Abstract

This paper discuss about embedding on the new interconnection network named Torus-Butterfly. Torus-Butterfly is the Cartesian product network that has constant degree and has smaller network cost than the other Cartesian product network. Torus-Butterfly network is a Cayley graph. From the properties of Cayley graphs which have Hamiltonian path, the linear array and 2D-Mesh can be embedded into this new Torus-Butterfly network with minimum dilation and expansion.

References

• Shi, Wei and Srimani, Pradip K, 1998. Hyper-Butterfly Network: A scalable Optimally Fault Tolerant Architecture, University of Colorado.
• Kini, N. Gopalakrishna, Kumar, M. Sathish, HS. Mruthyunja, 2010. Torus Embedded Hypercube Interconnection Network: A comparative Study, Journal on Computer Science and Engineering Vol 1(4), pp. 29-31.
• Alam, Jahangir, Kumar Rajesh, 2011. STH:A Highly Scalable and Economical Topology for Massively Parallel Systems, Indian Journal of Scince Technology, Vol. 4 No. 12 pp 1737-1748.
• Bermont, J-C, Darrot, O, Delmas and Prennes, S, 1995, Hamilton Cycle Decomposition of The Butterfly Network, Parallel Processing Letter, World Scientific Publishing Company pp 3-14.
• Liaw, sheng, chyang dan Chang, Gerard J. , Wide Diameters of Butterfly Networks, Taiwanese Journal of Mathematics, Vol 3, No. 1,pp. 83-88, March, 1999.
• Kothapalli, Kishore, 2008, Parallel Algorithms and Programming, cstar. iiit. ac. in/kkishore/cs5118/week2. pdf, pp3-6
• Hou, Xinmin, Xu, Jun-Ming and Xu, Min, 2009. The forwarding Indices of Wrapped Butterfly Networks, Networks,DOI 10. 1002/net.
• Guzide, Osman dan Wagh, Meghanad D, 2006. Mapping cycles and Trees on Wrap Around Butterfly Graphs, SIAM Journal Computation, vol. 35, No. 3, pp 741-765.
• Guzide, Osman dan Wagh Meghanad D, 2007. Enhanced Butterfly : A Cayley Graph with Node 5 Network, ISCA International Conference on Parallel and Distributed system, view as html www. informatik. unitrier. de/~ley/db/. . . /ISCApdcs2007. html.
• Xiang, yonghong, 2008. Interconnection Networks for Parallel and Distributed Computing, Department of Computer Sciences, University of Durham, United Kingdom.
• Mowshowitz, Abbe, Mitsuo, Valia and Benz, Graham, 2009, Topologist of Network Growth by Combination, City College.
• Day, Khaled, Al-Ayyoub, Abdel-Elah, 1997, The Cross Product Interconnection Networks, IEEE Transaction on Parallel and Distributed Systems, Vol. 8 No. 2, pp 109-118
• Latifah, Ernastuti, Kerami, Djati, 2012, Structural Properties of Torus-Butterfly Interconnection Network, IJCA, May Edition, Vol 46(16), pp 31-35
• Zhang, Zhen, 2011, Some Properties in Hexagonal Torus as Cayley Graph, ICICIS, Part II, pp. 422-428
• Ernastuti, 2008, The New Interconnection Network Topology: Extended Lucas Cube Topology, Dissertation, Gunadarma University
• Mooris, Dave, 2006, Open Problems on Hamiltonian Cycles in Cayley graphs, www. people. uleth. Ca/mdavemorris
• Seo, Jung-Hyun, Sim, Hyun, Park, Dae Hon, Park, Jang-Woo and Lee, Yang Sun, 2011, One-to-one Embedding between Honeycomb Mesh and Peterson-Torus Networks, Journal On coomunication Network, Vol. 2011 pp 1959-1971
• Wu, J. , 1997, Extended Fibonacci Cubes, IEEE Trans. On Parallel and Distributed Systems, Vol. 8 (12), pp. 1203-1210