通过全局k核实现网络鲁棒性
Network Robustness via Global k-cores
摘要：
网络鲁棒性是衡量网络抵御对抗攻击的能力。但并非网络的所有部分都是平等的。K-核是一种稠密的子图，可以捕捉到许多现实网络的一些关键属性。因此，以前的工作试图通过其k核的稳定性来建模网络鲁棒性。然而，这些方法只考虑一个核心价值，因此无法对全球网络弹性措施进行编码。在本文中，我们提出了一个新的概念，网络弹性，定义在所有的核心来解决这个限制。特别是，我们评估的稳定性下的节点删除相对于每个节点的初始核心的网络。我们的目标是通过一个组合问题来计算鲁棒性：找到b个最关键的节点来删除，使得从初始核心中掉下来的节点数量最大化。我们的贡献之一是表明，它是NP-困难的，以实现任何多项式因子的近似给定的目标。我们还提出了一个细粒度的复杂性分析，这个问题的镜头下的参数化复杂性理论的几个自然参数。此外，我们展示了我们的鲁棒性概念的两个应用：测量物种的进化和表征来自不同领域的网络。
英文摘要：
Network robustness is a measure a network's ability to survive adversarial attacks. But not all parts of a network are equal. K-cores, which are dense subgraphs, are known to capture some of the key properties of many real-life networks. Therefore, previous work has attempted to model network robustness via the stability of its k-core. However, these approaches account for a single core value and thus fail to encode a global network resilience measure. In this paper, we address this limitation by proposing a novel notion of network resilience that is defined over all cores. In particular, we evaluate the stability of the network under node removals with respect to each node's initial core. Our goal is to compute robustness via a combinatorial problem: find b most critical nodes to delete such that the number of nodes that fall from their initial cores is maximized. One of our contributions is showing that it is NP-hard to achieve any polynomial factor approximation of the given objective. We also present a fine-grained complexity analysis of this problem under the lens of parameterized complexity theory for several natural parameters. Moreover, we show two applications of our notion of robustness: measuring the evolution of species and characterizing networks arising from different domains.
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