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Dual of a complete graph as an interconnection network. (English) Zbl 0962.68140

Summary: A new class of interconnection network, 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.

MSC:

68R10 Graph theory (including graph drawing) in computer science
68M10 Network design and communication in computer systems

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