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Issue No.02 - February (1991 vol.40)
pp: 196-204
ABSTRACT
<p>Mesh-connected computers with multiple buses providing broadcast facilities along rows and columns are discussed. A tight bound of Theta (n/sup 1/8/) is established for the number of rounds required for semigroup computations on n values distributed on a two-dimensional rectangular mesh of size n with a bus on every row and column. The upper bound is obtained for a skewed rectangular mesh of dimensions n/sup 3/8/*n/sup 5/8/. This result is compared to the tight bound of Theta (n/sup 1/6/) for the same problem on the square (n/sup 1/2/*n/sup 1/2/) mesh. It is shown that in the presence of multiple buses, a skewed configuration may perform better than a square configuration for certain computational tasks. The result can be extended to the d-dimensional mesh, giving a lower bound of Omega (n/sup 1/d alpha /) and an upper bound of O(d2/sup d+1/ n/sup 1/d alpha /), where alpha =2/sup d/; these bounds are optimal within constant factors for any constant d. It is noted that for d<3, the results of are mostly of theoretical interest.</p>
INDEX TERMS
mesh connected computers; multiple buses; broadcast facilities; rows; columns; tight bound; semigroup computations; two-dimensional rectangular mesh; upper bound; skewed rectangular mesh; parallel architectures.
CITATION
"Square Meshes are Not Always Optimal", IEEE Transactions on Computers, vol.40, no. 2, pp. 196-204, February 1991, doi:10.1109/12.73589
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