Approximation Algorithms for Fair Range Clustering
This addresses fairness in clustering for applications like data analysis and resource allocation, providing theoretical guarantees for balanced representation across groups.
The paper tackles the fair range clustering problem by developing efficient constant factor approximation algorithms for fair range ℓ_p-clustering, which includes fair range k-center, k-median, and k-means as special cases, ensuring each demographic group is represented within specified bounds while minimizing clustering cost.
This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick $k$ centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of $n$ points in a metric space $(P,d)$ where each point belongs to one of the $\ell$ different demographics (i.e., $P = P_1 \uplus P_2 \uplus \cdots \uplus P_\ell$) and a set of $\ell$ intervals $[α_1, β_1], \cdots, [α_\ell, β_\ell]$ on desired number of centers from each group, the goal is to pick a set of $k$ centers $C$ with minimum $\ell_p$-clustering cost (i.e., $(\sum_{v\in P} d(v,C)^p)^{1/p}$) such that for each group $i\in \ell$, $|C\cap P_i| \in [α_i, β_i]$. In particular, the fair range $\ell_p$-clustering captures fair range $k$-center, $k$-median and $k$-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range $\ell_p$-clustering for all values of $p\in [1,\infty)$.