Modeling and shaping how information spreads through a network is a major research topic in network analysis. While initially the focus has been mostly on efficiency, recently fairness criteria have been taken into account in this setting. Most work has focused on the maximin criteria however, and thus still different groups can receive very different shares of information. In this work we propose to consider fairness as a notion to be guaranteed by an algorithm rather than as a criterion to be maximized. To this end, we propose three optimization problems that aim at maximizing the overall spread while enforcing strict levels of demographic parity fairness via constraints (either ex-post or ex-ante). The level of fairness hence becomes a user choice rather than a property to be observed upon output. We study this setting from various perspectives. First, we prove that the cost of introducing demographic parity can be high in terms of both overall spread and computational complexity, i.e., the price of fairness may be unbounded for all three problems and optimal solutions are hard to compute, in some case even approximately or when fairness constraints may be violated. For one of our problems, we still design an algorithm with both constant approximation factor and fairness violation. We also give two heuristics that allow the user to choose the tolerated fairness violation. By means of an extensive experimental study, we show that our algorithms perform well in practice, that is, they achieve the best demographic parity fairness values. For certain instances we additionally even obtain an overall spread comparable to the most efficient algorithms that come without any fairness guarantee, indicating that the empirical price of fairness may actually be small when using our algorithms.

翻译：建模和塑造信息在网络中的传播方式是网络分析领域的一个主要研究课题。虽然最初的重点主要集中在效率上，但近期公平性标准已被纳入此场景的考量。然而，大多数工作集中在最大化最小（maximin）准则上，因此不同群体仍可能接收到非常不同的信息份额。在本工作中，我们提出将公平性视为应由算法保障的概念，而非需要最大化的准则。为此，我们提出了三个优化问题，旨在最大化整体传播范围，同时通过约束（事后或事前）强制实施严格水平的人口统计平等。因此，公平性水平成为用户的选择，而非输出时需观察的属性。我们从多个视角研究此设定。首先，我们证明引入人口统计平等的代价在整体传播范围和计算复杂度两方面都可能很高，即对于所有三个问题，公平性的代价可能是无界的，且最优解难以计算，在某些情况下甚至难以近似求解，或当公平性约束可被违反时亦如此。针对其中一个问题，我们仍设计出一种具有常数近似因子和公平性违反的算法。我们还给出了两种启发式方法，允许用户选择可容忍的公平性违反程度。通过广泛的实验研究，我们表明我们的算法在实践中表现良好，即它们能实现最佳的人口统计平等值。对于某些实例，我们甚至获得了与无任何公平性保证的最高效算法相当的总体传播范围，这表明使用我们的算法时，公平性的经验代价实际上可能很小。