Optimal simulations between mesh-connected arrays of processors
Journal of the ACM (JACM)
On Embedding Rectangular Grids in Hypercubes
IEEE Transactions on Computers
Embedding Rectangular Grids Into Square Grids
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Embedding of grids into optimal hypercubes
SIAM Journal on Computing
Embedding Complete Binary Trees Into Butterfly Networks
IEEE Transactions on Computers
Efficient embeddings of trees in hypercubes
SIAM Journal on Computing
Cost Trade-offs in Graph Embeddings, with Applications
Journal of the ACM (JACM)
Preserving average proximity in arrays
Communications of the ACM
Computer Architecture and Parallel Processing
Computer Architecture and Parallel Processing
The channel assignment algorithm on RP(k) networks
ACSAC'05 Proceedings of the 10th Asia-Pacific conference on Advances in Computer Systems Architecture
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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脳t1 mesh into an s2脳t2 mesh, where si驴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 $\lfloor s_1/s_2 \rfloor + 2$ and congestion $\lfloor s_1/s_2 \rfloor + 4$ for the case s1驴s2, both of which almost match the lower bound $\lceil s_1/s_2 \rceil.$ Finally, for the case s1