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Embedding of Complete Binary Trees into Meshes with Row-Column Routing
May 1996 (vol. 7 no. 5)
pp. 493-497

Abstract—This paper considers the problem of embedding complete binary trees into meshes using the row-column routing and obtained the following results: a complete binary tree with 2p− 1 nodes can be embedded 1) with link congestion one into a ${9 \over 8}\sqrt{2^p}\times {9 \over 8}\sqrt{2^p}$ mesh when p is even and a $\sqrt{{\textstyle{9 \over 8}} {2^p}}\times \sqrt{{\textstyle{9 \over 8}} {2^p}}$ mesh when p is odd, and 2) with link congestion two into a $\sqrt{2^p}\times \sqrt{2^p}$ mesh when p is even, and a $\sqrt{2^{p-1}}\times 2\sqrt{2^{p-1}}$ mesh when p is odd.

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Index Terms:
Embedding, complete binary tree, mesh, row-column routing, link congestion.
Sang-Kyu Lee, Hyeong-Ah Choi, "Embedding of Complete Binary Trees into Meshes with Row-Column Routing," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 5, pp. 493-497, May 1996, doi:10.1109/71.503774
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