Generalized Double Ring Network Structures

This paper describes and studies generalizations of the well known double ring network structures. Two classes of structures are studied, the N2R(p; q) and N2R(p; q; r) structures, of which the former is a special case of the well known Generalized Petersen Graphs. Basic properties of these structures are shown, indicating that they form a suitable base for future access network infrastructures. The first result is that every N2R(p; q; r) structure is isomorph to a N2R(p; q) structure N2R(p; q′), and it is shown how q′ is determined. Consequently, the rest of the paper focuses on the N2R(p; q) structures. Results on the Generalized Petersen Graphs provide necessary and sufficient conditions for a N2R(p; q) structure to be node or edge symmetric, and a tablefree routing scheme always determining a shortest path between any pair of nodes is presented. Next, the performance in terms of average distances and diameters is evaluated and compared to the performance of double rings. This comparison shows that the N2R(p; q) structures are superior to the double rings with regard to distances. For example, a N2R(p; q) structure with 1000 nodes has average distance 12 and diameter 18, while a similar sized double ring has average distance 125.6 and diameter 251. Finally suggestions for further research is given.