Only when we understand how hackers think, can we defend against their attacks. Towards this end, this paper studies the cyber-attacks that aim to remove nodes or links from network topologies. We particularly focus on one type of such attacks called Maximum Vertex Coverage Attacks under Knapsack constraint (MVCAK), in which a hacker has a fixed budget to remove nodes from a network with the nodes involving different costs for removal, and the hacker’s goal is to maximize the number of links incident to the nodes removed. Since the MVCAK problem is NP-hard, we firstly propose an optimal solution by Integer Linear Program formulation. Secondly, we give an approximate solution by Linear Programming relaxation that achieves an approximation ratio of 3/4, outperforming the existing 1 - 1/sqrt(e) (about 0.39). Thirdly, since the straightforward implementation of our approximate solution has a high time complexity, we propose two heuristics to significantly reduce its complexity while preserving the approximation ratio. We formally prove the correctness and the effectiveness of these two heuristics. Finally, we conduct extensive experiments on both artificial and real-world networks, showing that our approximate solution produces almost the same results as the optimal solution in practice and has an acceptable running time.

中文翻译：

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背包约束下的最大顶点覆盖攻击优化

只有了解了黑客的想法，我们才能防御他们的攻击。为此，本文研究旨在从网络拓扑中删除节点或链接的网络攻击。我们特别关注一种称为背包约束下的最大顶点覆盖攻击 (MVCAK) 的此类攻击，其中黑客有固定预算从网络中删除节点，而这些节点的删除成本不同，黑客的目标是最大化与删除节点相关的链接数。由于MVCAK问题是NP-hard问题，我们首先通过整数线性规划公式提出了一个最优解。其次，我们通过线性规划松弛给出了一个近似解，其近似比为 3/4，优于现有的 1 - 1/sqrt(e)（约 0.39）。第三，由于我们的近似解的直接实现具有很高的时间复杂度，我们提出了两种启发式方法来显着降低其复杂度，同时保持近似率。我们正式证明了这两种启发式的正确性和有效性。最后，我们对人工和现实世界的网络进行了广泛的实验，表明我们的近似解产生的结果与实践中的最优解几乎相同，并且具有可接受的运行时间。