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<p><b>Abstract</b>—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 2<super><it>p</it></super>− 1 nodes can be embedded 1) with link congestion one into a <tmath>${9 \over 8}\sqrt{2^p}\times {9 \over 8}\sqrt{2^p}$</tmath> mesh when <it>p</it> is even and a <tmath>$\sqrt{{\textstyle{9 \over 8}} {2^p}}\times \sqrt{{\textstyle{9 \over 8}} {2^p}}$</tmath> mesh when <it>p</it> is odd, and 2) with link congestion two into a <tmath>$\sqrt{2^p}\times \sqrt{2^p}$</tmath> mesh when <it>p</it> is even, and a <tmath>$\sqrt{2^{p-1}}\times 2\sqrt{2^{p-1}}$</tmath> mesh when <it>p</it> is odd.</p>
Embedding, complete binary tree, mesh, row-column routing, link congestion.
Hyeong-Ah Choi, Sang-Kyu Lee, "Embedding of Complete Binary Trees into Meshes with Row-Column Routing", IEEE Transactions on Parallel & Distributed Systems, vol. 7, no. , pp. 493-497, May 1996, doi:10.1109/71.503774
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