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• W2038391896 abstract "We study an interconnection network that we call <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$3Torus(m,n)$</tex> </formula> obtained by pruning the <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$4m times 4n$</tex> </formula> torus (of links) so that the resulting network is regular of degree 3. We show that <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$3Torus(m,n)$</tex> </formula> retains many of the useful properties of tori (although, of course, there is a price to be paid due to the reduction in links). In particular, we show that <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$3Torus(m,n)$</tex> </formula> is node-symmetric; we establish closed-form expressions on the length of a shortest path joining any two nodes of the network; we calculate the diameter precisely; we obtain an upper bound on the average inter-node distance; we develop an optimal distributed routing algorithm; we prove that <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$3Torus(m,n)$</tex> </formula> has connectivity 3 and is Hamiltonian; we obtain a precise expression for (an upper bound on) the wide-diameter; and we derive optimal one-to-all broadcast and personalized one-to-all broadcast algorithms under both a one-port and all-port communication model. We also undertake a preliminary performance evaluation of our routing algorithm. In summary, we find that <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$3Torus(m,n)$</tex> </formula> compares very favourably with tori." @default.
• W2038391896 created "2016-06-24" @default.
• W2038391896 creator A5061350983 @default.
• W2038391896 date "2014-10-01" @default.
• W2038391896 modified "2023-09-26" @default.
• W2038391896 title "Interconnection Networks of Degree Three Obtained by Pruning Two-Dimensional Tori" @default.
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• W2038391896 doi "https://doi.org/10.1109/tc.2013.139" @default.
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