The function or performance of a network is strongly dependent on its robustness, quantifying the ability of the network to continue functioning under perturbations. While a wide variety of robustness metrics have been proposed, they have their respective limitations. In this paper, we propose to use the forest index as a measure of network robustness, which overcomes the deficiencies of existing metrics. Using such a measure as an optimization criterion, we propose and study the problem of breaking down a network by attacking some key edges. We show that the objective function of the problem is monotonic but not submodular, which impose more challenging on the problem. We thus resort to greedy algorithms extended for non-submodular functions by iteratively deleting the most promising edges. We first propose a simple greedy algorithm with a proved bound for the approximation ratio and cubic-time complexity. To confront the computation challenge for large networks, we further propose an improved nearly-linear time greedy algorithm, which significantly speeds up the process for edge selection but sacrifices little accuracy. Extensive experimental results for a large set of real-world networks verify the effectiveness and efficiency of our algorithms, demonstrating that our algorithms outperform several baseline schemes.

翻译：网络的功能或性能高度依赖于其鲁棒性，即网络在扰动下持续运行的能力。尽管已有多种鲁棒性度量指标被提出，但它们各自存在局限性。本文提出使用森林指数作为网络鲁棒性的度量指标，该指标弥补了现有指标的不足。以该度量作为优化准则，我们提出并研究了通过攻击若干关键边来瓦解网络的问题。研究表明，该问题的目标函数具有单调性但不具有子模性，这使问题更具挑战性。为此，我们采用面向非子模函数的扩展贪心算法，通过迭代删除最有潜力的边来求解。首先提出一种具有近似比理论保证且时间复杂度为立方级的简单贪心算法。为应对大规模网络的计算挑战，进一步提出一种改进的近线性时间贪心算法，该算法在显著加速边选择过程的同时几乎不损失精度。基于大量真实网络数据集的实验验证了所提算法的有效性和高效性，表明其性能优于多种基线方案。