Complex network infrastructure systems for power supply, communication, and transportation support our economic and social activities; however, they are extremely vulnerable to frequently increasing large disasters or attacks. Thus, the reconstruction of a damaged network is more advisable than an empirically performed recovery of the original vulnerable one. To reconstruct a sustainable network, we focus on enhancing loops so that they are not trees, which is made possible by node removal. Although this optimization corresponds with an intractable combinatorial problem, we propose self-healing methods based on enhancing loops when applying an approximate calculation inspired by statistical physics. We show that both higher robustness and efficiency are obtained in our proposed methods by saving the resources of links and ports when compared to ones in conventional healing methods. Moreover, the reconstructed network can become more tolerant than the original when some damaged links are reusable or compensated for as an investment of resource. These results present the potential of network reconstruction using self-healing with adaptive capacity in terms of resilience.

中文翻译：

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更宽容的重构网络使用自我修复来对抗节省资源的攻击

电力、通信、交通等复杂的网络基础设施系统支撑着我们的经济和社会活动；但是，它们极易受到频繁增加的大灾难或攻击的影响。因此，重建损坏的网络比根据经验对原始易受攻击的网络进行恢复更可取。为了重建一个可持续的网络，我们专注于增强循环，使它们不是树，这可以通过节点移除来实现。尽管这种优化对应于一个棘手的组合问题，但我们在应用受统计物理学启发的近似计算时提出了基于增强循环的自愈方法。我们表明，与传统修复方法相比，通过节省链路和端口资源，我们提出的方法可以获得更高的鲁棒性和效率。此外，当一些损坏的链路可重用或作为资源投资得到补偿时，重建网络可以变得比原始网络更具容忍度。这些结果展示了使用具有弹性自适应能力的自我修复进行网络重建的潜力。