Construction of Hamiltonian cycles by recurrent neural networks in graphs of distributed computer systems

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 suboptimal cycles with a length close to that of Hamiltonian ones are determined. Our experiments show that the iterative 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 on the number of torus nodes.