License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2019.12
URN: urn:nbn:de:0030-drops-111336
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Bandyapadhyay, Sayan ; Inamdar, Tanmay ; Pai, Shreyas ; Varadarajan, Kasturi

A Constant Approximation for Colorful k-Center

LIPIcs-ESA-2019-12.pdf (0.5 MB)


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.

BibTeX - Entry

  author =	{Sayan Bandyapadhyay and Tanmay Inamdar and Shreyas Pai and Kasturi Varadarajan},
  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 =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-111336},
  doi =		{10.4230/LIPIcs.ESA.2019.12},
  annote =	{Keywords: Colorful k-center, Euclidean Plane, LP Rounding, Outliers}

Keywords: Colorful k-center, Euclidean Plane, LP Rounding, Outliers
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

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