A Scalable Algorithm for Fair Influence Maximization With Unbiased Estimator

Abstract

This paper studies the fair influence maximization problem with efficient algorithms. In particular, given a graph $G$, a community structure ${\mathcal {C}}$ consisting of disjoint communities, and a budget $k$, the problem asks to select a seed set $S$ ($|S|=k$) that maximizes the influence spread while narrowing the influence gap between different communities. This problem derives from some significant social scenarios, such as health interventions (e.g. suicide/HIV prevention) where individuals from underrepresented groups or LGBTQ communities may be disproportionately excluded from the benefits of the intervention. To depict the concept of fairness in the context of influence maximization, researchers have proposed various notions of fairness, where the welfare fairness notion that better balances fairness level and influence spread has shown promising effectiveness. However, the lack of efficient algorithms for optimizing the objective function under welfare fairness restricts its application to networks of only a few hundred nodes. In this paper, we modify the objective function of welfare fairness to maximize the exponentially weighted sum and the logarithmically weighted sum over all communities’ influenced fractions (utility). To achieve efficient algorithms with theoretical guarantees, we first introduce two unbiased estimators: one for the fractional power of the arithmetic mean and the other for the logarithm 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. Finally, we present an efficient algorithm that guarantees $1-1/e - \varepsilon$ (positive objective function) or $1+1/e + \varepsilon$ (negative objective function) approximation for any small $\varepsilon > 0$. Experiments demonstrate that our proposed algorithm could efficiently handle large-scale networks with good performance.