Efficient Approximation Algorithms for Fair Influence Maximization under Maximin Constraint

2025-09-30

AI Summary

This paper studies the Fair Influence Maximization (FIM) problem, which seeks to maximize influence spread while ensuring a minimum influence share for the most disadvantaged group and minimizing inter-group influence disparity. To address the challenge that the fairness-aware objective is non-submodular—rendering classical greedy algorithms inapplicable—we propose the first “Intra-Group Maximization–Inter-Group Coordination” two-stage optimization framework. We theoretically establish that influence propagation within each group is submodular, enabling the design of approximation-guaranteed algorithms. Within groups, we apply a greedy strategy; across groups, we combine uniform and greedy selection. Our AGM-GS algorithm achieves a $(1 - 1/e - varepsilon)$-approximation ratio when no edges exist between groups; AGM-US guarantees an $Omega(1/m)(1 - 1/e - varepsilon)$ lower bound for arbitrary group structures, significantly improving the joint assurance of fairness and efficiency.

Technology Category

• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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

Problem

• Developing efficient algorithms for fair influence maximization with maximin constraints
• Addressing non-submodularity challenges in fair influence maximization optimization
• Proposing approximation frameworks to ensure fairness across disconnected and connected groups

Innovation

• Two-step optimization framework for fair influence maximization
• Inner-group greedy seed selection using submodularity property
• Across-group coordination with two approximation-guaranteed strategies