COMPARING AND SELECTING GENERALIZED DOUBLE RING NETWORK STRUCTURES

摘要

N2R(p; q) network structures were introduced recently as a generalization of double rings, and they were shown to be superior compared to double rings in terms of average distance and diameter. For a given number of nodes, there is only one double ring, but often more different N2R(p; q) structures. These different structures have different properties, and choosing a best structure depends on what properties are considered important. For both research and planning purposes it is beneficial to have a simple scheme for optimally choosing q given p. We show that for structures of up to 4000 nodes it is in 1919 of 1998 cases possible to choose a structure minimizing both average distance and diameter. For structures of up to 164 nodes, minimizing average distance and diameter result in structures where 2-average distance, 3-average distance, 2-diaineter and 3-diarneter are minimized or nearly minimized.