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Max-Min 3-Dispersion Problems

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Computing and Combinatorics (COCOON 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11653))

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Abstract

Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper we consider the 3-dispersion problem when P is a set of points on a plane. Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the \(L_{\infty }\) metric, and an O(n) time algorithm to solve the 3-dispersion problem in the \(L_1\) metric. Also we give an \(O(n^2\log n)\) time algorithm to solve the 3-dispersion problem in the \(L_2\) metric.

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Acknolwedgement

Shin-ichi Nakano was supported by JST CREST Grant Number JPMJCR1402. Takeaki Uno was supported by JST CREST Grant Number JPMJCR1401. Kunihiro Wasa was supported by JSPS KAKENHI Grant Number 19K20350 and JST CREST Grant Number JPMJCR1401.

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Authors and Affiliations

  1. Saitama University, Saitama, Japan

    Takashi Horiyama

  2. Gunma University, Maebashi, Japan

    Shin-ichi Nakano

  3. Kyushu Institute of Technology, Kitakyushu, Japan

    Toshiki Saitoh

  4. Kyoto University, Kyoto, Japan

    Koki Suetsugu

  5. Tohoku University, Sendai, Japan

    Akira Suzuki

  6. JAIST, Nomi, Japan

    Ryuhei Uehara

  7. National Institute of Informatics, Tokyo, Japan

    Takeaki Uno & Kunihiro Wasa

Authors
  1. Takashi Horiyama
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  2. Shin-ichi Nakano
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  3. Toshiki Saitoh
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  4. Koki Suetsugu
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  5. Akira Suzuki
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  6. Ryuhei Uehara
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  7. Takeaki Uno
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  8. Kunihiro Wasa
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Corresponding author

Correspondence to Shin-ichi Nakano .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Horiyama, T. et al. (2019). Max-Min 3-Dispersion Problems. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_24

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26175-7

  • Online ISBN: 978-3-030-26176-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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