Abstract:
An algorithm based on a recurrent neural Wang's network and the WTA (“Winner takes all”) principle is applied to the construction of Hamiltonian cycles in graphs of distributed computer systems (CSs). The algorithm is used for: 1) regular graphs (2D- and 3D-tori, and hypercubes) of distributed CSs and 2) 2D-tori disturbed by removing an arbitrary edge. The neural network parameters for the construction of Hamiltonian cycles and sub-optimal cycles with a length close to that of Hamiltonian ones are determined. Our experiments show that the iteration method (Jacobi, Gauss-Seidel, or SOR) used for solving the system of differential equations describing a neural network strongly affects the process of cycle construction and depends upon the number of torus nodes.
M. S. Tarkov, “Ob effektivnosti postroeniya gamiltonovykh tsiklov v grafakh raspredelennykh vychislitelnykh sistem rekurrentnymi neironnymi setyami”, UBS, 43 (2013), 157–171
Tarkov M.S., “On the Efficient Construction of Hamiltonian Cycles in Distributed Computer Systems by Recurrent Neural Networks”, 2013 International Siberian Conference on Control and Communications (Sibcon), ed. Stukach O., IEEE, 2013
M. S. Tarkov, “Mapping parallel programs onto multicore computer systems by Hopfield networks”, Opt. Mem. Neural Networks, 22:3 (2013), 148
Mikhail S. Tarkov, 2013 International Siberian Conference on Control and Communications (SIBCON), 2013, 1
Tarkov M.S., “On Mapping Graphs of Parallel Programs Onto Graphs of Distributed Computer Systems by Recurrent Neural Networks”, Parallel Computing Technologies, Lecture Notes in Computer Science, 6873, ed. Malyshkin V., Springer-Verlag Berlin, 2011, 358–367
M. S. Tarkov, A. V. Rzhanov's, “Mapping graphs Of parallel programs onto graphs of distributed computer systems by recurrent neural networks”, Opt. Mem. Neural Networks, 20:2 (2011), 107
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