  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.
