Embedding of Tree Machines into Hypercubes

In this paper, we present that a tree machine can be embedded into incomplete hypercube with expansion 1, load 1, dilation 2 and congestion 2. This result is better than the expansion (2+2)/(2+2-2) in [14]. Then we consider how to embed a large tree machine into a hypercube for considering load-balance. We have shown that a tree machine TMh (h1) can be embedded into a hypercube Hh+1 with dilation 1, congestion 2 and load 2, and a tree machine TMh can be embedded into Hn (hn1) with dilaton 1, congestion 3 and load 2+2. The load of these embeddings is well balanced.