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

Construction of Hamiltonian cycles in a graph of distributed computer system with $n$ vertices by a recurrent neural network is considered. The method of partial sums is proposed to reduce time of differential equations solution, which describe the neural network, from $O(n^3)$ to $O(n^2)$. It is shown that the neural network algorithm which uses partial sums is competitive with known permutation methods.