Influence propagation in social networks is a central problem in modern social network analysis, with important societal applications in politics and advertising. A large body of work has focused on cascading models, viral marketing, and finite-horizon diffusion. There is, however, a need for more developed, mathematically principled \emph{adversarial models}, in which multiple, opposed actors strategically select nodes whose influence will maximally sway the crowd to their point of view. In the present work, we develop and analyze such a model based on harmonic functions and linear diffusion. We prove that our general problem is NP-hard and that the objective function is monotone and submodular; consequently, we can greedily approximate the solution within a constant factor. Introducing and analyzing a convex relaxation, we show that the problem can be approximately solved using smooth optimization methods. We illustrate the effectiveness of our approach on a variety of example networks.

翻译：社交网络中的影响力传播是现代社交网络分析的核心问题，在政治和广告领域具有重要的社会应用。大量研究聚焦于级联模型、病毒式营销和有限时域扩散。然而，当前亟需发展更完善、基于数学原理的**对抗模型**，其中多个对立行动者策略性地选择节点，使其影响力能最大程度地将群体导向自身观点。在本研究中，我们基于调和函数与线性扩散构建并分析了此类模型。我们证明了该通用问题是NP难的，且目标函数具有单调性和子模性；因此，我们可以通过贪心算法在常数因子内逼近最优解。通过引入并分析凸松弛形式，我们证明了该问题可采用平滑优化方法进行近似求解。我们在多种示例网络上验证了所提方法的有效性。