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Embedding Complete Binary Trees Into Butterfly Networks
July 1991 (vol. 40 no. 7)
pp. 853-863

The authors present embeddings of complete binary trees into butterfly networks with or without wrap-around connections. Let m be an even integer and q=m+(log m)-1. The authors show how to embed a 2/sup q+1/-1-node complete binary tree T(q) into a (m+1)2/sup m+1/-node wrap-around butterfly B/sub w/(m+1) with a dilation of 4, and how to embed T(q) into a (m+2)2/sup m+2/-node wrap-around butterfly B/sub w/(m+2) with an optimal dilation of 2. They also present an embedding of a wrap-around butterfly B/sub w/(m) into a (m+1)2/sup m/-node no-wrap-around butterfly B(m) with a dilation of 3. Using this embedding it is shown that T(q) can be embedded into a no-wrap butterfly B(m+1) (resp. B(m+2)) with a dilation of 8 (resp. 5).

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Index Terms:
embeddings; complete binary trees; butterfly networks; wrap-around connections; multiprocessor interconnection networks; trees (mathematics).
A.K. Gupta, S.E. Hambrusch, "Embedding Complete Binary Trees Into Butterfly Networks," IEEE Transactions on Computers, vol. 40, no. 7, pp. 853-863, July 1991, doi:10.1109/12.83623
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