Node-ranking schemes for the star networks

In this paper, three new node-ranking schemes for the star graph are presented and evaluated. These node-ranking schemes efficiently "embed" grids, pipelines, and reconfigurable multiple ring networks (cases of torus networks). These schemes improve similar known results on the star graph. They also allow efficient mapping of a wide class of algorithms into the star graph and hence facilitating further testing for the viability of the star graph as a potential interconnection network for large-scale multiprocessor systems. The proposed node-ranking schemes outperform their hypercube counterparts in terms of communication cost. Finally, two algorithms for solving systems of linear equations are given. These algorithms are based on the proposed grid and pipeline schemes to carry out matrix triangulation and backward substitution, respectively.