Skip to main content

Research Repository

Advanced Search

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

Stewart, I.A.

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



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.


Stewart, I. (2014). Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Transactions on Computers, 63(10), 2473-9340.

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 Jan 28, 2014
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
Keywords Interconnection network, Torus, Degree 3, Shortest paths, Routing, Broadcasting.
Publisher URL


Accepted Journal Article (407 Kb)

Copyright Statement
© 2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

You might also like

Downloadable Citations