Abstract
In this paper a new neural network model that generalizes Hopfleld model is proposed. It allows to implement an algorithm similar to the Dijkstra’s one in order to solve the shortest path problem on a weighted graph. With this neural and parallel implementation, the presented model is adapted to possible modifications in the graph. Moreover, it is possible to solve other related problems with the same structure.
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References
Ali M.K.M. and Kamoun F. Neural Networks for shortest path computation and routing in computer networks. IEEE Trans. N.N. 4, 941–54, (1993).
Brodal, G. S., Träff, J. L. & Zaroliagis, C. D. A parallel priority data structure with applications. Proc. 11th Int. Par. Processing Symp., 689–93, (1997).
Cavalieri S., Di Stefano A. and Mirabella O., Optimal Path Determination in a Graph by Hopfield Neural Network. Neural Networks 7-2, 397–404, (1994).
Dijkstra, E. W. A note on two problems in connection with graphs. Numerische Mathematik, 1, 269–71, (1959).
Grimaldi, Ralph. Matemática Discreta y Combinatoria. Cap 13.1, (1999).
Mateti, P. & Deo N., Parallel Alg. for Single Source SPP. Computing 29, 31–49, (1982).
Mérida Casermeiro, E. Red Neuronal Recurrente Multivaluada para el rec. patrones y la optimiz. comb. Ph.D. dissertation. University of Málaga, Spain, (in Spanish), 2000.
Mérida Casermeiro, E., Galán Marín, G. & Muñoz Pérez, J. An efficient multiv. Hopfield N. for the T.S.P. Neural Procc. Letters. 14, 203–16, (2001).
Mérida Casermeiro, E., Muñoz Pérez, J. and Benítez Rochel, R. A recurrent multivalued N.N. for N-Queens Problem. LNCS 2084, 522–29, (2001).
Mohr T. and Pasche C, A Parallel Shortest Path Alg., Computing 40 767–86, (1988).
Paige, R. and Kruskal, C. Parallel algorithms for shortest paths problems. Proceedings International Conf. on Parallel Processing, 14–19, (1989).
Park D-C. and Choi S-E. A N.N. based multi-destination routing algorithm for communication network. IEEE Int. Joint Conf. N.N. 2, 1673–78, (1998).
Rauch H.E. and Winarske T. Neural Networks for routing communication traffic. IEEE Cont. Syst. Mag, 26–30, (1988).
Serpen, Gursen and Parvin, Azadeh. On the performance of Hopfield network for graph search problem. Neurocomputing 14, 365–81, (1997).
Zhang L. and Thomopoulos S. C. A., N.N. implem. of the shortest path alg. for traffic routing in comm. networks. Proc. Int. Conf. N.N. II, 591, (1989).
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Mérida-Casermeiro, E., Muñoz-Pérez, J., Benítez-Rochel, R. (2003). Neural Implementation of Dijkstra’s Algorithm.. In: Mira, J., Álvarez, J.R. (eds) Computational Methods in Neural Modeling. IWANN 2003. Lecture Notes in Computer Science, vol 2686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44868-3_44
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DOI: https://doi.org/10.1007/3-540-44868-3_44
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