A group construction method with applications to deriving pruned interconnection networks

作者：Xiao Wenjun^*; Parhami Behrooz

来源：IEEE Transactions on Parallel and Distributed Systems, 2007, 18(5): 637-643.

DOI：10.1109/TPDS.2007.1002

• algebraic structure
• Cayley graph
• distributed system
• geometric group theory
• interconnection network
• network diameter
• parallel processor architecture
• pruning scheme
• VLSI realization

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 kD 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.

• 出版日期2007-5
• 单位华南理工大学