This Article 
 Bibliographic References 
 Add to: 
Topological Properties of Hypercubes
July 1988 (vol. 37 no. 7)
pp. 867-872
The n-dimensional hypercube is a highly concurrent loosely coupled multiprocessor based on the binary n-cube topology. Machines based on the hypercube topology have been advocated as ideal parallel architectures for their powerful interconnection features. The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing. A

[1] L. M. Adams, "Iterative algorithms for large sparse linear systems on parallel computers," Ph.D. dissertation, Univ. Virginia,Appl. Math., 1982. Also available as NASA Contractor Rep. 166027.
[2] S. N. Bhatt and I. C. F. Ipsen, "How to imbed trees in hypercubes," Res. Rep. 443, Dep. Comput. Sci., Yale Univ., 1985.
[3] L. N. Bhuyan and D. P. Agrawal, "Generalized hypercube and hyperbus structures for a computer network,"IEEE Trans. Comput., vol. C-33, pp. 323-333, 1984.
[4] S. A. Browning, "The tree machine: A highly concurrent computing environment," Tech. Rep. TR-3760, Dep. Comput. Sci., California Instit. Technol., 1980.
[5] A. Gottlieb, R. Grishman, C. P. Kruskal, K. P. McAuliffe, L. Rudolph, and M. Snir, "The NYU Ultracomputer-Designing a MIMD shared memory parallel computer,"IEEE Trans. Comput., vol. C-32, pp. 175-189, 1983.
[6] E. M. Reingold, J. Nievergelt, and N. Deo,Combinatorial Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1977.
[7] Y. Saad and M. H. Schultz, "Topological properties of hypercubes," Res. Rep. 389, Dep. Comput. Science, Yale Univ., 1985.
[8] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 22-33, Jan. 1985.
[9] A. Y. Wu, "Embedding of tree networks into hypercubes,"J. Parallel Distributed Comput., vol. 2, pp. 238-249, 1985.

Index Terms:
topological properties; hypercubes; highly concurrent loosely coupled multiprocessor; binary n-cube topology; parallel architectures; graph-theory; multiprocessing systems; parallel architectures.
Y. Saad, M.H. Schultz, "Topological Properties of Hypercubes," IEEE Transactions on Computers, vol. 37, no. 7, pp. 867-872, July 1988, doi:10.1109/12.2234
Usage of this product signifies your acceptance of the Terms of Use.