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Approximation and Complexity of the Capacitated Geometric Median Problem

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Computer Science – Theory and Applications (CSR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12730))

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Abstract

In the Capacitated Geometric Median problem, we are given n points in d-dimensional real space and an integer m, the goal is to locate a new point in space (center) and choose m of the input points to minimize the sum of Euclidean distances from the center to the chosen points. We show that this problem admits an “almost exact” polynomial-time algorithm in the case of fixed d and an approximation scheme PTAS in high dimensions. On the other hand, we prove that, if the dimension of space is not fixed, Capacitated Geometric Median is strongly NP-hard and does not admit a scheme FPTAS unless P \(=\) NP.

The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project 0314-2019-0014).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Vladimir Shenmaier

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  1. Vladimir Shenmaier
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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Rahul Santhanam

  2. Innovations & HighTech, Moscow Institute of Physics and Technology, Moscow, Russia

    Daniil Musatov

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Shenmaier, V. (2021). Approximation and Complexity of the Capacitated Geometric Median Problem. In: Santhanam, R., Musatov, D. (eds) Computer Science – Theory and Applications. CSR 2021. Lecture Notes in Computer Science(), vol 12730. Springer, Cham. https://doi.org/10.1007/978-3-030-79416-3_26

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  • DOI: https://doi.org/10.1007/978-3-030-79416-3_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79415-6

  • Online ISBN: 978-3-030-79416-3

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