Chapter

Discrete and Computational Geometry

Volume 2866 of the series Lecture Notes in Computer Science pp 9-13

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

  • Jin AkiyamaAffiliated withResearch Institute of Educational Development, Tokai University
  • , Rika MochizukiAffiliated withSchool of Administration and Informatics, University of Shizuoka
  • , Nobuaki MutohAffiliated withSchool of Administration and Informatics, University of Shizuoka
  • , Gisaku NakamuraAffiliated withResearch Institute of Educational Development, Tokai University

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Abstract

Given n points inside a unit square (circle), let d n (c n ) denote the maximum value of the minimum distance between any two of the n points. The problem of determining d n (c n ) and identifying the configuration of that yields d n (c n ) 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.