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.

翻译：本研究探讨了通过公平子集概念融入公平性约束的相关聚类泛化问题。迄今为止，公平相关聚类问题已从多个视角被研究，但在参数化复杂度范式下仍缺乏详细分析。我们通过提供该问题在多种结构图参数（包括树宽、树深和顶点覆盖数）下的可处理性结果来填补这一空白；鉴于该问题在严格受限输入上已知的NP难特性，我们的结果恰好位于可处理性的边界。