Analysis and design of an analog sorting network

An analog sorting neural network is presented. First, existing order representations are discussed and a generalized order representation is introduced. The sorting problem is then formulated as the assignment problem. Based on the assignment problem formulation, the neural network architecture is described. Design principles and an op-amp based circuit realization of the analog neural network are delineated. Three illustrative examples are also discussed to demonstrate the capability and performance of the analog neural network. The proposed analog neural network is shown to be capable of monotonic and bitonic sorting and suitable for hardware implementation.

[1]  D. T. LEE,et al.  An On-Chip Compare/Steer Bubble Sorter , 1981, IEEE Transactions on Computers.

[2]  Rhys S. Francis,et al.  A Benchmark Parallel Sort for Shared Memory Multiprocessors , 1988, IEEE Trans. Computers.

[3]  Yoshiyasu Takefuji,et al.  A super-parallel sorting algorithm based on neural networks , 1990 .

[4]  H. Peter Hofstee,et al.  Distributed Sorting , 1990, Sci. Comput. Program..

[5]  Dharma P. Agrawal,et al.  Efficient sorting with CCD's and magnetic bubble memories , 1981, IEEE Transactions on Computers.

[6]  Hiroto Yasuura,et al.  The Parallel Enumeration Sorting Scheme for VLSI , 1982, IEEE Transactions on Computers.

[7]  R. Brockett.  Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems , 1991 .

[8]  Selim G. Akl,et al.  Parallel Sorting Algorithms , 1985 .

[9]  Nicola Santoro,et al.  Distributed Sorting , 1985, IEEE Transactions on Computers.

[10]  Wen-Tsuen Chen,et al.  A Neural Sorting Network with O(1) Time Complexity , 1993, Inf. Process. Lett..

[11]  Yoshiyasu Takefuji.  A two-step parallel sorting algorithm based on neural networks , 1990 .

[12]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[13]  M. Atkins,et al.  Sorting by Hopfield net , 1989, International 1989 Joint Conference on Neural Networks.

[14]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[15]  M. Malek,et al.  A Fault-Tolerant Systolic Sorter , 1988, IEEE Trans. Computers.

[16]  Jun Wang.  Analogue neural network for solving the assignment problem , 1992 .

[17]  Jun Wang.  Analysis and design of a recurrent neural network for linear programming , 1993 .

[18]  Taek Mu Kwon,et al.  A parallel sorting network without comparators: A neural network approach , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[19]  Franco P. Preparata,et al.  A Minimum Area VLSI Network for O(log n) Time Sorting , 1985, IEEE Transactions on Computers.

[20]  Yuen-Hsien Tseng,et al.  Solving sorting and related problems by quadratic perceptrons , 1992 .

[21]  Viktor K. Prasanna,et al.  Optimal VLSI Sorting with Reduced Number of Processors , 1991, IEEE Trans. Computers.