Constant-Factor Approximation Algorithms for Socially Fair k-Clustering

06/22/2022
by   Mehrdad Ghadiri, et al.
10

We study approximation algorithms for the socially fair (ℓ_p, k)-clustering problem with m groups, whose special cases include the socially fair k-median (p=1) and socially fair k-means (p=2) problems. We present (1) a polynomial-time (5+2√(6))^p-approximation with at most k+m centers (2) a (5+2√(6)+ϵ)^p-approximation with k centers in time n^2^O(p)· m^2, and (3) a (15+6√(6))^p approximation with k centers in time k^m·poly(n). The first result is obtained via a refinement of the iterative rounding method using a sequence of linear programs. The latter two results are obtained by converting a solution with up to k+m centers to one with k centers using sparsification methods for (2) and via an exhaustive search for (3). We also compare the performance of our algorithms with existing bicriteria algorithms as well as exactly k center approximation algorithms on benchmark datasets, and find that our algorithms also outperform existing methods in practice.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset