Efficient Approximation Algorithms for Fair Influence Maximization under Maximin Constraint

TL;DR

This work tackles Fair Influence Maximization under the maximin constraint, where the objective is to maximize the worst-off groups influence share. It introduces a two-step framework: Inner-group Maximization (IGM) that exploits submodularity of each group via greedy IMM to select high-quality seeds per group, followed by Across-group Maximization (AGM) that coordinates seeds across groups using Uniform Selection (AGM-US) with a group-structure-aware bound and Greedy Selection (AGM-GS) with strong guarantees when groups are disconnected. Theoretical results show AGM-GS achieves a (1 - 1/e - ) approximation under disjoint groups, while AGM-US guarantees roughly (m/m)(1 - 1/e - ) regardless of connectivity; extensive experiments on five real networks confirm that AGM-GS often yields the best practical performance with favorable fairness-utility trade-offs. Overall, the framework provides scalable, provable, and empirically effective solutions for fair diffusion under maximin fairness, with clear guidance on when to prefer each AGM strategy.

Abstract

Aiming to reduce disparities of influence across different groups, Fair Influence Maximization (FIM) has recently garnered widespread attention. The maximin constraint, a common notion of fairness adopted in the FIM problem, imposes a direct and intuitive requirement that asks the utility (influenced ratio within a group) of the worst-off group should be maximized. Although the objective of FIM under maximin constraint is conceptually straightforward, the development of efficient algorithms with strong theoretical guarantees remains an open challenge. The difficulty arises from the fact that 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

Figures (3)

• Figure 1: Comparison results on the AVC network.
• Figure 2: Comparison results on the ENZ and PRO network.
• Figure 3: Comparison results on the UVM and UCSC network.

Theorems & Definitions (7)

• Definition 1
• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2
• proof