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# Constant Factor Approximation for Capacitated k-Center with Outliers

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LIPIcs.STACS.2014.251.pdf
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## Cite As

Marek Cygan and Tomasz Kociumaka. Constant Factor Approximation for Capacitated k-Center with Outliers. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 251-262, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.STACS.2014.251

## Abstract

The k-center problem is a classic facility location problem, where given an edge-weighted graph G=(V,E) one is to find a subset of k vertices S, such that each vertex in V is "close" to some vertex in S. The approximation status of this basic problem is well understood, as a simple 2-approximation algorithm is known to be tight. Consequently different extensions were studied. In the capacitated version of the problem each vertex is assigned a capacity, which is a strict upper bound on the number of clients a facility can serve, when located at this vertex. A constant factor approximation for the capacitated k-center was obtained last year in [Cygan, Hajiaghayi and Khuller, FOCS'12], which was recently improved to a 9-approximation in [An, Bhaskara and Svensson, arXiv'13]. In a different generalization of the problem some clients (denoted as outliers) may be disregarded. Here we are additionally given an integer p and the goal is to serve exactly p clients, which the algorithm is free to choose. In [Charikar et al., SODA'01] the authors presented a 3-approximation for the k-center problem with outliers. In this paper we consider a common generalization of the two extensions previously studied separately, i.e. we work with the capacitated k-center with outliers. We present the first constant factor approximation algorithm with approximation ratio of 25 even for the case of non-uniform hard capacities.
##### Keywords
• approximation algorithms
• k-center
• capacities
• outliers
• LP rounding

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