This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Group Construction Method with Applications to Deriving Pruned Interconnection Networks
May 2007 (vol. 18 no. 5)
pp. 637-643

Abstract—A number of low degree and, thus, low complexity, Cayley-graph interconnection structures, such as honeycomb and diamond networks, are known to be derivable by systematic pruning of 2D or 3D tori. In this paper, we extend these known pruning schemes via a general algebraic construction based on commutative groups. We show that, under certain conditions, Cayley graphs based on the constructed groups are pruned networks when Cayley graphs of the original commutative groups are k{\rm D} tori. Thus, our results offer a general mathematical framework for synthesizing and exploring pruned interconnection networks that offer lower node degrees and, thus, smaller VLSI layout and simpler physical packaging. Our constructions also lead to new insights, as well as new concrete results, for previously known interconnection schemes such as honeycomb and diamond networks.

Index Terms:
Algebraic structure, Cayley graph, distributed system, geometric group theory, interconnection network, network diameter, parallel processor architecture, pruning scheme, VLSI realization.
Citation:
Wenjun Xiao, Behrooz Parhami, "A Group Construction Method with Applications to Deriving Pruned Interconnection Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 18, no. 5, pp. 637-643, May 2007, doi:10.1109/TPDS.2007.1002
Usage of this product signifies your acceptance of the Terms of Use.