Gaussian Interconnection Networks

This paper explores dense Gaussian Networks, which are interconnection networks based on dense Circulant graphs of degree four. Gaussian networks exhibit better distance related characteristics than equivalent topologies such as Tori. We will show that the Gaussian integers, or the set of complex numbers with integer coefficients, constitute the appropriate mathematical model to deal with these Circulant graphs. Labeling the nodes in a Circulant graph by means of Gaussian integers provides a network in which nodes are identified by their integer coordinates in the plane. By using this new labeling we address two important issues: unicast packet routing and optimal broadcast routing.