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The Journal of Supercomputing

, Volume 69, Issue 1, pp 121–138 | Cite as

Some properties and algorithms for the hyper-torus network

  • Jong-Seok Kim
  • Sung Won Kim
  • Ke Qiu
  • Hyeong-Ok LeeEmail author
Article

Abstract

The hyper-torus network based on a three-dimensional hypercube was introduced recently. The hyper-torus \(QT(m,n)\) performs better than mesh type networks with a similar number of nodes in terms of the network cost. In this paper, we prove that if \(n\) is even, the bisection width of \(QT(m,n)\) is \(6n\), whereas it is \(6n+2\) if it is odd. Second, we show that \(QT(m,n)\) contains a Hamiltonian cycle. In addition, its one-to-all and all-to-all broadcasting algorithms are introduced. All of these broadcasting algorithms are asymptotically optimal.

Keywords

Interconnection network Hyper-torus Bisection width  Hamiltonian cycle Broadcasting 

Notes

Acknowledgments

We thank the reviewers for their comments and suggestions which have substantially improved our presentation. This research was supported by Basic Science research program through the National research Foundation of KOREA (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A4A01014439).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jong-Seok Kim
    • 1
  • Sung Won Kim
    • 2
  • Ke Qiu
    • 3
  • Hyeong-Ok Lee
    • 4
    Email author
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA
  2. 2.Department of Information and Communication EngineeringYeungnam UniversityGyeongsanSouth Korea
  3. 3.Department of Computer scienceBrock UniversitySaint CatharinesCanada
  4. 4.Department of Computer EducationSunchon National University SunchonSouth Korea

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