Public opinion governance in social networks is critical for public health campaigns, political elections, and commercial marketing. In this paper, we addresse the problem of maximizing overall opinion in social networks by strategically modifying the internal opinions of key nodes. Traditional matrix inversion methods suffer from prohibitively high computational costs, prompting us to propose two efficient sampling-based algorithms. Furthermore, we develop a deterministic asynchronous algorithm that exactly identifies the optimal set of nodes through asynchronous update operations and progressive refinement, ensuring both efficiency and precision. Extensive experiments on real-world datasets demonstrate that our methods outperform baseline approaches. Notably, our asynchronous algorithm delivers exceptional efficiency and accuracy across all scenarios, even in networks with tens of millions of nodes.

翻译：社交网络中的舆论治理对于公共卫生运动、政治选举和商业营销至关重要。本文研究了通过策略性地修改关键节点的内部观点来最大化社交网络整体观点的问题。传统的矩阵求逆方法计算成本过高，为此我们提出了两种基于采样的高效算法。此外，我们开发了一种确定性异步算法，通过异步更新操作和渐进优化精确识别最优节点集合，确保了效率与精度。在真实数据集上的大量实验表明，我们的方法优于基线方法。值得注意的是，我们的异步算法在所有场景下均表现出卓越的效率和准确性，即使在包含数千万节点的网络中也是如此。