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Advances in Computer Science and Engineering

Advances in Computer Science and Engineering
Volume 2, Issue 1, Pages 1 - 14 (March 2008)

AN IMPROVED DYNAMICS IN HOPFIELD NEURAL NETWORK FOR FINDING A NEAR-MAXIMUM INDEPENDENT SET OF A CIRCLE GRAPH Rong-Long Wang (Japan), Shan-Shan Guo (Japan) and Kozo Okazaki (Japan) Received December 16, 2007 References:
[1] D. H. Ackley, G. E. Hinton and T. J. Sejnowski, A learning algorithm for Boltzman machines, Cognitive Science 9 (1985), 147-169. [2] J. E. Burns, The maximum independent set problem for cubic planar graph, Networks 19 (1989), 373-378. [3] E. Choukhmane and J. Franco, An approximation algorithm for the maximum independent set problem in cubic planar graphs, Networks 16 (1986), 349-356. [4] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Free-man, San Francisco, CA, 1979. [5] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, New York, 1979. [6] F. Gavril, Algorithms on circular-arc graphs, Networks 4 (1974), 357-369. [7] M. Goldberg and T. Spencer, A new parallel algorithm for the maximal independent set problem, SIAM J. Comput. 18(2) (1989), 419-427. [8] J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. U.S. 79 (1982), 2554-2558. [9] J. J. Hopfield, Neurons with graded response have collective computation properties like those of two-state neurons, Proc. Nat. Acad. Sci. U.S. 81 (1982), 3088-3092. [10] J. J. Hopfield and D. W. Tank, Neural computation of decisions in optimization problems, Bio. Cybern. 52 (1985), 141-152. [11] J. J. Hopfield and D. W. Tank, Simple neural optimization networks: An a/d converter, signal decision circuit, and a linear programming circuit, IEEE Trans. Circuits Syst. 33(5) (1986), 533-541. [12] J. J. Hopfield and D. W. Tank, Computing with neural circuits: a model, Science 233 (1986), 625-633. [13] W. L. Hsu, The coloring and maximum independent set problems on planar perfect graphs, J. ACM 35(3) (1988), 535-563. [14] R. M. Karp, Complexity of Computers, R. E. Miller and J. W. Thatcher, eds., Plenum, New York, 1972. [15] R. M. Karp and A. Wigderson, A fast parallel algorithm for the maximum independent set problem, J. ACM 32(4) (1985), 762-773. [16] M. Luby, A simple parallel algorithm for the maximal independent set problem, SIAM J. Comput. 15(4) (1986), 1036-1053. [17] S. Masuda and K. Nakajima, The maximum independent set of a circular-arc graph, SIAM J. Comput. 17(1) (1988), 41-52. [18] K. J. Supowit, Finding a maximum planar subset of a set of nets in a channel, IEEE Trans. Circuits Devices 6 (1987), 78-88. [19] Yoshiyasu Takefuji, Li-Lin Chen, Kuo-Chun Lee and John Huffman, Parallel algorithms for finding a near-maximum independent set of a circle graph, IEEE Trans. Neural Networks 1(3) (1990), 263-267.

Keywords and phrases: Hopfield neural network, local minimum, maximum independent set, circle graph.

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