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| ASCII Text | x | ||
| C.-T. Ho, "An Observation on the Bisectional Interconnection Networks," IEEE Transactions on Computers, vol. 41, no. 7, pp. 873-877, July, 1992. | |||
| BibTex | x | ||
| @article{ 10.1109/12.256455, author = {C.-T. Ho}, title = {An Observation on the Bisectional Interconnection Networks}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {7}, issn = {0018-9340}, year = {1992}, pages = {873-877}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.256455}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - An Observation on the Bisectional Interconnection Networks IS - 7 SN - 0018-9340 SP873 EP877 EPD - 873-877 A1 - C.-T. Ho, PY - 1992 KW - observation; bisectional interconnection networks; n-dimensional folded hypercube; Hamming distance; isomorphism; bitwise Exclusive-OR; predefined bit string patterns; binary matrix; hypercube networks. VL - 41 JA - IEEE Transactions on Computers ER - | |||
It is shown that the bisectional interconnection network (BIN) of 2/sup n/ nodes for any even n is isomorphic to the n-dimensional folded hypercube (FHC), an n-dimensional hypercube with additional edges between any two nodes that are of Hamming distance n apart. This observation leads to simplification for the proofs of many interesting properties for the BIN. Inspired by the isomorphism between BIN and FHC, the class of topologies in which nodes are represented by bit strings and two nodes are adjacent if and only if the bitwise Exclusive-OR of their addresses fall in a set of predefined bit string patterns are studied. A few theorems are given to characterize the topology from the mathematical properties of the binary matrix derived from the definition of edges.
[1] G. B. Adams and H. J. Siegel, "The extra stage cube: A fault-tolerant interconnection network for supersystems,"IEEE Trans. Comput., vol. 31, pp. 443-454, May 1982.
[2] J. Bondy and U. Murthy,Graph Theory with Applications. New York: American Elsevier, 1976.
[3] A. Ghafoor, T. R. Bashkow, and I. Ghafoor, "Bisectional fault-tolerant communication architecture for supercomputer systems,"IEEE Trans. Comput., vol. 38, pp. 1425-1446, Oct. 1989.
[4] C.-T. Ho, "Full bandwidth communications on folded hypercubes," inProc. 1990 Int. Conf. Parallel Processing, vol. I, Penn State, 1990, pp. 276-280.
[5] S. Latifi and A. El-Amawy, "On folded hypercubes," inProc. 1989 Int. Conf. Parallel Processing, vol. I, Penn State, 1989, pp. 180-187.
[6] F. J. Meyer and D. K. Pradhan, "Flip-trees: Fault-tolerant graphs with wide containers,"IEEE Trans. Comput., vol. 37, pp. 472-478, Apr. 1988.
[7] A. S. Wagner, "Embedding trees in the hypercube," Ph.D. dissertation, Univ. of Toronto, 1987.