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Issue No.06 - June (1996 vol.45)
pp: 766-767
ABSTRACT
<p><b>Abstract</b>—We show that a <it>k</it>×<it>n</it> diagonal mesh is isomorphic to a <tmath>${\textstyle{{n+k} \over 2}}\times {\textstyle{{n+k} \over 2}}-{\textstyle{{n-k} \over 2}}\times {\textstyle{{n-k} \over 2}}$</tmath> twisted toroidal mesh, i.e., a network similar to a standard <tmath>${\textstyle{{n+k} \over 2}}\times {\textstyle{{n+k} \over 2}}$</tmath> toroidal mesh, but with opposite handed twists of <tmath>${\textstyle{{n-k} \over 2}}$</tmath> in the two directions, which results in a loss of <tmath>$\left( {{\textstyle{{n-k} \over 2}}} \right)^2$</tmath> nodes.</p>
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