An <i>O</i>(<i>n</i>²)-Time Algorithm for Computing a Max-Min 3-Dispersion on a Point Set in Convex Position

• KOBAYASHI Yasuaki

  Kyoto University

• NAKANO Shin-ichi

  Gunma University

• UCHIZAWA Kei

  Yamagata University

• UNO Takeaki

  National Institute of Informatics

• YAMAGUCHI Yutaro

  Osaka University

• YAMANAKA Katsuhisa

  Iwate University

Abstract

Given a set P of n points and an integer k, we wish to place k facilities on points in P so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem, and the set of such k points is called a k-dispersion of P. Note that the 2-dispersion problem corresponds to the computation of the diameter of P. Thus, the k-dispersion problem is a natural generalization of the diameter problem. In this paper, we consider the case of k=3, which is the 3-dispersion problem, when P is in convex position. We present an O(n²)-time algorithm to compute a 3-dispersion of P.

Journal

• IEICE Transactions on Information and Systems

  IEICE Transactions on Information and Systems E105.D (3), 503-507, 2022-03-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• dispersion problem
• facility location

Details

• CRID: 1390291767471245056
• NII Article ID: 130008165607
• DOI: 10.1587/transinf.2021fcp0013
• ISSN: 17451361
• ISSN: 09168532
• Web Site: https://www.jstage.jst.go.jp/article/transinf/E105.D/3/E105.D_2021FCP0013/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed