Abstract
The efficient mapping of numerical problems over parallel architectures is a desirable and challenging task. Bi-Swapped Networks (BSN) is a new class of network architecture related to the family of Swapped or Optical Transpose Interconnection System (OTIS) Networks. The architectural advancement of BSN ensures vertex symmetry and thus improves algorithmic efficiency. Further, it ensures regularity, modularity, scalability, robustness of the network. In the present article, parallel implementation of Lagrange’s interpolation over BSN-Mesh is performed. The architectural properties of BSN make it a desirable network for the efficient parallel mapping over it. The parallel algorithm for LaGrange’s interpolation is designed over BSN-Mesh and then analyzed accordingly. The proposed parallel algorithm claims to map LaGrange’s interpolation over BSN-Mesh in 12(n−1) electronic and five optical moves.
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References
H. Sarbazi-Azad, M. Ould-Khaoua, L.M. Mackenzie and S.G. Akl, “A parallel algorithm for Lagrange interpolation on the star graph”, Journal of Parallel and Distributed Computing 62, 605–621 (2002).
H. Sarbazi-Azad, M. Ould-Khaoua, L.M. Mackenzie and G. Min, “An efficient parallel algorithm for Lagrange interpolation and its performance”, In The Fourth International Conference on High Performance Computing in the Asia-Pacific Region, Volume P, May 14–17, Beijing, China (2000).
S.S. Gupta, D. Das and B.P. Sinha, “A fast parallel algorithm for polynomial interpolation using Lagrange formula”, In Proceedings of the International Conference on High Performance Computing, Dec. 27–30, New Delhi, India (1995).
H. Sarbazi-Azad, M. Ould-Khaoua and L.M. Mackenzie, “A parallel algorithm for Lagrange interpolation on k-ary n-cubes”, ACPC Conference, 85–95, (1999).
B. Goertzel, “Lagrange interpolation on a processor tree with ring connections”, J. Parallel Distributed. Comp. 22 (2) (1994) 321–323.
S. Sengupta, D. Das, B.P. Sinha, M. Ghosh, “A Fast parallel algorithm for polynomial interpolation using Lagrange’s formula”, in: Proceedings of the International Conference on High Performance Computing (HiPC), New Delhi (1995), pp. 701–706.
P.K. Jana, B.P. Sinha, “Efficient parallel algorithms for Lagrange and Hermite interpolation”, Int. J. Appl. Sci. Comput. 4 (2) (1998) 118–136.
P.K. Jana, “Finding polynomial zeros on a multi-mesh of trees (MMT)”, in: H. Mohanty, C. Baral (Eds.), Trends in Information Technology, Proceedings of the 2nd International Conference on Information Technology, (CIT’99), Bhubaneswar, India (1999), Tata Mc- Graw-Hill, December 20–22.
Wenjun. Xiao, Weidong. Chen, Mingxin. He, Wenhong. Wei and B. Parhami, “Biswapped Network and Their Topological Properties”, Proceedings-Eighth ACIS International Conference on Software Eng., Artific. Intelligence, Networking, and Parallel/Distributed Computing, 2007, pp. 193–198.
Wenjun Xiaoa, Behrooz Parhamib*, Weidong Chena, Mingxin Hea and WenhongWeia, “Biswapped networks: a family of interconnection architectures with advantages over swapped or OTIS networks”, International Journal of Computer Mathematics, Vol. 88, No. 13, September 2011, Taylor and francis, 2669–2684.
Wenhong Wei, Wenjun Xiao. “Algorithms of Basic Communication Operation on the Biswapped Network”, The 8th International Conference on Computational Science, 2008, 5101: 347–354.
Yulian Yu, Wenhong Wei. “Load balancing on the biswapped network”, Proceedings of the 2nd International Conference on Intelligent Networks and Intelligent Systems, 2009, pp. 146–149.
W. Xiao, B. Parhami, W. Chen, M. He, W. Wei, “Fully Symmetric Swapped Networks Based on Bipartite Cluster Connectivity,” Information Processing Letters, vol. 110, 2010, pp. 211–215.
B. Parhami, “Swapped interconnection networks: Topological, performance, and robustness attributes”, J. Parallel Distrib. Comput. 65 (2005), pp. 1443–1452.
S.G. Akl, The Design, Analysis of Parallel Algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1989, New Delhi, 2000, pp. 202–206.
B. Goertzel, “Lagrange interpolation on a processor tree with ring connections”, Journal of Parallel and Distributed Computing 22, 321–323 (1994).
H. Sarbazi-Azad, M. Ould-Khaoua, L.M. Mackenzie and S.C. Aki, “Parallel Lagrange interpolation on the star graph”, In Proc. IEEE and ACM Int. Parallel Distributed Processing Symposium, (IPDPS’2000), May 1–5, Cancun, Mexico (2000), pp. 777–782.
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The author is indebted to Department of Computer Science and Engineering, BIT Mesra, Ranchi, for facilitating all necessary facilities for the accomplishment of research.
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Ashish Gupta, Sarkar, B.K. (2017). Parallel Algorithm for LaGrange’s Interpolation on BSN-Mesh. In: Singh, R., Choudhury, S. (eds) Proceeding of International Conference on Intelligent Communication, Control and Devices . Advances in Intelligent Systems and Computing, vol 479. Springer, Singapore. https://doi.org/10.1007/978-981-10-1708-7_77
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DOI: https://doi.org/10.1007/978-981-10-1708-7_77
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