Dual of a Complete Graph as an Interconnection Network

A new class of interconnection networks, the hypernetworks, has been proposed recently. Hypernetworks are characterized by hypergraphs. Compared with point-to-point networks, they allow for increased resource-sharing and communication bandwidth utilization, and they are especially suitable for optical interconnects. In this paper, we propose a scheme for deriving new hypernetworks using hypergraph duals. As an example, we investigate the dual, K*_n, of the n-vertex complete graph K_n and show that it has many desirable properties. We also present a set of fundamental data communication algorithms for K*_n. Our results indicate that the K*_n hypernetwork is a useful and promising interconnection structure for high-performance parallel and distributed computing systems.