Control Strategies to Optimize Graph Coloring via M-CNNs with Locally-Active NbOx Memristors

This work proposes reliable methods for solving issues while solving the vertex coloring optimisation problem. It has been shown that networks of capacitively-coupled memristor oscillators can be used for computing the solution to this problem. In this paper we first investigate the negative impact of an unbalanced number of connections per cell on the performance of the network and compensate for the non-uniform coupling structure by readjusting the capacitive loads of the oscillators. The undesired effect, which device-to-device variability, affecting the NbOx threshold switch, employed in each cell, has on the functionality of the proposed array, is then studied, and its strength is reduced through an adaptation of the memristors' operating points. One of the most crucial issues, affecting the memristor computing engine, appears when the solution of the optimisation problem attains a local minimum, keeping therein subsequently. In the last part of this manuscript we propose two control strategies, which allow the array to bypass impasse scenarios of this kind, facilitating the convergence of the solution toward the global minimum of the optimisation problem.