This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Shortest-Path Routing Algorithm for Incomplete WK-Recursive Networks
April 1997 (vol. 8 no. 4)
pp. 367-379

Abstract—The WK-recursive networks own two structural advantages: expansibility and equal degree. A network is expansible if no changes to node configuration and link connection are necessary when it is expanded, and of equal degree if its nodes have the same degree no matter what the size is. However, the number of nodes contained in a WK-recursive network is restricted to dt, where d > 1 is the size of the basic building block and t≥ 1 is the level of expansion. The incomplete WK-recursive networks, which were proposed to relieve this restriction, are allowed to contain an arbitrary number of basic building blocks, while preserving the advantages of the WK-recursive networks.

Designing shortest-path routing algorithms for incomplete networks is in general more difficult than for complete networks. The reason is that most incomplete networks lack a unified representation. One of the contributions of this paper is to demonstrate a useful representation, i.e., the multistage graph representation, for the incomplete WK-recursive networks. On the basis of it, a shortest-path routing algorithm is then proposed. With O(d·t) time preprocessing, this algorithm takes O(t) time for each intermediate node to determine the next node along the shortest path.

[1] S.B. Akers, D. Harel, and B. Krishnamurthy, "The Star Graph: An Attractive Alternative to the n-cube," Proc. Int'l Conf. Parallel Processing, pp. 393-400, 1987.
[2] G.H. Chen and D.R. Duh, "Topological Properties, Communication, and Computation on WK-Recursive Networks," Networks, vol. 24, no. 6, pp. 303-317, 1994.
[3] N. Deo and C. Pang, "Shortest-Path Algorithms: Taxonomy and Annotation," Networks, vol. 14, pp. 275-323, 1984.
[4] D.R. Duh and G.H. Chen, “Topological Properties of WK-Recursive Networks,” J. Parallel and Distributed Computing, vol. 23, pp. 468-474, 1994.
[5] D.R. Duh and G. H. Chen, "On the Rabin Number Problem," manuscript.
[6] R. Fernandes, "Recursive Interconnection Networks for Multicomputer Networks," Proc. Int'l Conf. Parallel Processing, vol. 1, pp. 76-79, 1992.
[7] R. Fernandes and A. Kanevsky, "Hierarchical WK-Recursive Topologies for Multicomputer Systems," Proc. Int'l Conf. Parallel Processing, vol. 1, pp. 315-318, 1993.
[8] R. Fernandes and A. Kanevsky, "Substructure Allocation in Recursive Interconnection Networks," Proc. Int'l Conf. Parallel Processing, vol. 1, pp. 319-322, 1993.
[9] R. Fernandes, D.K. Friesen, and A. Kanevsky, "Efficient Routing and Broadcasting in Recursive Interconnection Networks," Proc. Int'l Conf. Parallel Processing, pp. 51-58, 1994.
[10] R. Fernandes, D.K. Friesen, and A. Kanevsky, “Embedding Rings in Recursive Networks,” Proc. IEEE Symp. Parallel and Distributed Processing, pp. 273-280, 1994.
[11] A. Iazzetta, C. Sanges, and U. Scafuri, "Special Multicast Wormhole Routing for WK-Networks," manuscript.
[12] H.P. Katseff, "Incomplete Hypercubes," IEEE Trans. Computers, vol. 37, no. 5, pp. 604-608, May 1988.
[13] S. Latifi and N. Bagherzadeh, "Incomplete Star: An Incrementally Scalable Network Based on the Star Graph," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 97-102, Jan. 1994.
[14] S. Latifi and N. Bagherzadeh, "On Clustered-Star Graph and Its Properties," manuscript.
[15] L.M. Ni and P.K. McKinley, "A Survey of Wormhole Routing Techniques in Direct Networks," Computer, vol. 26, no. 2, pp. 62-76, Feb. 1993.
[16] S. Ponnuswamy and V. Chaudhary, "Embedding of Cycles in Rotator and Incomplete Rotator Graphs," Proc. Int'l Symp. Parallel and Distributed Processing, pp. 603-610, Oct. 1994.
[17] C.P. Ravikumar, A. Kuchlous, and G. Manimaran, "Incomplete Star Graph: Aan Economical Fault-Tolerant Interconnection Network," Proc. Int'l Conf. Parallel Processing, vol. 1, pp. 83-90, 1993.
[18] M.Y. Su, "On the Study of Incomplete WK-Recursive Network," Ph.D. dissertation, Dept. of Computer Science and Information Engineering, National Taiwan Univ., Taipei, Taiwan, Jan. 1997.
[19] G.D. Vecchia and C. Sanges, “A Recursively Scalable Network VLSI Implementation,” Future Generation Computer Systems, vol. 4, no. 3, pp. 235-243, 1988.
[20] G.D. Vecchia and C. Sanges, "An Optimized Broadcasting Technique for WK-Recursive Topologies," Future Generation Computer Systems, vol. 4, no. 3, pp. 353-357, 1989/90.

Index Terms:
Graph-theoretic interconnection network, incomplete WK-recursive network, multistage graph representation, routing, shortest-path routing algorithm, WK-recursive network.
Citation:
Ming-Yang Su, Gen-Huey Chen, Dyi-Rong Duh, "A Shortest-Path Routing Algorithm for Incomplete WK-Recursive Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 4, pp. 367-379, April 1997, doi:10.1109/71.588608
Usage of this product signifies your acceptance of the Terms of Use.