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On Embedding Between 2D Meshes of the Same Size
August 1997 (vol. 46 no. 8)
pp. 880-889

Abstract—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 s1×t1 mesh into an s2×t2 mesh, where siti(i = 1, 2), s1t1 = s2t2, 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 $\lfloor s_1/s_2 \rfloor + 2$ and congestion $\lfloor s_1/s_2 \rfloor + 4$ for the case s1s2, both of which almost match the lower bound $\lceil s_1/s_2 \rceil.$ Finally, for the case s1 < s2, we present an embedding which has a dilation less than or equal to $2\sqrt {s_1}.$

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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, Aug. 1997, doi:10.1109/12.609277
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