On Embedding Between 2D Meshes of the Same Size

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 si ≤ ti (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 s1/s2 + 2 and congestion s1/s2 + 4 for the case s1 ≥ s2, both of which almost match the lower bound s1/s2. Finally, for the case s1 < s2, we present an embedding which has a dilation less than or equal to 2 1 s .