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

47 Citations (Scopus)

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

Fingerprint

Min-max
Packing
Disjoint
Circle
Exact Solution
Configuration
Unit
Optimization

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Maranas, Costas D. ; Floudas, Christodoulos A. ; Pardalos, Panos M. / New results in the packing of equal circles in a square. In: Discrete Mathematics. 1995 ; Vol. 142, No. 1-3. pp. 287-293.
@article{928d277f6b35485aacdd447fd0787384,
title = "New results in the packing of equal circles in a square",
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.",
author = "Maranas, {Costas D.} and Floudas, {Christodoulos A.} and Pardalos, {Panos M.}",
year = "1995",
month = "7",
day = "15",
doi = "10.1016/0012-365X(93)E0230-2",
language = "English (US)",
volume = "142",
pages = "287--293",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

New results in the packing of equal circles in a square. / Maranas, Costas D.; Floudas, Christodoulos A.; Pardalos, Panos M.

In: Discrete Mathematics, Vol. 142, No. 1-3, 15.07.1995, p. 287-293.

Research output: Contribution to journalArticle

TY - JOUR

T1 - New results in the packing of equal circles in a square

AU - Maranas, Costas D.

AU - Floudas, Christodoulos A.

AU - Pardalos, Panos M.

PY - 1995/7/15

Y1 - 1995/7/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000625923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000625923&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(93)E0230-2

DO - 10.1016/0012-365X(93)E0230-2

M3 - Article

VL - 142

SP - 287

EP - 293

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -