The main focus of this paper is the presentation of reliable methods for the determination of the optimum coloring of a graph, commonly known in the literature as vertex coloring problem. It has been shown that networks of capacitively coupled oscillators can be used to solve vertex coloring problems. In this paper we address the negative impact of an unbalanced number of couplings for the oscillators on the performance of the network and compensate for this non-uniform coupling structure by an adjustment in the network itself. The negative effect of the memristor device-to-device variability of the $\text {NbO}_{\text {x}}$ memristor on the array functionality will be investigated and reduced via an adaptation of the memristor operating point. The main improvement in network performance is achieved by setting up a control procedure allowing the network to bypass the local solutions and converge to the global one. Two strategies inspired by global optimization algorithms will be proposed to allow the network to overcome sub-optimal solutions, and find the solution corresponding to the absolute minimum of a performance measure function of the vertex coloring problem.

中文翻译：

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使用NbO改进了顶点着色ₓ 基于忆阻器的振荡网络

本文的主要重点是介绍确定图的最佳着色的可靠方法，在文献中通常将其称为顶点着色问题。已经表明，电容耦合振荡器的网络可以用来解决顶点着色问题。在本文中，我们解决了振荡器耦合数量不平衡对网络性能的负面影响，并通过网络本身的调整来补偿这种不均匀的耦合结构。忆阻器器件之间的可变性对器件的负面影响 $ \ text {NbO} _ {\ text {x}} $ 将通过调整忆阻器工作点来研究和减少阵列忆阻器的功能。网络性能的主要改善是通过建立控制程序来实现的，该控制程序允许网络绕过本地解决方案并收敛到全局解决方案。将提出两种受全局优化算法启发的策略，以允许网络克服次优解，并找到与顶点着色问题的性能度量函数的绝对最小值相对应的解。