In this paper, we explore the relationship between Minimum Feedbackability Set (MFS) and Feedbackability Set (FS) of complex networks and use simulated annealing algorithm to obtain a relatively fast and reliable estimation of the MFS. Then, we implement this method to estimate the MFS of some real-world networks and explore whether the topological features influence the size of MFS. Additionally, we propose an optimal perturbation strategy to enhance the feedbackability of complex networks. Finally, we also research the intricate relationship between the structural properties and the feedbackability of various networks perturbed by optimal and random perturbation strategies.

中文翻译：

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估计和增强复杂网络的反馈能力

在本文中，我们探讨了复杂网络的最小反馈能力集（MFS）和反馈能力集（FS）之间的关系，并使用模拟退火算法获得了相对快速和可靠的MFS估计。然后，我们实现了这种方法来估计一些现实世界网络的 MFS，并探索拓扑特征是否影响 MFS 的大小。此外，我们提出了一种最佳扰动策略来增强复杂网络的可反馈性。最后，我们还研究了受最优和随机扰动策略扰动的各种网络的结构特性与可反馈性之间的复杂关系。