SGHC - A NEW CLASS OF OPTIMALLY FAULT-TOLERANT NETWORKS

A new class of interconnection network topology is proposed for parallel and distributed processing. The interconnection is based on the Generalized Hypercube and the Supercube systems. Given the number of nodes N and the desired diameter k, a topology can be constructed. The node degree of each node is between k(left perpendicula-k square-root N right perpendicular) - 1) and ((2k - 1)(inverted left perpendicular k square-root N inverted right perpendicular - 1) - 1). The connectivity of the network is at least k(left perpendicular k square-root N right perpendicular - 1). It has been shown that the connectivity of the network is equal to the minimum node degree. In this sense it is an optimally fault-tolerant network. In addition, there exist at least k(left perpendicular k square-root N right perpendicular - 1) paths of length less-than-or-equal-to k + 1 between any two nodes in an N-node super generalized hypercube with specified diameter k.