Algebraic Models for the Cube Connected Cycles and Shuffle Exchange Graphs

Interconnection networks often constrain the performance of multi-cores chips or parallel computers. Cube Connected Cycles (CCC) is an attractive interconnection network because of its symmetry, small constant node degree and a small diameter. This paper develops an algebraic model for the CCC using the direct product of a cyclic group and a finite field. This model allows the use of powerful algebraic techniques to study the structural properties of the network. This paper exploits these techniques to find optimal paths in the CCC and to explore the relationships between the Cube Connected Cycles, the Shuffle Exchange and the deBruijn networks.