A GENERALIZATION OF HYPERCUBIC NETWORKS BASED ON THEIR CHORDAL RING STRUCTURES
Ding-Ming Kwai, Behrooz Parhami · Parallel Processing Letters · 1996
We prove that the hypercube and cube-connected cycles (CCC) networks can be viewed as chordal rings with periodic connection patterns and show how the period, chord length, and network size are related in each case. It is well-known that CCC is a subgraph of the hypercube; i.e., it can be derived by pruning the latter. We formulate a more general pruning strategy that leads to a spectrum of useful networks ranging from the hypercube at one end to CCC and CCC-like structures at the other. The resulting unified view of a large class of networks with varying cost and performance parameters leads to better understanding of the networks, facilitates comparisons, explicates the available cost/performance/reliability tradeoffs, and allows the construction of portable parametrized algorithms that can run on each instance of the general architecture at optimal speed.