eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-06
12:1
12:14
10.4230/LIPIcs.ESA.2019.12
article
A Constant Approximation for Colorful k-Center
Bandyapadhyay, Sayan
1
Inamdar, Tanmay
1
Pai, Shreyas
1
Varadarajan, Kasturi
1
Department of Computer Science, University of Iowa, Iowa City, IA, USA
In this paper, we consider the colorful k-center problem, which is a generalization of the well-known k-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius rho, such that with k balls of radius rho, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a "pseudo-approximation" algorithm that works in any metric space, and an approximation algorithm that works for a special class of instances in the plane. The latter algorithm uses a novel connection to a certain matching problem in graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol144-esa2019/LIPIcs.ESA.2019.12/LIPIcs.ESA.2019.12.pdf
Colorful k-center
Euclidean Plane
LP Rounding
Outliers