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.
@InProceedings{bandyapadhyay_et_al:LIPIcs.ESA.2019.12, author = {Bandyapadhyay, Sayan and Inamdar, Tanmay and Pai, Shreyas and Varadarajan, Kasturi}, title = {{A Constant Approximation for Colorful k-Center}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {12:1--12:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.12}, URN = {urn:nbn:de:0030-drops-111336}, doi = {10.4230/LIPIcs.ESA.2019.12}, annote = {Keywords: Colorful k-center, Euclidean Plane, LP Rounding, Outliers} }
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