Efficient embedding K-ary complete trees into hypercubes

Dilated embedding and precise embedding of K-ary complete trees into hypercubes are studied. For dilated embedding, a nearly optimal algorithm is proposed which embeds a K-ary complete tree of height h, T _K(h), into an (h-1)[logK]+[log(K+2)] dimensional hypercube with dilation max(2, φ(K)*), φ(K+2). For precise embedding, we show a (K-1)h+1 dimensional hypercube is large enough to contain T_K (h) as its subgraph for K⩾3