A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Group action graphs and parallel architectures
SIAM Journal on Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Honeycomb Networks: Topological Properties and Communication Algorithms
IEEE Transactions on Parallel and Distributed Systems
Pruned three-dimensional toroidal networks
Information Processing Letters
A Unified Formulation of Honeycomb and Diamond Networks
IEEE Transactions on Parallel and Distributed Systems
Introduction to Parallel Processing: Algorithms and Architectures
Introduction to Parallel Processing: Algorithms and Architectures
IEEE Transactions on Parallel and Distributed Systems
Incomplete k-ary n-cube and its derivatives
Journal of Parallel and Distributed Computing
On routing and diameter of metacyclic graphs
International Journal of Computer Mathematics
Optimal routing algorithm and diameter in hexagonal torus networks
APPT'07 Proceedings of the 7th international conference on Advanced parallel processing technologies
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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.