Fair Set Cover

TL;DR

This paper introduces Fair Set Cover, an extension of the classic set cover problem that incorporates fairness constraints like demographic parity, along with algorithms that efficiently balance fairness and solution quality.

Contribution

It formulates the fair set cover problem, studies its computational hardness, and develops approximation algorithms that ensure fairness with minimal impact on efficiency.

Findings

Algorithms guarantee zero-unfairness under certain conditions.

Fairness constraints cause only a slight increase in solution size.

Computational time remains comparable to traditional set cover.

Abstract

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 guarantee 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.