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On embedding between 2D meshes of the same size

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3 Author(s)
Shen, X. ; Comput. Sci. Telecommun. Program, Missouri Univ., Kansas City, MO, USA ; Weifa Liang ; Qing Hu

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. The authors study how to embed an s1×t1 mesh into an s2×t2 mesh, where si⩽ti (i=1, 2), s1⩽t1=s2t2, such that the minimum dilation and congestion can be achieved. First, they present a lower bound on the dilations and congestions of such embeddings for different cases. Then, they propose an embedding with dilation [s1 /s2]+2 and congestion [s1/s2]+4 for the case s2⩾s2, both of which almost match the lower bound [s1/s2]. Finally, for the case s 1<s2, we present an embedding which has a dilation less than or equal to 2√s1

Published in:

Computers, IEEE Transactions on  (Volume:46 ,  Issue: 8 )

Date of Publication:

Aug 1997

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