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Asymmetry in k-Center Variants

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Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (RANDOM 2003, APPROX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2764))

Abstract

This paper explores three concepts: the k-center problem, some of its variants, and asymmetry. The k-center problem is a fundamental clustering problem, similar to the k-median problem. Variants of k-center may more accurately model real-life problems than the original formulation. Asymmetry is a significant impediment to approximation in many graph problems, such as k-center, facility location, k-median and the TSP.

We demonstrate an O(log* n)-approximation algorithm for the asymmetric weightedk-center problem. Here, the vertices have weights and we are given a total budget for opening centers. In the p-neighbor variant each vertex must have p (unweighted) centers nearby: we give an O(log* k)-bicriteria algorithm using 2k centers, for small p.

Finally, the following three versions of the asymmetric k-center problem we show to be inapproximable: priorityk-center, k-supplier, and outliers with forbidden centers.

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Author information

Authors and Affiliations

  1. Theory Department, The IT University of Copenhagen, Denmark

    Inge Li Gørtz

  2. Department of Computer Science, Princeton University,  

    Anthony Wirth

Authors
  1. Inge Li Gørtz
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  2. Anthony Wirth
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Editor information

Editors and Affiliations

  1. Computer Science Department, Princeton University, 35 Olden Street, 08540, Princeton, NJ

    Sanjeev Arora

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Battelle Bâtiment A, Centre Universitaire d’Informatique, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. University of California, Los Angeles

    Amit Sahai

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© 2003 Springer-Verlag Berlin Heidelberg

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Li Gørtz, I., Wirth, A. (2003). Asymmetry in k-Center Variants. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds) Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques. RANDOM APPROX 2003 2003. Lecture Notes in Computer Science, vol 2764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45198-3_6

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  • DOI: https://doi.org/10.1007/978-3-540-45198-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40770-6

  • Online ISBN: 978-3-540-45198-3

  • eBook Packages: Springer Book Archive

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