Techniques for Generalized Colorful k-Center Problems

by   Georg Anegg, et al.

Fair clustering enjoyed a surge of interest recently. One appealing way of integrating fairness aspects into classical clustering problems is by introducing multiple covering constraints. This is a natural generalization of the robust (or outlier) setting, which has been studied extensively and is amenable to a variety of classic algorithmic techniques. In contrast, for the case of multiple covering constraints (the so-called colorful setting), specialized techniques have only been developed recently for k-Center clustering variants, which is also the focus of this paper. While prior techniques assume covering constraints on the clients, they do not address additional constraints on the facilities, which has been extensively studied in non-colorful settings. In this paper, we present a quite versatile framework to deal with various constraints on the facilities in the colorful setting, by combining ideas from the iterative greedy procedure for Colorful k-Center by Inamdar and Varadarajan with new ingredients. To exemplify our framework, we show how it leads, for a constant number γ of colors, to the first constant-factor approximations for both Colorful Matroid Supplier with respect to a linear matroid and Colorful Knapsack Supplier. In both cases, we readily get an O(2^γ)-approximation. Moreover, for Colorful Knapsack Supplier, we show that it is possible to obtain constant approximation guarantees that are independent of the number of colors γ, as long as γ=O(1), which is needed to obtain a polynomial running time. More precisely, we obtain a 7-approximation by extending a technique recently introduced by Jia, Sheth, and Svensson for Colorful k-Center.


page 1

page 10


A Technique for Obtaining True Approximations for k-Center with Covering Constraints

There has been a recent surge of interest in incorporating fairness aspe...

Fair Clustering with Multiple Colors

A fair clustering instance is given a data set A in which every point is...

Tight FPT Approximation for Constrained k-Center and k-Supplier

In this work, we study a range of constrained versions of the k-supplier...

Locating Charging Stations: Connected, Capacitated and Prize- Collecting

In this paper, we study locating charging station problem as facility lo...

Non-Uniform k-Center and Greedy Clustering

In the Non-Uniform k-Center problem, a generalization of the famous k-ce...

Approximating Fair k-Min-Sum-Radii in ℝ^d

The k-center problem is a classical clustering problem in which one is a...

Correlation Clustering Generalized

We present new results for LambdaCC and MotifCC, two recently introduced...

Please sign up or login with your details

Forgot password? Click here to reset