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Capacitated Center Problems with Two-Sided Bounds and Outliers

  • Hu Ding
  • Lunjia Hu
  • Lingxiao Huang
  • Jian Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

Abstract

In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices V, we want to find a subset of vertices S, called centers, such that the maximum cluster radius is minimized. Moreover, each center in S should satisfy some capacity constraint, which could be an upper or lower bound on the number of vertices it can serve. Capacitated k-center problems with one-sided bounds (upper or lower) have been well studied in previous work, and a constant factor approximation was obtained.

We are the first to study the capacitated center problem with both capacity lower and upper bounds (with or without outliers). We assume each vertex has a uniform lower bound and a non-uniform upper bound. For the case of opening exactly k centers, we note that a generalization of a recent LP approach can achieve constant factor approximation algorithms for our problems. Our main contribution is a simple combinatorial algorithm for the case where there is no cardinality constraint on the number of open centers. Our combinatorial algorithm is simpler and achieves better constant approximation factor compared to the LP approach.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Computer Science and EngineeringMichigan State UniversityEast LansingUSA
  2. 2.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingChina

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