Shortest-path routing algorithm and topological properties for two-level hypernet networks

Although many networks have been proposed as the topology of a large-scale parallel and distributed system. Most of them are neither expansible nor of equal degree. The inexpansibility and inequality of node degrees will make their VLSI implementation more difficult and more expensive. The hypernet, which was proposed by Hwang and Ghosh, represents a family of recursively scalable networks that are both expansible and of equal degree. In addition to the two merits, the hypernet has proven efficient for communication and computation. But, unfortunately, most topological properties and the problem of shortest-path routing for the hypernet are still unsolved. In this paper, we are concerned with the hypernet of two levels, we obtain the following results: (1) a shortest-path routing algorithm, (2) the diameter, (3) the connectivity, and (4) embedding of a ring, a torus, and a hypercube.