Symmetric degree-four chordal ring networks

Techniques for analysing symmetric chordal ring networks of degree four are presented and expressions for the network diameter and the mean internode distance are derived. The network incorporates the maximum number of nodes for a given diameter, and has a communications cost, measured either as network diameter or as the mean internode distance, of O( square root (N)). Possible modifications to this network include breaking the ring to provide communications with a host computer, and a nonoptimal chordal displacement to allow a cellular array to be mapped onto the chordal ring. Such networks provide a practical means of networking processors such as the transputer, and the results presented in this paper have been verified on a network of transputers. The work originated from a study of the way in which the INMOS transputer could be best applied to image processing.