Fairness in influence maximization has been a very active research topic recently. Most works in this context study the question of how to find seeding strategies (deterministic or probabilistic) such that nodes or communities in the network get their fair share of coverage. Different fairness criteria have been used in this context. All these works assume that the entity that is spreading the information has an inherent interest in spreading the information fairly, otherwise why would they want to use the developed fair algorithms? This assumption may however be flawed in reality -- the spreading entity may be purely \emph{efficiency-oriented}. In this paper we propose to study two optimization problems with the goal to modify the network structure by adding links in such a way that efficiency-oriented information spreading becomes \emph{automatically fair}. We study the proposed optimization problems both from a theoretical and experimental perspective, that is, we give several hardness and hardness of approximation results, provide efficient algorithms for some special cases, and more importantly provide heuristics for solving one of the problems in practice. In our experimental study we then first compare the proposed heuristics against each other and establish the most successful one. In a second experiment, we then show that our approach can be very successful in practice. That is, we show that already after adding a few edges to the networks the greedy algorithm that purely maximizes spread surpasses all fairness-tailored algorithms in terms of ex-post fairness. Maybe surprisingly, we even show that our approach achieves ex-post fairness values that are comparable or even better than the ex-ante fairness values of the currently most efficient algorithms that optimize ex-ante fairness.

翻译：影响力最大化中的公平性近来已成为一个非常活跃的研究课题。此背景下的大多数工作研究如何找到（确定性的或概率性的）种子策略，使得网络中的节点或社区获得其应得的覆盖份额。该领域使用了不同的公平性标准。所有这些工作都假设信息传播实体本身具有公平传播的内在兴趣，否则它们为何要使用所开发的公平算法？然而，这一假设在现实中可能存在缺陷——传播实体可能纯粹是"效率导向型"的。本文提出研究两个优化问题，目标是通过添加链接来修改网络结构，使效率导向的信息传播"自动"变得公平。我们从理论和实验两个角度研究了所提出的优化问题，即给出了若干难度结果和近似难度结果，为某些特殊情况提供了高效算法，更重要的是，提供了解决其中一个实际问题的启发式方法。在实验研究中，我们首先对提出的启发式方法进行相互比较，并确定了最成功的方法。在第二个实验中，我们证明了我们的方法在实践中可以非常成功。具体而言，我们证明了仅向网络添加少量边后，纯粹最大化传播的贪婪算法在事后公平性方面便超越了所有专门针对公平性设计的算法。令人惊讶的是，我们甚至证明了我们的方法所达到的事后公平性值，与当前优化事前公平性的最高效算法所达到的事前公平性值相当，甚至更优。