Improved coverings of a square with six and eight equal circles

J.B.M. Melissen, Peter Schuur

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

In a recent article, Tarnai and Gáspár used computer simulations to find thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius.
Original languageEnglish
Article numberR32
Pages (from-to)-
JournalElectronic journal of combinatorics
Volume3
Issue number1
Publication statusPublished - 1997

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Simulated annealing
Circle
Covering
Computer simulation
Covering Radius
Simulated Annealing
Computer Simulation
Lower bound

Keywords

  • METIS-124529
  • IR-95963

Cite this

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Improved coverings of a square with six and eight equal circles. / Melissen, J.B.M.; Schuur, Peter.

In: Electronic journal of combinatorics, Vol. 3, No. 1, R32, 1997, p. -.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Schuur, Peter

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AB - In a recent article, Tarnai and Gáspár used computer simulations to find thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius.

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KW - IR-95963

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VL - 3

SP - -

JO - Electronic journal of combinatorics

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SN - 1077-8926

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