Issue No. 07 - July (1991 vol. 40)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.83623
<p>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).</p>
embeddings; complete binary trees; butterfly networks; wrap-around connections; multiprocessor interconnection networks; trees (mathematics).
A. Gupta and S. Hambrusch, "Embedding Complete Binary Trees Into Butterfly Networks," in IEEE Transactions on Computers, vol. 40, no. , pp. 853-863, 1991.