Influence maximization problem has been studied extensively with the development of online social networks. Most of the existing works focus on the maximization of influence spread under the assumption that the number of influenced users determines the success of a product promotion. However, the profit of some products such as online game depends on the interactions among users besides the number of users. In this paper, we take both the number of active users and the user-to-user interactions into account and propose the interaction-aware influence maximization problem. To address this practical issue, we analyze its complexity and modularity, propose the sandwich theory which is based on decomposing the non-submodular objective function into the difference of two submodular functions and design two iterated sandwich algorithms which are guaranteed to get data dependent approximation solution. Through real data sets, we verify the effectiveness of our proposed algorithms.

随着在线社交网络的发展，影响最大化的问题已被广泛研究。现有的大多数作品都集中在影响力传播最大化的假设下，即受影响用户的数量决定了产品促销的成功。但是，诸如在线游戏之类的某些产品的利润不仅取决于用户数量，还取决于用户之间的交互。在本文中，我们同时考虑了活跃用户的数量和用户之间的交互，并提出了交互感知影响力最大化问题。为了解决这一实际问题，我们分析了其复杂性和模块化性，提出了基于将非亚模目标函数分解为两个亚模函数之差的三明治理论，并设计了两个迭代的三明治算法，可以保证得到依赖于数据的近似解。通过真实的数据集，我们验证了我们提出的算法的有效性。