We study the influence minimization problem: given a graph $G$ and a seed set $S$, blocking at most $b$ nodes or $b$ edges such that the influence spread of the seed set is minimized. This is a pivotal yet underexplored aspect of network analytics, which can limit the spread of undesirable phenomena in networks, such as misinformation and epidemics. Given the inherent NP-hardness of the problem under the IC and LT models, previous studies have employed greedy algorithms and Monte Carlo Simulations for its resolution. However, existing techniques become cost-prohibitive when applied to large networks due to the necessity of enumerating all the candidate blockers and computing the decrease in expected spread from blocking each of them. This significantly restricts the practicality and effectiveness of existing methods, especially when prompt decision-making is crucial. In this paper, we propose the AdvancedGreedy algorithm, which utilizes a novel graph sampling technique that incorporates the dominator tree structure. We find that AdvancedGreedy can achieve a $(1-1/e-\epsilon)$-approximation in the problem under the LT model. Experimental evaluations on real-life networks reveal that our proposed algorithms exhibit a significant enhancement in efficiency, surpassing the state-of-the-art algorithm by three orders of magnitude, while achieving high effectiveness.

翻译：我们研究影响力最小化问题：给定图$G$和种子集$S$，通过最多阻塞$b$个节点或$b$条边，使得种子集的影响力传播最小化。这是网络分析中一个关键但尚未充分探索的方面，它可以限制网络中不良现象（如虚假信息和流行病）的传播。鉴于该问题在IC和LT模型下具有固有的NP-hard性质，以往的研究采用贪心算法和蒙特卡洛模拟进行求解。然而，现有的技术在大规模网络应用时变得成本高昂，因为需要枚举所有候选阻塞点并计算阻塞每个阻塞点所带来的预期传播减少量。这严重限制了现有方法的实用性和有效性，尤其是在需要快速决策的场景下。在本文中，我们提出了AdvancedGreedy算法，该算法利用了一种融合支配树结构的新型图采样技术。我们发现，在LT模型下，AdvancedGreedy能够实现该问题的$(1-1/e-\epsilon)$近似比。在真实网络上的实验评估表明，我们提出的算法在效率上显著提升，比现有最优算法高出三个数量级，同时实现了高有效性。