The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts, such as assembling a small team of individuals that collectively satisfy a range of expertise requirements. However, despite its broad application spectrum and significant potential impact, set cover has yet to be studied through the lens of fairness. Therefore, in this paper, we introduce Fair Set Cover, which aims not only to cover with a minimum-size set but also to satisfy demographic parity in its selection of sets. To this end, we develop multiple versions of fair set cover, study their hardness, and devise efficient approximation algorithms for each variant. Notably, under certain assumptions, our algorithms always guarantees zero-unfairness, with only a small increase in the approximation ratio compared to regular set cover. Furthermore, our experiments on various data sets and across different settings confirm the negligible price of fairness, as (a) the output size increases only slightly (if any) and (b) the time to compute the output does not significantly increase.

翻译：算法决策的潜在危害已将算法公平性提升为计算机科学的核心议题之一。集合覆盖是计算机科学的基本问题之一，具有多种社会性应用，例如组建一个能够共同满足一系列专业知识要求的小型团队。然而，尽管其应用范围广泛且潜在影响显著，集合覆盖问题尚未从公平性视角进行研究。为此，本文提出公平集合覆盖问题，其目标不仅在于使用最小规模的集合进行覆盖，还要求集合选择满足人口统计学均等性。我们构建了多种公平集合覆盖版本，研究了它们的计算难度，并为每个变体设计了高效的近似算法。值得注意的是，在特定假设下，我们的算法始终能保证零不公平性，且相较于常规集合覆盖仅需小幅增加近似比。此外，我们在各类数据集和不同设定下的实验证实了公平性的可忽略代价：(a) 输出规模仅轻微扩大（若有），(b) 计算输出的时间并未显著增加。