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Doing the Twist: Diagonal Meshes Are Isomorphic to Twisted Toroidal Meshes
June 1996 (vol. 45 no. 6)
pp. 766-767

Abstract—We show that a k×n diagonal mesh is isomorphic to a ${\textstyle{{n+k} \over 2}}\times {\textstyle{{n+k} \over 2}}-{\textstyle{{n-k} \over 2}}\times {\textstyle{{n-k} \over 2}}$ twisted toroidal mesh, i.e., a network similar to a standard ${\textstyle{{n+k} \over 2}}\times {\textstyle{{n+k} \over 2}}$ toroidal mesh, but with opposite handed twists of ${\textstyle{{n-k} \over 2}}$ in the two directions, which results in a loss of $\left( {{\textstyle{{n-k} \over 2}}} \right)^2$ nodes.

[1] K.W. Tang and S.A. Padubidri, “Diagonal and Toroidal Mesh Networks,” IEEE Trans. Computers, vol. 43, no. 7, pp. 815-826, July 1994.
[2] A. Davis, J. Anderson, W.S. Coates, R.W. Hon, I.N. Robinson, S.V. Robison, and K.S. Stevens, "The Architecture of FAIM-1," Computer, vol. 20, no. 1, pp. 55-65, Jan. 1987.

Index Terms:
Interconnection networks, grid networks, mesh-connected topologies, diagonal mesh, toroidal mesh.
Citation:
Barak A. Pearlmutter, "Doing the Twist: Diagonal Meshes Are Isomorphic to Twisted Toroidal Meshes," IEEE Transactions on Computers, vol. 45, no. 6, pp. 766-767, June 1996, doi:10.1109/12.506434
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