Abstract
In this paper, we propose a saturation binary neuron model and use it to construct a Hopfield-type neural network called saturation binary neural network to solve the bipartite sub-graph problem. A large number of instances have been simulated to verify the proposed algorithm, with the simulation result showing that our algorithm finds the solution quality is superior to the compared algorithms.
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References
Garey, M.R., Johnson, D.S., Stockmeyer, L.J.: Some simplified NP-complete graph problem. Theor. Comput. Sci., 237–267 (1976)
Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85–104. Plenum, New York (1972)
Even, S., Shiloach, Y.: NP-completeness of several arrangement problems. Technical Report 43, Department of computer Science, Technion, Haifa Israel (1975)
Bondy, J.A., Locke, S.C.: Largest bipartite subgraph in triangle-free graphs with maximum degree three. J. Graph Theory, 477–504 (1986)
Grotscheland, M., Pulleyblank, W.R.: Weakly bipartite graphs and the max-cut problem. Oper. Res. Lett., 23–27 (1981)
Barahona, F.: On some weakly bipartite graph. Oper. Res. Lett. 2(5), 239–242 (1983)
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. U.S. 79, 2554–2558 (1982)
Hopfield, J.J.: Neurons with graded response have collective computation properties like those of two-state neurons. Proc. Nat. Acad. Sci. U.S. 81, 3088–3092 (1982)
Hopfield, J.J., Tank, D.W.: ’Neural’ computation of decisions in optimization problems. Bio. Cybern. 52, 141–152 (1985)
Hopfield, J.J., Tank, D.W.: Simple ’Neural’ optimization networks: An a/d converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circuits Syst. 33(5), 533–541 (1986)
Hopfield, J.J., Tank, D.W.: Computing with neural circuits: A model. Science 233, 625–633 (1986)
Lee, K.C., Funabiki, N., Takefuji, Y.: A parallel improvement algorithm for the bipartite subgraph problem. IEEE Trans. Neural Networks 3(1), 139–145 (1992)
Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Ackley, D.H., Hinton, G.E., Sejnowski, T.J.: A learning algorithm for Boltzman Machines. Cognitive Science 9, 147–169 (1985)
McCulloch, W.S., Pitts, W.H.: A logical calculus of ideas immanent in nervous activity. Bull. Math. Biophys 5, 115–133 (1943)
Takefuji, Y., Lee, K.C.: An artificial hysteresis binary neuron: A model suppressing the oscillatory behaviors of neural dynamics. Biol. Cybern. 64, 353–356 (1991)
Wang, R.L., Tang, Z., Cao, Q.P.: A Hopfield Network Learning Method for Bipartite Subgraph Problem. IEEE Trans. Neural Networks 15(6), 1458–1465 (2004)
Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing: An experimental evaluation; Part 1, graph partitioning. Operations Research 37(6), 865–892 (1989)
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Zhang, C., Zhao, LQ., Wang, RL. (2012). A Saturation Binary Neural Network for Bipartite Subgraph Problem. In: Huang, DS., Gan, Y., Premaratne, P., Han, K. (eds) Bio-Inspired Computing and Applications. ICIC 2011. Lecture Notes in Computer Science(), vol 6840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24553-4_10
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DOI: https://doi.org/10.1007/978-3-642-24553-4_10
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