On Three-Dimensional Layout of Interconnection Networks (Extended Abstract)

In this paper we deal with the layout of interconnection networks on three-dimensional grids. In particular, in the first part we prove a general formula for calculating an exact value for the lower bound on the volume. The we introduce the new notion of k-3D double channel routing and we use it to exhibit an optimal three-dimensional layout for butterfly networks. Finally, we show a method to lay out multigrid and X-tree networks in optimal volume