Approximation Algorithms for Fair Range Clustering
share
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 = P_1 ⊎ P_2 ⊎⋯⊎ P_ℓ) and a set of ℓ intervals [α_1, β_1], ⋯, [α_ℓ, β_ℓ] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ℓ_p-clustering cost (i.e., (∑_v∈ P d(v,C)^p)^1/p) such that for each group i∈ℓ, |C∩ P_i| ∈ [α_i, β_i]. In particular, the fair range ℓ_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 ℓ_p-clustering for all values of p∈ [1,∞).
READ FULL TEXT
