Given its vast application on online social networks, Influence Maximization (IM) has garnered considerable attention over the last couple of decades. Due to the intricacy of IM, most current research concentrates on estimating the first-order contribution of the nodes to select a seed set, disregarding the higher-order interplay between different seeds. Consequently, the actual influence spread frequently deviates from expectations, and it remains unclear how the seed set quantitatively contributes to this deviation. To address this deficiency, this work dissects the influence exerted on individual seeds and their higher-order interactions utilizing the Sobol index, a variance-based sensitivity analysis. To adapt to IM contexts, seed selection is phrased as binary variables and split into distributions of varying orders. Based on our analysis with various Sobol indices, an IM algorithm dubbed SIM is proposed to improve the performance of current IM algorithms by over-selecting nodes followed by strategic pruning. A case study is carried out to demonstrate that the explanation of the impact effect can dependably identify the key higher-order interactions among seeds. SIM is empirically proved to be superior in effectiveness and competitive in efficiency by experiments on synthetic and real-world graphs.

翻译：鉴于其在在线社交网络中的广泛应用，影响力最大化在过去几十年中引起了广泛关注。由于影响力最大化的复杂性，当前大多数研究集中于估计节点的一阶贡献以选择种子集，忽略了不同种子之间的高阶相互作用。因此，实际影响力传播常常偏离预期，并且尚不清楚种子集如何定量地导致这种偏差。为了解决这一不足，本文利用基于方差的敏感性分析——Sobol指数，剖析了单个种子所施加的影响力及其高阶相互作用。为了适应影响力最大化环境，种子选择被表述为二元变量，并分解为不同阶数的分布。基于对不同Sobol指数的分析，我们提出了一种名为SIM的影响力最大化算法，该算法通过过度选择节点再辅以策略性剪枝，来提升现有影响力最大化算法的性能。通过案例研究，我们展示了影响力效应的解释能够可靠地识别种子之间的关键高阶相互作用。在合成图与真实世界图上的实验表明，SIM在有效性方面具有优越性，且在效率上具有竞争力。