Edge-disjoint embedding of large full binary trees into hypercubes

We present two embedding methods of the full binary tree into the hypercube when the tree has greater number of nodes than the hypercube. Both methods map the tree edges onto the edge-disjoint paths of the hypercube(each hypercube edge being considered as two anti-parallel directed edges), and distribute the same level tree nodes evenly to the hypercube nodes. One embedding method with the optimal dilation has a load factor greater than the optimal valve by one. And the other embedding method with the optimal load factor has a dilation greater than the optimal value by one. Furthermore, we show that both the dilation and load factor can not be optimized simultaneously when the same level tree nodes are evenly distributed.