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Embedding complete binary trees into butterfly networks

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2 Author(s)
Gupta, A.K. ; Dept. of Comput. Sci., Western Michigan Univ., Kalamazoo, MI, USA ; Hambrusch, S.E.

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 2q+1-1-node complete binary tree T(q) into a (m+1)2m+1-node wrap-around butterfly Bw(m+1) with a dilation of 4, and how to embed T(q) into a (m+2)2m+2-node wrap-around butterfly Bw(m+2) with an optimal dilation of 2. They also present an embedding of a wrap-around butterfly Bw (m) into a (m+1)2m-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)

Published in:

Computers, IEEE Transactions on  (Volume:40 ,  Issue: 7 )