Measures and Optimization for Robustness and Vulnerability in Disconnected Networks

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