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Computing Plurality Points and Condorcet Points in Euclidean Space

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

This work concerns two kinds of spatial equilibria. Given a multiset of n points in Euclidean space equipped with the ℓ2-norm, we call a location a plurality point if it is closer to at least as many given points as any other location. A location is called a Condorcet point if there exists no other location which is closer to an absolute majority of the given points. In d-dimensional Euclidean space ℝd, we show that the plurality points and the Condorcet points are equivalent. When the given points are not collinear, the Condorcet point (which is also the plurality point) is unique in ℝd if such a point exists. To the best of our knowledge, no efficient algorithm has been proposed for finding the point if the dimension is higher than one. In this paper, we present an O(n d − 1 logn)-time algorithm for any fixed dimension d ≥ 2.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, 106

    Yen-Wei Wu, Wei-Yin Lin & Kun-Mao Chao

  2. Graduate Institute of Biomedical Electronics and Bioinformatics, National Taiwan University, Taipei, Taiwan, 106

    Kun-Mao Chao

  3. Graduate Institute of Networking and Multimedia, National Taiwan University, Taipei, Taiwan, 106

    Kun-Mao Chao

  4. Institute of Information and Decision Sciences, National Taipei College of Business, Taipei, Taiwan, 100

    Hung-Lung Wang

Authors
  1. Yen-Wei Wu
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  2. Wei-Yin Lin
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  3. Hung-Lung Wang
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  4. Kun-Mao Chao
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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© 2013 Springer-Verlag Berlin Heidelberg

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Wu, YW., Lin, WY., Wang, HL., Chao, KM. (2013). Computing Plurality Points and Condorcet Points in Euclidean Space. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_64

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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