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A.K. Gupta, S.E. Hambrusch, "Embedding Complete Binary Trees Into Butterfly Networks," IEEE Transactions on Computers, vol. 40, no. 7, pp. 853863, July, 1991.  
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@article{ 10.1109/12.83623, author = {A.K. Gupta and S.E. Hambrusch}, title = {Embedding Complete Binary Trees Into Butterfly Networks}, journal ={IEEE Transactions on Computers}, volume = {40}, number = {7}, issn = {00189340}, year = {1991}, pages = {853863}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.83623}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Embedding Complete Binary Trees Into Butterfly Networks IS  7 SN  00189340 SP853 EP863 EPD  853863 A1  A.K. Gupta, A1  S.E. Hambrusch, PY  1991 KW  embeddings; complete binary trees; butterfly networks; wraparound connections; multiprocessor interconnection networks; trees (mathematics). VL  40 JA  IEEE Transactions on Computers ER   
The authors present embeddings of complete binary trees into butterfly networks with or without wraparound connections. Let m be an even integer and q=m+(log m)1. The authors show how to embed a 2/sup q+1/1node complete binary tree T(q) into a (m+1)2/sup m+1/node wraparound 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 wraparound butterfly B/sub w/(m+2) with an optimal dilation of 2. They also present an embedding of a wraparound butterfly B/sub w/(m) into a (m+1)2/sup m/node nowraparound butterfly B(m) with a dilation of 3. Using this embedding it is shown that T(q) can be embedded into a nowrap butterfly B(m+1) (resp. B(m+2)) with a dilation of 8 (resp. 5).
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