Max-min 3-dispersion problems

Takashi Horiyama; Shin Ichi Nakano; Toshiki Saitoh; Koki Suetsugu; Akira Suzuki; Ryuhei Uehara; Takeaki Uno; Kunihiro Wasa

doi:10.1587/transfun.2020DMP0003

Max-min 3-dispersion problems

Takashi Horiyama, Shin Ichi Nakano, Toshiki Saitoh, Koki Suetsugu, Akira Suzuki, Ryuhei Uehara, Takeaki Uno, Kunihiro Wasa

情報科学研究科 (研究科レベル所属のみ)

研究成果: Article › 査読

抄録

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 (2-dimensional space). 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_∞ metric, and an O(n) time algorithm to solve the 3-dispersion problem in the L₁ metric. Also, we give an O(n² log n) time algorithm to solve the 3-dispersion problem in the L₂ metric.

本文言語	English
ページ（範囲）	1101-1107
ページ数	7
ジャーナル	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
巻	E104A
号	9
DOI	https://doi.org/10.1587/transfun.2020DMP0003
出版ステータス	Published - 2021

ASJC Scopus subject areas

信号処理
コンピュータグラフィックスおよびコンピュータ支援設計
電子工学および電気工学
応用数学

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10.1587/transfun.2020DMP0003

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title = "Max-min 3-dispersion problems",

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 (2-dimensional space). 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∞ metric, and an O(n) time algorithm to solve the 3-dispersion problem in the L1 metric. Also, we give an O(n2 log n) time algorithm to solve the 3-dispersion problem in the L2 metric.",

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author = "Takashi Horiyama and Nakano, {Shin Ichi} and Toshiki Saitoh and Koki Suetsugu and Akira Suzuki and Ryuhei Uehara and Takeaki Uno and Kunihiro Wasa",

note = "Funding Information: Shin-ichi Nakano was supported by JST CREST Grant Number JPMJCR1402. Ryuhei Uehara was supported by JSPS KAKENHI Grant Number 18H04091 and 20K20311. 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. Publisher Copyright: Copyright {\textcopyright} 2021 The Institute of Electronics, Information and Communication Engineers",

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AU - Horiyama, Takashi

AU - Nakano, Shin Ichi

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AU - Suetsugu, Koki

AU - Suzuki, Akira

AU - Uehara, Ryuhei

AU - Uno, Takeaki

AU - Wasa, Kunihiro

N1 - Funding Information: Shin-ichi Nakano was supported by JST CREST Grant Number JPMJCR1402. Ryuhei Uehara was supported by JSPS KAKENHI Grant Number 18H04091 and 20K20311. 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. Publisher Copyright: Copyright © 2021 The Institute of Electronics, Information and Communication Engineers

PY - 2021

Y1 - 2021

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Max-min 3-dispersion problems

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