Diversity-aware clustering: Computational Complexity and Approximation Algorithms

Diversity is an essential design choice across numerous real-world contexts, spanning social environments [1], organizational structures [2], and demographic studies [3]. Embracing diversity entails acknowledging and incorporating multifaceted characteristics within groups. This concept holds profound relevance in addressing real-world challenges, particularly in scenarios where intersectionality -- the interconnected nature of social categorizations such as gender, ethnicity, religion, socio-economic status and sexual orientation -- plays a pivotal role [4, 5]. Consider the task of constituting a representative committee that accurately mirrors the demography of a broader population. In the pursuit of diversifying, and recognizing its significance in the context of fairness, it is imperative to ensure representation from various groups based on their gender, ethnicity, and economic status, among other [6]. In reality, individuals belong to multiple social categories, for example, a person could be a woman of a specific ethnic background and economic group.