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

  • Jin Akiyama
  • Rika Mochizuki
  • Nobuaki Mutoh
  • Gisaku Nakamura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2866)

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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References

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    Donovan, J.: Packing Circles in Squares and Circles Page, http://home.att.net/~donovanhse/Packing/index.html
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    Szabó, P.G., Csendes, T., Casado, L.G., García, I.: Equal circles packing in a square I – Problem setting and bounds for optimal solutions. New Trends in Equilibrium Systrems, 1–15 (2000)Google Scholar

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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