Fair Correlation Clustering Meets Graph Parameters

2026-02-17

AI Summary

This work investigates the fair correlation clustering problem under fairness constraints, aiming to balance fairness and computational efficiency. It presents the first systematic analysis of this problem from the perspective of parameterized complexity, leveraging structural graph parameters—such as treewidth, treedepth, and vertex cover number—to design an algorithmic framework. The primary contribution lies in establishing fixed-parameter tractability of the problem with respect to several classic graph parameters, thereby delineating precise solvability boundaries under different parameterizations. These results provide a solid theoretical foundation and practical algorithmic support for efficiently solving fair correlation clustering instances.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so far lacked a detailed analysis from the parameterized complexity paradigm. We close this gap by providing tractability results for the problem under a variety of structural graph parameterizations, including treewidth, treedepth and the vertex cover number; our results lie at the very edge of tractability given the known NP-hardness of the problem on severely restricted inputs.

Problem

• Fair Correlation Clustering
• parameterized complexity
• graph parameters
• fairness constraints
• computational tractability

Innovation

• Fair Correlation Clustering
• parameterized complexity
• treewidth
• treedepth
• vertex cover number