Embedding Algorithm between [ 2 2n-k ×2 k ] Torus and HFN(n,n), HCN(n,n)

In this paper, we will analysis embedding between torus and interconnection networks HFN(n,n), HCN(n,n). First, we will prove that torus can be embedded into HFN(n,n) with dilation 3, congestion 4 and the average dilation is less than 2. And we will show that torus can be embedded into HCN(n,n) with dilation 3 and the average dilation is less than 2. Also, we will prove that interconnection networks HFN(n,n) and HCN(n,n) can be embedded into torus with dilation O(n). These results mean so many developed algorithms in torus can be used efficiently in HFN(n,n) and HCN(n,n).

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