Fair Influence Maximization (FIM) seeks to mitigate disparities in influence across different groups and has recently garnered increasing attention. A widely adopted notion of fairness in FIM is the maximin constraint, which directly requires maximizing the utility (influenced ratio within a group) of the worst-off group. Despite its intuitive formulation, designing efficient algorithms with strong theoretical guarantees remains challenging, as the maximin objective does not satisfy submodularity, a key property for designing approximate algorithms in traditional influence maximization settings. In this paper, we address this challenge by proposing a two-step optimization framework consisting of Inner-group Maximization (IGM) and Across-group Maximization (AGM). We first prove that the influence spread within any individual group remains submodular, enabling effective optimization within groups. Based on this, IGM applies a greedy approach to pick high-quality seeds for each group. In the second step, AGM coordinates seed selection across groups by introducing two strategies: Uniform Selection (US) and Greedy Selection (GS). We prove that AGM-GS holds a $(1-1/e-\varepsilon)$ approximation to the optimal solution when groups are completely disconnected, while AGM-US guarantees a roughly $\frac{1}{m}(1-1/e-\varepsilon)$ lower bound regardless of the group structure, with $m$ denoting the number of groups.

翻译：公平影响力最大化旨在缓解不同群体间影响力分布的差异，近年来受到日益广泛的关注。FIM中一种广泛采用的公平性概念是最大化最小约束，该约束直接要求最大化最弱势群体的效用（即群体内部被影响的比例）。尽管该目标具有直观的表述，但由于最大化最小目标不满足子模性（传统影响力最大化场景中设计近似算法的关键性质），设计具有强理论保证的高效算法仍具挑战性。本文通过提出包含组内最大化与跨组最大化两阶段优化框架应对这一挑战。我们首先证明任意单群体内的影响力传播仍保持子模性，从而支持群体内部的有效优化。基于此，IGM采用贪心策略为每个群体选取高质量种子节点。在第二阶段，AGM通过引入均匀选择与贪心选择两种策略协调跨群体的种子选择。我们证明当群体间完全无连接时，AGM-GS对最优解具有$(1-1/e-\varepsilon)$近似比；而无论群体结构如何，AGM-US均可保证约$\frac{1}{m}(1-1/e-\varepsilon)$的下界，其中$m$表示群体数量。