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

Abs t r ac t . 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. Then 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 multig~d and X-tree networks in optimal volume.