Information cascade in online social networks can be rather negative, e.g., the spread of rumors may trigger panic. To limit the influence of misinformation in an effective and efficient manner, the influence minimization (IMIN) problem is studied in the literature: given a graph G and a seed set S, blocking at most b vertices such that the influence spread of the seed set is minimized. In this paper, we are the first to prove the IMIN problem is NP-hard and hard to approximate. Due to the hardness of the problem, existing works resort to greedy solutions and use Monte-Carlo Simulations to solve the problem. However, they are cost-prohibitive on large graphs since they have to enumerate all the candidate blockers and compute the decrease of expected spread when blocking each of them. To improve the efficiency, we propose the AdvancedGreedy algorithm (AG) based on a new graph sampling technique that applies the dominator tree structure, which can compute the decrease of the expected spread of all candidate blockers at once. Besides, we further propose the GreedyReplace algorithm (GR) by considering the relationships among candidate blockers. Extensive experiments on 8 real-life graphs demonstrate that our AG and GR algorithms are significantly faster than the state-of-the-art by up to 6 orders of magnitude, and GR can achieve better effectiveness with its time cost close to AG.

翻译：在线社交网络中的信息级联可能产生负面影响，例如谣言传播会引发恐慌。为有效且高效地限制虚假信息的影响，学界研究提出了最小化影响（IMIN）问题：给定图G和种子集S，通过阻断最多b个顶点，使种子集的影响传播最小化。本文首次证明IMIN问题是NP难问题且难以近似。由于该问题的难解性，现有研究采用贪心策略并借助蒙特卡洛模拟求解，但这类方法需枚举所有候选阻断顶点并计算阻断每个顶点时预期传播范围的下降量，在大规模图上计算成本极高。为提升效率，我们基于一种结合支配树结构的新型图采样技术提出AdvancedGreedy算法（AG），可一次性计算所有候选阻断顶点预期传播范围的下降量。此外，我们进一步考虑候选阻断顶点间的关系提出GreedyReplace算法（GR）。在8个真实网络上的大量实验表明，AG和GR算法的速度比现有最优方法快最高6个数量级，且GR能在时间成本接近AG的情况下获得更优效果。