
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
W.J. Hsu, "Fibonacci CubesA New Interconnection Technology," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 1, pp. 312, January, 1993.  
BibTex  x  
@article{ 10.1109/71.205649, author = {W.J. Hsu}, title = {Fibonacci CubesA New Interconnection Technology}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {4}, number = {1}, issn = {10459219}, year = {1993}, pages = {312}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.205649}, 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  Fibonacci CubesA New Interconnection Technology IS  1 SN  10459219 SP3 EP12 EPD  312 A1  W.J. Hsu, PY  1993 KW  Index Termssubgraph embedding; interconnection topology; Fibonacci cube; recurrent structures;sparse interconnections; Boolean cube; hypercube; supergraph; faulttolerant computing;node connectivity; system communication primitives; graph theory; multiprocessorinterconnection networks; topology VL  4 JA  IEEE Transactions on Parallel and Distributed Systems ER   
A novel interconnection topology called the Fibonacci cube is shown to possessattractive recurrent structures in spite of its asymmetric and relatively sparseinterconnections. Since it can be embedded as a subgraph in the Boolean cube(hypercube) and it is also a supergraph of other structures, the Fibonacci cube may findapplications in faulttolerant computing. For a graph with N nodes, the diameter, theedge connectivity, and the node connectivity of the Fibonacci cube are in the logarithmicorder of N. It is also shown that common system communication primitives can beimplemented efficiently.
[1] S. G. Akl,Parallel Sorting Algorithms. Orlando, FL: Academic, 1985.
[2] L. N. Bhuyan and D. P. Agrawal, "Generalized hypercube and hyperbus structures for a computer network,"IEEE. Trans. Comput., vol. C33, pp. 323333, 1984.
[3] G. Birkoff and T. C. Bartee,Modern Applied Algebra.New York: McGrawHill, 1970.
[4] D. P. Bertsekas and J. N. Tsitsiklis,Parallel and Distributed Computations. Englewood Cliffs, NJ: PrenticeHall, 1989.
[5] J. P. Fishburn and R. A. Finkel, Quotient networks,"IEEE Trans. Comput., vol. C31, no. 4, pp. 288295, 1982.
[6] A. Gibbons,Algorithmic Graph Theory.Cambridge, MA: Cambridge University Press, 1985. ch. 4.
[7] R. L. Graham, D. E. Knuth, and O. Patashnik, "Special numbers," inConcrete Mathematics.Reading, MA: AddisonWesley, 1989, ch. 6.
[8] J. P. Hayes,Computer Architecture and Organization. New York: McGrawHill, 1988.
[9] E. Horowitz and S. Sahni,Fundamentals of Computer Algorithms. Rockville, MD: Computer Sci. Press, 1978.
[10] IEEE Comput. Mag., Special Issue on Interconnection Networks, vol. 20, 1987.
[11] C. T. Ho and S. L. Johnsson, "On the embedding of arbitrary meshes in Boolean cubes with expansion two and dilation two," inProc. Int. Conf. Parallel Processing, 1987, pp. 188191.
[12] C. T. Ho and S. L. Johnsson, "Embedding meshes in boolean cubes by graph decomposition,"J. Parallel and Distrib. Computing, Apr. 1990, pp. 325339.
[13] W.J. Hsu, Fibonacci cubesA new computer architecture for parallel processing," Tech. Rep. CPS9004, Michigan State Univ., Oct. 1990.
[14] W.J. Hsu and J.S. Liu, Fibonacci codes as formal languages," Tech. Rep. CPS9104, Michigan State Univ., May 1991.
[15] D. E. Knuth,The Art of Computer Programming, Vol. 1. Reading, MA: AddisonWesley, 1973.
[16] J.S. Liu and W.J. Hsu, "On embedding rings and meshes in Fibonacci cubes," Tech. Rep. CPS9101, Jan. 1991.
[17] X. Lin, L. M. Ni, and W.J. Hsu, A foundation for multicast communication in multicomputers," Tech. Rep., CPS892 (ACS12), Michigan State Univ., Jan. 1989.
[18] F. P. Preparata and J. Vuillemin, "The cubeconnected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300309, May 1981.
[19] M. Quinn,Designing Efficient Algorithms for Parallel Computers. New York: McGrawHill, 1987.
[20] Y. Saad and M. H. Schultz, "Topological properties of the hypercubes,"IEEE Trans. Comput., vol. 37, no. 7, pp. 867872, July 1988.
[21] Stone, H. S. 1987.HighPerformance Computer Architecture. Reading, Mass., AddisonWesley.
[22] H. J. Siegel,Interconnection Networks for LargeScale Parallel Processing: Theory and Case Studies. Lexington, MA: Lexington Books, 1985.
[23] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 2233, Jan. 1985.
[24] C.L. Wu and T.Y. Feng,Interconnection Networks for Parallel and Distributed Processing, Computer Society Press, Los Alamitos, Calif., Order No. 574, 1984.