A Systematic Design of Cellular Permutation Arrays
Authors: 
A. Y. Oruç, A. ThirumalaiAuthors Info & Claims
A. Y. Oruç, A. ThirumalaiAuthors Info & ClaimsPages 1447 - 1451
Abstract
A parametrized design technique is presented of cellular permutation arrays based on coset decompositions of symmetric groups. A type of permutation cell referred to as a coset generator is introduced to customize the propagation delay, fan-in, fan-out, and number of edges in the target network. To aid in the design process, a cost function is derived expressing the number of edges in terms of the number of inputs and the sizes of cells. The results provide a spectrum of networks which vary with the size of the coset generator used and range from a simple bipartite graph to several cellular permutation arrays reported in the literature.
References
[1]
{1} S. Bandyopadhyay, S. Basu, and K. Choudhury, "A cellular permuter array," IEEE Trans. Comput., vol. C-21, pp. 1116-1119, Oct. 1972.
[2]
{2} V. E. Benes, Mathematical Theory of Connecting Networks and Telephone Traffic. New York: Academic, 1965.
[3]
{3} T. Feng, "A survey of interconnection networks," IEEE Computer Mag., vol. 14, pp. 12-27, Dec. 1981.
[4]
{4} W. H. Kautz et al., "Cellular interconnection arrays," IEEE Trans. Comput., vol. C-17, pp. 443-451, May 1968.
[5]
{5} S. A. Nadkarni, "The design and performance evaluation of hybrid cellular interconnection arrays," M.Sc. thesis, Rensselaer Polytechnic Institute, Troy, NY, Aug. 1985.
[6]
{6} A. Y. Oruç, "Designing cellular permutation networks through coset decompositions of symmetric groups," J. Parallel Distrib. Comput., pp. 30-45, Aug. 1987.
[7]
{7} A. Y. Oruç and M. Y. Oruç, "Linear-time algorithms for programming cellular permutation arrays," in Proc. ACM Nat. Comput. Sci. Conf., Cincinnati, OH, 1986, pp. 129-136.
[8]
{8} A. Y. Oruç and S. Schneider, "Coset networks for parallel processors," J. Supercomput., pp. 23-39, 1989.
[9]
{9} H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing: Theory and Case Studies. Lexington, MA: Lexington Books.
[10]
{10} K. J. Thurber, "Circuit switching technology: A state of the art survey," in Conf. Proc.--Compcon 1978 Fall Conf., Sept. 1978, pp. 116-124.
Index Terms
- A Systematic Design of Cellular Permutation Arrays
Recommendations
A Transform for NAND Network Design
A transform that operates on the interconnection topology of a NAND network is presented. The output connecting a designated gate to the network is deleted and is connected instead to a number of other gates in the network. The entire transform may be ...
Decomposition of Permutation Networks
The problem of decomposing an arbitrary permutation of a large number of elements into a number of permutations of smaller numbers of elements has become important recently in rearrangeable switching networks and in interconnectors for computer ...
Comments
Information & Contributors
Information
Published In
Copyright © Copyright © 1989 IEEE. All Rights Reserved.
Publisher
IEEE Computer Society
United States
Publication History
Published: 01 October 1989
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 29 Jul 2024