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Capacitated Center Problems with Two-Sided Bounds and Outliers

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Algorithms and Data Structures (WADS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10389))

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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.

HD is supported by the start-up fund from Michigan State University.

LJH, LXH and JL are supported in part by the National Basic Research Program of China grants 2015CB358700, 2011CBA00300, 2011CBA00301, and the National NSFC grants 61033001, 61632016, 61361136003.

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Author information

Authors and Affiliations

  1. Computer Science and Engineering, Michigan State University, East Lansing, MI, USA

    Hu Ding

  2. Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

    Lunjia Hu, Lingxiao Huang & Jian Li

Authors
  1. Hu Ding
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  2. Lunjia Hu
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  3. Lingxiao Huang
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  4. Jian Li
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Corresponding author

Correspondence to Lingxiao Huang .

Editor information

Editors and Affiliations

  1. Computer Science, University of Toronto , Toronto, Ontario, Canada

    Faith Ellen

  2. Computer Science, Memorial University of Newfoundland , St. John’s, Newfoundland and Labrador, Canada

    Antonina Kolokolova

  3. Carleton University, Ottawa, Ontario, Canada

    Jörg-Rüdiger Sack

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Ding, H., Hu, L., Huang, L., Li, J. (2017). Capacitated Center Problems with Two-Sided Bounds and Outliers. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_28

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  • DOI: https://doi.org/10.1007/978-3-319-62127-2_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62126-5

  • Online ISBN: 978-3-319-62127-2

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