The main benefits of a three-dimensional layout of interconnection networks
are the savings in material (measured as volume) and the shortening of wir
es. The result presented in this paper is a general formula for calculating
a lower bound on the volume. Moreover, for butterfly and X-tree networks w
e show layouts optimizing the maximum wire length and whose upper bounds on
the volume are close to the lower bounds. (C) 2001 Elsevier Science B.V. A
ll rights reserved.