"IEEE Trans. Comput., vol. C38, no. 7, pp. 10001011, Jul. 1989.
[3] R. K. Das, K. Mukhopadhyaya, and B. P. Sinha, "Bridged and twisted hypercubes with reduced diameters," inProc. Int. Conf. Parallel Processing, Aug. 1721, pp. I72I75, 1992.
[4] A. Esfahanian, L. M. Ni, and B. E. Sagan, "The twistedNcube with application to microprocessing,"IEEE Trans. Comput., vol. 40, no. 1, pp. 8893, Jan. 1991.
[5] A. E. Amawy and S. Latifi, "Bridged hypercube networks,"J. Parallel Distrib. Computing, pp. 9095, Sept. 1990.
[6] N.F. Tzeng and S. Wei, "Enhanced hypercubes,"IEEE Trans. Comput., vol. 40, no. 3, pp. 284293, Mar. 1991.
[7] P. A. J. Hilberts, M. R. J. Koopman, and J. L. A. van de Snepscheut, "The twisted cube," inParallel Architectures and Languages Europe, Lecture Notes in Computer Science. Berlin: SpringerVerlag, June 1987, pp. 152159.
[8] S. Abraham and K. Padmanabhan, "Twisted cube: A study in asymmetry,"J. Parallel Distrib. Computing, vol. 13, pp. 104110, Nov. 1991.