Influence maximization is a key problem seeking to identify users who will diffuse information to influence the largest number of other users in a social network. A drawback of the influence maximization problem is that it could be socially irresponsible to influence users many of whom would be harmed, due to their demographics, health conditions, or socioeconomic characteristics (e.g., predominantly overweight people influenced to buy junk food). Motivated by this drawback and by the fact that some of these vulnerable users will be influenced inadvertently, we introduce the problem of finding a set of users (seeds) that limits the influence to vulnerable users while maximizing the influence to the non-vulnerable users. We define a measure that captures the quality of a set of seeds as an additively smoothed ratio (ASR) between the expected number of influenced non-vulnerable users and the expected number of influenced vulnerable users. Then, we develop methods which aim to find a set of seeds that maximizes the measure: greedy heuristics, an approximation algorithm, as well as several variations of the approximation algorithm. We evaluate our methods on synthetic and real-world datasets and demonstrate they substantially outperform a state-of-the-art competitor in terms of both effectiveness and efficiency. We also demonstrate that the variations of our approximation algorithm offer different trade-offs between effectiveness and efficiency.

影响力最大化是寻求识别将传播信息以影响社交网络中最大数量其他用户的用户的关键问题。影响最大化问题的一个缺点是，影响由于其人口统计学，健康状况或社会经济特征（例如，超重人群受到影响而购买垃圾食品）而使许多人受到伤害的用户在社会上是不负责任的。由于这一缺陷以及某些弱势用户将受到无意影响的事实，我们引入了以下问题：寻找一组用户（种子），以限制对弱势用户的影响，同时最大限度地提高对非弱势用户的影响。我们定义了一种措施，可以将一组种子的质量作为受影响的非脆弱用户的预期数量与受影响的脆弱用户的预期数量之间的累加平滑比率（ASR）。然后，我们开发旨在寻找一组种子的方法，这些种子可以最大化度量：贪婪启发式算法，近似算法以及近似算法的多种变体。我们在合成数据集和真实数据集上评估了我们的方法，并论证了它们在有效性和效率上都远远超过了最先进的竞争对手。我们还证明了近似算法的变体在有效性和效率之间提供了不同的权衡。