Approximation Algorithms for Fair Range Clustering
Published in ICML 2023, Hawaii, USA, 2023
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 ℓ different demographics (i.e., P = P1 ⊎ P2 ⊎ · · · ⊎ Pℓ) and a set of ℓ intervals [α1, β1], · · · , [αℓ, βℓ] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ℓp-clustering cost such that for each group i ∈ ℓ, |C ∩ Pi| ∈ [αi, βi]. In particular, the fair range ℓp-clustering captures fair range k-center, k-median and k-means as its special cases. In this work, we provide an efficient constant factor approximation algorithm for the fair range ℓp-clustering for all values of p ∈ [1, ∞).
Recommended citation: Hotegni, S.S., Mahabadi, S. and Vakilian, A., 2023, July. Approximation Algorithms for Fair Range Clustering. In International Conference on Machine Learning (pp. 13270-13284). PMLR.