Nearly Optimal Three Dimensional Layout of Hypercube Networks

In this paper we consider the three-dimensional layout of hypercube networks. Namely, we study the problem of laying hypercube networks out on the three-dimensional grid with the properties that all nodes are represented as rectangular slices and lie on two opposite sides of the bounding box of the layout volume. We present both a lower bound and a layout method providing an upper bound on the layout volume and the maximum wire-length of the hypercube network.