New results in the packing of equal circles in a square

Costas D. Maranas, Christodoulos A. Floudas, Panos M. Pardalos

Research output: Contribution to journalArticle

50 Scopus citations

Abstract

The problem of finding the maximum diameter of n equal mutually disjoint circles inside a unit square is addressed in this paper. Exact solutions exist for only n = 1, ..., 9,10,16,25,36 while for other n only conjectural solutions have been reported. In this work a max-min optimization approach is introduced which matches the best reported solutions in the literature for all n ≤ 30, yields a better configuration for n = 15, and provides new results for n = 28 and 29.

Original languageEnglish (US)
Pages (from-to)287-293
Number of pages7
JournalDiscrete Mathematics
Volume142
Issue number1-3
DOIs
StatePublished - Jul 15 1995

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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