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A Parallel Algorithm for Computing Fourier Transforms on the Star Graph
May 1994 (vol. 5 no. 5)
pp. 525-531

The n-star graph, denoted by S/sub n/, is one of the graph networks that have beenrecently proposed as attractive alternatives to the n-cube topology for interconnectingprocessors in parallel computers. We present a parallel algorithm for the computation ofthe Fourier transform on the star graph. The algorithm requires O(n/sup 2/) multiply-addsteps for an input sequence of n! elements, and is hence cost-optimal with respect tothe sequential algorithm on which it is based. This is believed to be the first algorithm,and the only one to date, for the computation of the Fourier transform on the star graph.

[1] S. B. Akers, D. Harel, and B. Krishnamurthy, "The star graph: An attractive alternative to then-cube,"Proc. Int. Conf. Parallel Process., 1987, pp. 393-400.
[2] S. B. Akers and B. Krishnamurthy, "A group-theoretic model for symmetric interconnection networks,"IEEE Trans. Comput., vol. 38, pp. 555-566, 1989.
[3] Selim G. Akl,The Design and Analysis of Parallel Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[4] S. G. Akl, J. Duprat, and A. G. Ferreira, "Building Hamiltonian circuits and paths in star graphs," Tech. Rep. 90-22, Laboratoire de l'Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, France, Mar. 1990.
[5] W. T Cochran et al., "'What is the fast Fourier transform?,"IEEE Trans. Audio Electroacoust., vol. AU-15, pp. 45-55, June 1967.
[6] J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series,"Math. Comput., vol. 19, pp. 297-301, 1965.
[7] P. Fragopoulou, "Parallel algorithms for the Fourier and other mathematical transforms," M.Sc. thesis, Dept. of Computing and Inform. Sci., Queen's University, Kingston, ON, Canada, Aug. 1990.
[8] A. Menn and A. K. Somani, "An efficient sorting algorithm for the star graph interconnection network,"Proc. Int. Conf. Parallel Process., vol. III, 1990, pp. 1-8.
[9] M. Nigam, S. Sahni, and B. Krishnamurthy, "Embedding Hamiltonians and hypercubes in star interconnection graphs,"Proc. Int. Conf. Parallel Process., vol. III, 1990, pp. 340-343.
[10] D. S. Parker, "Notes on shuffle/exchange-type switching networks,"IEEE Trans. Comput., vol. C-29, pp. 213-223, 1980.
[11] M. C. Pease, "The indirect binaryn-cube microprocessor array,"IEEE Trans. Comput., vol. C-26, pp. 458-473, 1977.
[12] F. P. Preparata and J. Vuillemin, "The cube-connected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300-309, May 1981.
[13] K. Qiu, H. Meijer, and S. Akl, "Decomposing a star graph into disjoint cycles,"Inform. Processing Lett., no. 39, pp. 125-129, 1991.
[14] H. S. Stone, "Parallel processing with the perfect shuffle,"IEEE Trans. Comput., vol. C-20, pp. 153-161, 1971.
[15] C. D. Thompson, "Fourier transforms in VLSI,"IEEE Trans. Comput., vol. C-32, pp. 1047-1057, 1983.
[16] E. H. Wold and A. Despain, "Pipeline and parallel-pipeline FFT processors for VLSI implementations,"IEEE Trans. Comput., vol. C-33, pp. 414-426, 1984.
[17] C. N. Zhang, "Multidimensional systolic networks for discrete Fourier transform," inProc. 11th Annu. Int. Symp. Comput. Architecture, Ann Arbor, MI, 1984, pp. 21-27.

Index Terms:
Index TermsFourier transforms; multiprocessor interconnection networks; graph theory; parallelalgorithms; computational complexity; parallel algorithm; Fourier transforms; star graph;interconnecting processors; parallel computers
P. Fragopoulou, S.G. Akl, "A Parallel Algorithm for Computing Fourier Transforms on the Star Graph," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 5, pp. 525-531, May 1994, doi:10.1109/71.282562
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