Maximin Distance for n Points in a Unit Square or a Unit Circle

  • Jin Akiyama
  • Rika Mochizuki
  • Nobuaki Mutoh
  • Gisaku Nakamura
Conference paper

DOI: 10.1007/978-3-540-44400-8_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2866)
Cite this paper as:
Akiyama J., Mochizuki R., Mutoh N., Nakamura G. (2003) Maximin Distance for n Points in a Unit Square or a Unit Circle. In: Akiyama J., Kano M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg

Abstract

Given n points inside a unit square (circle), let dn(cn) denote the maximum value of the minimum distance between any two of the n points. The problem of determining dn(cn) and identifying the configuration of that yields dn(cn) has been investigated using geometric methods and computer-aided methods in a number of papers. We investigate the problem using a computer-aided search and arrive at some approximations which improve on earlier results for n=59, 73 and 108 for the unit square, and also for n=70, 73, 75 and 77, ⋯ , 80 for the unit circle. The associated configurations are identified for all the above-mentioned improved results.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Rika Mochizuki
    • 2
  • Nobuaki Mutoh
    • 2
  • Gisaku Nakamura
    • 1
  1. 1.Research Institute of Educational DevelopmentTokai UniversityTokyoJapan
  2. 2.School of Administration and InformaticsUniversity of ShizuokaShizuokaJapan

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