Fair Correlation Clustering Meets Graph Parameters

TL;DR

This paper analyzes the computational complexity of fair correlation clustering with fairness constraints, providing new tractability results based on graph parameters like treewidth, treedepth, and vertex cover.

Contribution

It offers the first detailed parameterized complexity analysis of fair correlation clustering, identifying conditions under which the problem is tractable.

Findings

Tractability results for treewidth, treedepth, and vertex cover parameters.

The problem remains NP-hard on severely restricted inputs.

Provides a complexity landscape for fair correlation clustering.

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.