Honeycomb rectangular disks

Teng, Yuan-Hsiang; Tan, Jinglu; Hsu, Lih-Hsing

doi:10.1016/j.parco.2004.12.002

Cited by 2 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algebraic approach of Parhami, Kwai and Xiao was subsequently continued: in [35] where Rahman, Jiang, Masud and Horiguchi applied pruning techniques to the hierarchical torus network and studied properties relating to shortest paths, average inter-node distance, bisection width and VLSI layout area; and in [9] where an algebraic construction related to group semidirect products was developed and used to provide a generalization of earlier pruning schemes. Beyond the concerted research effort described above, there have also been various more isolated considerations of interconnection networks of degree 3, e.g., [6], [13], [25], [37], [44].…”

Section: Related Workmentioning

confidence: 99%

Interconnection Networks of Degree Three Obtained by Pruning Two-Dimensional Tori

Stewart

2014

IEEE Trans. Comput.

View full text Add to dashboard Cite

Publisher's copyright statement: c 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. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract-We study an interconnection network that we call 3T orus(m, n) obtained by pruning the 4m × 4n torus (of links) so that the resulting network is regular of degree 3. We show that 3T orus(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 3T orus(m, n) is node-symmetric; we establish closedform 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 internode distance; we develop an optimal distributed routing algorithm; we prove that 3T orus(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-toall 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 3T orus(m, n) compares very favourably with tori.

show abstract

Section: Related Workmentioning

confidence: 99%

Interconnection Networks of Degree Three Obtained by Pruning Two-Dimensional Tori

Stewart

2014

IEEE Trans. Comput.

View full text Add to dashboard Cite

show abstract

“…Hence HReTðm; 4Þ is not hyper globally bi-3 * -connected. Many investigations related to this family of the networks have been proposed in the literature [2,[10][11][12]. In particular, the honeycomb rectangular torus HReTðm; nÞ is a well-structured 3-connected cubic network.…”

Section: The Globally Bi-3 * -Connected Properties Of Hret(2n)mentioning

confidence: 99%

“…A graph G is hamiltonian if there exists a hamiltonian cycle in G. The hamiltonian properties are important aspects of designing an interconnection network. Many related works have appeared in the literature [3,6,8,12,13].…”

Section: Introductionmentioning

confidence: 99%