Fair Set Cover

2024-05-19

arXiv.org

AI Summary

This work introduces fairness constraints into the classical Set Cover problem, proposing the Fair Set Cover model to simultaneously satisfy coverage requirements and ensure demographic parity across sensitive attributes (e.g., gender, age). Methodologically, we formulate multiple scalable fairness-aware modeling paradigms that guarantee zero unfairness under reasonable assumptions, and design efficient approximation algorithms with provable theoretical approximation ratios. We further establish the computational complexity of the problem—proving both NP-hardness and APX-hardness—for the first time. Experiments across diverse real-world datasets demonstrate that our algorithms incur negligible overhead: solution size increases by less than 1.5% on average, runtime remains essentially unchanged, and performance is robust across varying fairness thresholds. Our core contribution lies in pioneering the integration of algorithmic fairness with combinatorial optimization, delivering a solution that is both theoretically rigorous—supported by hardness results and approximation guarantees—and practically deployable.

Technology Category

• Machine Learning: Ethics, Bias, and Fairness
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 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.

Problem

• Fairness
• Set Coverage
• Diversity

Innovation

• Fairness
• Diverse Set Cover
• Efficient Resource Consumption