Some properties and algorithms for the hyper-torus network
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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.
KeywordsInterconnection network Hyper-torus Bisection width Hamiltonian cycle Broadcasting
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).
- 1.Seo JH, Lee HO, Jang MS (2008) Petersen-torus networks for multicomputer systems. In: Proceedings of the 4th international conference on networked computing and advanced, information management, pp 567–571Google Scholar
- 6.Vaidya AS, Rao PS, Shankar SR (1993) A class of hypercube-like networks, Proceedings of the 5th IEEE symposium on parallel and distributed processing, Dallas, Dec, pp 800–803Google Scholar
- 7.Yeh CH, Varvarigos EA, Parhami B (1999) Efficient VLSI layouts of hypercubic networks. In: Proceedings of the 7th symposium on the frontiers of massively parallel computation, Feb., pp 98–105Google Scholar
- 8.Ki WS, Lee HO, Oh JC (2009) The new torus network design based on 3-dimensional hypercube. In: Proceedings of the 11th international conference on advanced communication technology, pp 615–620Google Scholar
- 10.Hsu Lh, Lin CK (2008) Graph theory and interconnection networks. CRC Press, Boca RatonGoogle Scholar
- 12.Garey MR, Johnson DS (1979) Computers and intractability, a guide to the theory of NP-completeness, Freeman, San FranciscoGoogle Scholar
- 21.Ho CT, Johnsson L (1986) Distributed routing algorithms for broadcasting and personalized communication in hypercubes. In: Proceedings of international conference on Parallel Processing, pp 640–648Google Scholar
- 23.Stewart IA (2014) Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Trans Comput (to appear)Google Scholar