This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Embedding Hierarchical Hypercube Networks into the Hypercube
September 1997 (vol. 8 no. 9)
pp. 897-902

Abstract—The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embeddings, the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes a new embedding method, based on matrix transformations, for optimally embedding hierarchical hypercube networks (HHNs) into the hypercube (binary n-cube). Thus, this embedding method has practical importance in enhancing the capabilities and extending the usefulness of the hypercube, since hierarchical hypercube networks have proven to be very cost-effective for a wide range of applications.

[1] S.G. Akl, The Design and Analysis of Parallel Algorithms. Orlando, Fl.: Academic Press, 1989.
[2] M.Y. Chan and F.Y.L. Chin, "On Embedding Rectangular Grids in Hypercubes," IEEE Trans. Computers, vol. 37, no. 10, pp. 1,285-1,288, Oct. 1988.
[3] S.P. Dandamudi and D.L. Eager, "Hierarchical Interconnection Networks for Multicomputer Systems," IEEE Trans. Computers, pp. 786-797, 1990.
[4] E. Dekel, D. Nassimi, and S. Sahni, "Parallel Matrix and Graph Algorithms," SIAM J. Computers, pp. 657-675, 1981.
[5] A. Edelman, S. Heller, and S.L. Johnsson, "Index Transformation Algorithms in a Linear Algebra Framework," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 12, pp. 1,302-1,309, Dec. 1994.
[6] K. Ghose and K.R. Desai, "Hierarchical Cubic Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 4, pp. 427-435, Apr. 1995.
[7] M. Hamdi and S.W. Song, "On Embedding Various Networks Into the Hypercube Using Matrix Transformations," Proc. Int'l Parallel Processing Symp., pp. 650-654, 1996.
[8] M. Hamdi and R.W. Hall, "RCC-FULL: An Effective Network for Parallel Computations," J. Parallel and Distributed Computing to appear in 1997.
[9] M. Hamdi, "A Class of Recursive Interconnection Networks: Architectural Characteristics and Hardware Cost," IEEE Trans. Circuits and Systems, pp. 805-816, Dec. 1994.
[10] K. Hwang and J. Ghosh, "Hypernet: A Communication Efficient Architecture for Constructing Massively Parallel Computers," IEEE Trans. Computers, pp. 1,450-1,466, 1987.
[11] J.M. Kumar and L.M. Patnaik, "Extended Hypercube: A Hierarchical Interconnection Network of Hypercubes," IEEE Trans. Parallel and Distributed Systems, pp. 45-57, 1992.
[12] S. Laksmivarahan and S.K. Dhall, "A New Hierarchy of Hypercube Interconnection Schemes for Parallel Computers," J. Supercomputing, pp. 81-107, 1988.
[13] T.H. Lai and W. White, "Mapping Pyramid Algorithms into Hypercubes," J. Parallel and Distributed Computing, pp. 42-54, 1990.
[14] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[15] Y. Saad and M. Schultz, "Topological Properties of Hypercubes," IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[16] A.Y. Wu, "Embedding of Tree Networks Into Hypercubes," J. Parallel and Distributing Computing, pp. 238-249, 1985.

Index Terms:
Dilation, embedding, hypercube, hierarchical networks, interconnection networks.
Citation:
Mounir Hamdi, Siang W. Song, "Embedding Hierarchical Hypercube Networks into the Hypercube," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 9, pp. 897-902, Sept. 1997, doi:10.1109/71.615435
Usage of this product signifies your acceptance of the Terms of Use.