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Issue No.08 - August (1997 vol.46)
pp: 880-889
ABSTRACT
<p><b>Abstract</b>—Mesh is one of the most commonly used interconnection networks and, therefore, embedding between different meshes becomes a basic embedding problem. Not only does an efficient embedding between meshes allow one mesh-connected computing system to efficiently simulate another, but it also provides a useful tool for solving other embedding problems. In this paper, we study how to embed an <it>s</it><sub>1</sub>×<it>t</it><sub>1</sub> mesh into an <it>s</it><sub>2</sub>×<it>t</it><sub>2</sub> mesh, where <it>s</it><sub><it>i</it></sub>≤<it>t</it><sub><it>i</it></sub>(<it>i</it> = 1, 2), <it>s</it><sub>1</sub><it>t</it><sub>1</sub> = <it>s</it><sub>2</sub><it>t</it><sub>2</sub>, such that the minimum dilation and congestion can be achieved. First, we present a lower bound on the dilations and congestions of such embeddings for different cases. Then, we propose an embedding with dilation <tmath>$\lfloor s_1/s_2 \rfloor + 2$</tmath> and congestion <tmath>$\lfloor s_1/s_2 \rfloor + 4$</tmath> for the case <it>s</it><sub>1</sub>≥<it>s</it><sub>2</sub>, both of which almost match the lower bound <tmath>$\lceil s_1/s_2 \rceil.$</tmath> Finally, for the case <it>s</it><sub>1</sub> < <it>s</it><sub>2</sub>, we present an embedding which has a dilation less than or equal to <tmath>$2\sqrt {s_1}.$</tmath></p>
INDEX TERMS
Dilation, embedding, mesh, parallel processing, vertex partition.
CITATION
Xiaojun Shen, Weifa Liang, Qing Hu, "On Embedding Between 2D Meshes of the Same Size", IEEE Transactions on Computers, vol.46, no. 8, pp. 880-889, August 1997, doi:10.1109/12.609277
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