This Article 
 Bibliographic References 
 Add to: 
On Optimizing Diameter and Average Distance of Directed Interconnected Networks
March 1993 (vol. 42 no. 3)
pp. 353-358

A generic approach to constructing the topology of fixed degree directed networks for a given node degree and size is proposed. The topology has minimum diameter and makes it possible to answer Maekawa's problem partially. In addition, an expansion operator Ex(x,n) is provided to scale the network size. Fast routing algorithms for these networks that have logarithmic time complexity while using constant buffer size are presented.

[1] K. E. Batcher, "The Flip Network in STARAN," inProc. 1976, Int. Conf. Parallel Processing, pp. 65-71.
[2] F. W. Burton and M. M. Huntbach, "Virtual tree machines,"IEEE Trans. Comput., vol. C-33, pp. 278-280, Mar. 1984.
[3] N. G. de Bruijn,A Combinatorial Problem, Koninklijke Netherlands, Academic Van Wetenschapen, Proc. vol. 49, Part 20, 1946, pp. 758-764.
[4] H. Braun, "Massiv parallele Algorithmen für kombinatorische Optimierungs probleme und ihre Implementierung auf einem Parallelrechner," Dissertation (doctoral thesis), Karlsruhe 1990.
[5] H. Braun and F. C. Stephan, "Optimal multiprocessor interconnection networks for divide-and-conquer algorithms," Interner Bericht Nr 12/89, Fakultät für Informatik, Universität Karlsruhe F.R.G., 1989.
[6] H. Braun and F. C. Stephan, "Interconnection networks with minimal diameter," inProc. 5th Int. Symp. Comput. and Inform. Sci., 1990.
[7] B. Elspas, "Topological constraints on interconnection-limited logic,"Switching Circuit Theory and Logical Design, vol. S-164, pp. 133-147, Oct. 1964.
[8] M. A. Fiol, J. L. A. Yebra, I. Alegre, and M. Valero, "A discrete optimization problem in local networks and data alignment,"IEEE Trans. Comput., vol. C-36, no. 6, pp. 702-713, June 1987.
[9] L. R. Goke and G. J. Lipovski, "Banyan networks for partitioning multiprocessor systems," inProc. 1st Annu. Symp. Comput. Architecture, Dec. 1973, pp. 21-28.
[10] J. Kienhöfer,Rückgekoppelte Baumrechner und Programmierung, Angewandte Informatik, Apr. 1989, pp. 143-151.
[11] D. H. Lawrie, "Access and alignment of data in an array processor,"IEEE Trans. Comput., vol. C-24, no. 12, pp. 1145-1155, Dec. 1975.
[12] P. P. Li, "A parallel execution model for logic programming," Ph.D. dissertation, California Instit. of Technol., Pasadena, CA, 1986.
[13] M. Maekawa, "Optimal processor interconnection topologies, inProc. 8 Annu. Comp. Arch. Symp., Houston 1981,Sigarch Newsletters, vol. 9, no. 3, pp. 171-177.
[14] F. J. Peters, "Tree machines and divide-and-conquer algorithms," inProc. Conf. Analysing Problem-Classes and Programming Parallel Comput., Nurnburg, F. R. Germany, June 1981, pp. 25-36.
[15] U. Raabe, M. Lobjinski, M. Horn, Verbindungsstrukturen für Mikroprozessoren, Informatik-Spektrum, Nov. 1988, 195-206.
[16] M. L. Schlumberger, "DeBruijn communication networks," Ph.D. dissertation, Stanford Univ., Stanford, 1974.
[17] M. R. Samathan and D. K. Pradhan, "The De Bruijn multiprocessor network: A versatile sorting network," inIEEE Proc. 12th Int. Symp. Comput. Architecture, Boston, MA, June 1985, pp. 360-367.
[18] H. S. Stone, "Parallel processing with the perfect shuffle,"IEEE Trans. Comput., vol. C-20, pp. 153-161, Feb. 1971.
[19] F. C. Stephan, Untersuchungen von parallelen Rechnernetzwerken mit beschräktem Grad, Dipolmarbeit am Institut für Logik, Komplexität und Deduktionssysteme, Technische Hochschule Karlsruhe, F.R.G., 1988.
[20] R. M. Storwick, "Improved construction techniques for (d, k)-graphs,"IEEE Trans. Comput., vol. C-19, 1214-1216, Dec. 1970.
[21] C.-L. Wu and T.-Y. Feng, "On a class of multistage interconnection networks,"IEEE Trans. Comput., vol. C-29, no. 8, pp. 694-702, Aug. 1980.
[22] C.-L. Wu and T.-Y. Feng, "The universaility of the shuffle-exchange network,"IEEE Trans. Comput., vol. C-30, no. 5, pp. 324-332, May 1981.
[23] W. Wöst, "Introduction to tree computers," Interner Bericht 12/82, Institut für Logik, Komplexität und Deduktionssysteme, Universität Karlsruhe, F.R.G..

Index Terms:
Maekawa problem; diameter; average distance; directed interconnected networks; routing algorithms; logarithmic time complexity; buffer size; computational complexity; directed graphs; minimisation of switching nets; multiprocessor interconnection networks.
H. Braun, F.C. Stephan, "On Optimizing Diameter and Average Distance of Directed Interconnected Networks," IEEE Transactions on Computers, vol. 42, no. 3, pp. 353-358, March 1993, doi:10.1109/12.210177
Usage of this product signifies your acceptance of the Terms of Use.