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A Constant Approximation for Colorful k-Center

Authors Sayan Bandyapadhyay, Tanmay Inamdar, Shreyas Pai, Kasturi Varadarajan

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Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Computational geometry
Keywords
  • Colorful k-center
  • Euclidean Plane
  • LP Rounding
  • Outliers

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Abstract

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.

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Sayan Bandyapadhyay, Tanmay Inamdar, Shreyas Pai, and Kasturi Varadarajan. A Constant Approximation for Colorful k-Center. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ESA.2019.12

Author Details

Sayan Bandyapadhyay
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA
Tanmay Inamdar
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA
Shreyas Pai
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA
Kasturi Varadarajan
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA

Funding

The first, second and fourth authors are partially supported by the National Science Foundation under Grant CCF-1615845.

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