Scalable Fair Influence Maximization

TL;DR

This paper introduces a scalable algorithm for fair influence maximization in networks, balancing influence spread and community fairness, by adapting reverse influence sampling and approximation techniques.

Contribution

It proposes an efficient, scalable algorithm for welfare fairness-based influence maximization using reverse influence sampling and unbiased estimators.

Findings

Achieves a $(1 - 1/e - \, \varepsilon)$ approximation guarantee.

Introduces an unbiased estimator for fractional powers of the arithmetic mean.

Demonstrates scalability to large networks with efficient computation.

Abstract

Given a graph $G$, a community structure $\mathcal{C}$, and a budget $k$, the fair influence maximization problem aims to select a seed set $S$ ($|S|\leq k$) that maximizes the influence spread while narrowing the influence gap between different communities. While various fairness notions exist, the welfare fairness notion, which balances fairness level and influence spread, has shown promising effectiveness. However, the lack of efficient algorithms for optimizing the welfare fairness objective function restricts its application to small-scale networks with only a few hundred nodes. In this paper, we adopt the objective function of welfare fairness to maximize the exponentially weighted summation over the influenced fraction of all communities. We first introduce an unbiased estimator for the fractional power of the arithmetic mean. Then, by adapting the reverse influence sampling (RIS) approach, we convert the optimization problem to a weighted maximum coverage problem. We also analyze the number of reverse reachable sets needed to approximate the fair influence at a high probability. Further, we present an efficient algorithm that guarantees $1-1/e - \varepsilon$ approximation.