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Interconnection networks of degree three obtained by pruning two-dimensional tori

Stewart, I.A.

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Abstract

We study an interconnection network that we call 3Torus(m,n) obtained by pruning the 4m x 4n torus (of links) so that the resulting network is regular of degree 3. We show that 3Torus(m,n) 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 3Torus(m,n) is node-symmetric; we establish closed-form expressions on the 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 3Torus(m,n) 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 3Torus(m,n) compares very favourably with tori.

Citation

Stewart, I. (2014). Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Transactions on Computers, 63(10), 2473-9340. https://doi.org/10.1109/tc.2013.139

Journal Article Type Article
Acceptance Date Jun 22, 2013
Online Publication Date Jul 1, 2013
Publication Date Oct 1, 2014
Deposit Date Jun 27, 2013
Publicly Available Date Mar 28, 2024
Journal IEEE Transactions on Computers
Print ISSN 0018-9340
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 63
Issue 10
Pages 2473-9340
DOI https://doi.org/10.1109/tc.2013.139
Keywords Interconnection network, Torus, Degree 3, Shortest paths, Routing, Broadcasting.
Publisher URL http://doi.ieeecomputersociety.org/10.1109/TC.2013.139

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