Generation and Analysis of a Dataset of Optimal Double-Loop Circulant Networks

Abstract

Optimal circulant networks are of practical interest as graph models of reliable communication networks for supercomputer systems and networks on a chip. A large dataset of parameters of optimal double-loop circulant networks with a number of nodes of up to 50,000 and 451,000 points has been constructed. The dataset contains, for each number of vertices, all generators corresponding to optimal or suboptimal (in the absence of optimal) descriptions of the graph. This made it possible to find analytical dependencies of the parameters that define families of optimal graphs. Based on the analysis of the constructed dataset, the solution to the problem of determining optimal two-dimensional circulant networks is studied. A process is automated for determining analytical, parametric descriptions of the families of optimal double-loop networks, described polynomials of diameter. Having applied the methods of integrating differential evolution and reduced local search to the analysis of the generated dataset, we rediscovered a number of previously known families and found more than 200 new, different from all those known in literature, families of optimal double-loop networks with generators of linear and quadratic types of polynomials. Our new ap­proach can be applied to studing datasets of other promising classes of graphs and networks.