Abstract
A unified vector sorting algorithm (VSA) is proposed, which sortsN arbitrary numbers with clog2 N-bits on an SIMD multi-processor system (SMMP) with\(p = \frac{{N^{1 + \varepsilon } }}{u}\) processors and a composite interconnected network in\(T = \frac{c}{\varepsilon }\left( {4\log _2 N - 2\log _2 u + 10u} \right)\) time, wherec is an arbitrary positive constant. When ε is an arbitrary small positive constant andu=log2 N, it is anO(logN) algorithm and\(p = \frac{{N^{1 + \varepsilon } }}{{log_2 N}}\); when\(\varepsilon = \frac{1}{{log N}}\) andu=2log2 N, it is an optimal algorithm (\(p = \frac{N}{{log_2 N}}\),T =O(log2 N),pT =O(N logN)); whereu=1,c=1 and ε=0.5 (a constant).
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References
Batcher K E. Sorting networks and their applications. In 1968Spring Joint Comput. Conf. AFIPS Proc., Vol.32, Washington, D.C., 1968, pp.307–314.
Muller D E, Preparata F P. Bounds to complexities of networks for sorting and for switching.JACM, 1975, 22(2): 195–201.
Valiant L G. Parallelism in comparison problems.SIAM J. Computer, 1975, 4(3): 355–384.
Thompson C D, Kung H T. Sorting on a mesh-connected parallel computer.CACM, 1977, 20(4): 263–271.
Preparata F P. New parallel-sorting schemes.IEEE Trans. on Computers, 1978, C-27(7): 669–673.
Hirschberg D S. Fast parallel sorting algorithms.CACM, 1978, 21(8): 657–661.
Ajtai M, Komlos J, Szemeredi E. AnO (n logn) sorting network. InProc. of 15th ACM Symp. Theory of Computing, 1983, pp.1–9.
Leighton T. Tight Bounds on the complexity of parallel soring.IEEE Trans. Computers, 1985, C-34(4): 344–354.
Bilardi G, Preparata F P. A minimum area VLSI network forO(logn) time sorting.IEEE Trans. Computers, 1985, C-34(4): 336–343.
Reif J H, Valiant L G. A logarithmic time sort for linear size networks.JACM, 1987, 34(1): 60–76.
Alnuweiri H M, Prasanna Kumar V K. Optimal VLSI sorting with reduced number of processors.IEEE Trans. Computers, 1991, C-40(1): 105–110.
Guan Xiaojun, Langston M A. Time-space optimal parallel merging and sorting.IEEE Trans. on Computers, 1991, C-40(5): 596–602.
Wang B F, Chen G H, Lin F C. Constant time soring on a processor array with a reconfigurable bus system.IPL, 1990, 34: 187–192.
Vaidyanathan R. Sorting on PRAMs with reconfigurable buses.IPL, 1992, 42: 203–208.
Knuth D E. The Art of Computer Programming, Vol. 3, Sorting and Searching. Addison-Wesley Publishing Company, 1973.
Kogge P M, Stone H S. A parallel algorithm for efficient solution of a general class of recurrrence equations.IEEE Trans. Computers, 1973, C-22(8): 789–792.
Feng T Y. Data manipulating functions in parallel processors and their implementation.IEEE Trans. Computers, C-23(3): 309–318.
Leighton T. Introduction to Parallel Algorithms and Architectures. Morgan Kaufmann Publishers, Inc., 1992, pp.439–446.
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Gao Qingshi received his B.S. degree in mathematics from Peking University in 1957. Then he joined the Institute of Computing Technology, The Chinese Academy of Sciences (CAS). In 1979, he had the Professor approintment, and in 1980 he became a Academician of CAS. Now he is the Director of Institute of Intelligence, Language and Computer Science, Beijing University of Science and Technology. His main research interests include parallel algorithm and parallel computer architecture, natural languages and machine translation, discovery and problem solving, human intelligence, and its simulation and application.
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Gao, Q. A unifiedO(logN) and optimal sorting vector algorithm. J. of Comput. Sci. & Technol. 10, 470–475 (1995). https://doi.org/10.1007/BF02948343
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DOI: https://doi.org/10.1007/BF02948343