Database analysis of optimal double-loop networks

Optimal circulant networks are of practical interest as models of reliable low-latency communication networks for multiprocessor cluster systems and on-chip networks. The authors are the first to construct a large dataset of optimal diameter double-loop circulant networks with up to 50 thousand nodes, containing a complete set of optimal graph generators. The analysis of the dataset has been carried out in order to study the problem of finding analytically defined families of optimal graphs. Two new algorithms for automatically finding analytical descriptions of optimal graphs families described by polynomials in diameter have been developed. Using the implemented algorithms, a large number of new analytically described families of optimal networks have been found and tested using validation over the entire range of changes in the diameters of the dataset graphs. The found families of optimal networks can be used when scaling information transmission algorithms in double-loop circulant structures.