The influence maximization problem has become one of the fundamental combinatorial optimization problems over the past decade due to its extensive applications in social networks. Although a \(1-1/e\) approximation ratio is easily obtained using a greedy algorithm for the submodular case, how to solve the non-submodular case and enhance the solution quality deserve further study. In this paper, based on the marginal increments, we devise a non-negative decomposition property for monotone function and a non-increasing decomposition property for monotone submodular function (NDP). According to the exchange improvement (EI), a necessary condition for an optimal solution is also proposed. With the help of NDP and EI condition, an exchange improvement algorithm is proposed to improve further the quality of the solution to the non-submodular influence maximization problem. For the influence maximization, we devise effective methods to compute the influence spread and marginal gain in a successive iteration update manner. These methods make it possible to calculate the influence spread directly and accurately. Next, we design a data-dependent approximation algorithm for a non-submodular topology change problem from a marginal increment perspective.

由于影响力最大化问题在社交网络中的广泛应用，在过去十年中，它已成为基本的组合优化问题之一。虽然是\（1-1 / e \）对于子模态，使用贪婪算法很容易获得近似值，如何解决非子模态和提高求解质量值得进一步研究。本文基于边际增量，设计了单调函数的非负分解性质和单调子模函数（NDP）的非增加分解性质。根据交换改进（EI），还提出了最佳解决方案的必要条件。借助NDP和EI条件，提出了一种交换改进算法，以进一步提高非亚模量影响最大化问题的求解质量。对于影响最大化，我们设计了有效的方法以连续迭代更新的方式计算影响范围和边际增益。这些方法使得可以直接而准确地计算影响扩散。接下来，我们从边际增量的角度为非亚模块拓扑变化问题设计了一种与数据相关的近似算法。