On the efficient construction of hamiltonian cycles in distributed computer systems by recurrent neural networks

The construction of Hamiltonian cycles in the graph of distributed computer system with n vertices by a recurrent neural network is described. A method of partial sums is proposed to reduce from O(n
³
) to O(n
²
) the time for solving differential equations which describe the neural network. It is shown that the neural network algorithm, using the partial sums, is not inferior than known permutation methods by the time of the cycle building.