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Diskretn. Anal. Issled. Oper., 2015, Volume 22, Number 6, Pages 5–28 (Mi da830)  

This article is cited in 3 scientific papers (total in 3 papers)

Multiple circle coverings of an equilateral triangle, square, and circle

Sh. I. Galiev, A. V. Khorkov

Kazan National Research Technological University, 10 K. Marx St., 420011 Kazan, Russia

Abstract: We study $k$-fold coverings of an equilateral triangle, square, and circle with $n$ congruent circles of the minimum possible radius $r^*_{n,k}$. We describe mathematical models for these problems and algorithms for their solving. We also prove optimality of the constructed coverings for certain $n$ and $k$, $1<k\le n$. For $n\le15$ and $1<k\le n$, we present the best found (possibly, improvable) values of circles radii ensuring the $k$-fold covering of the equilateral triangle, square or a circle. Ill. 4, tab. 3, bibliogr. 39.

Keywords: multiple covering with congruent circles, equilateral triangle, square, circle, minimum covering problem.

DOI: https://doi.org/10.17377/daio.2015.22.482

Full text: PDF file (475 kB)
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Bibliographic databases:

UDC: 519.7
Received: 17.03.2015
Revised: 20.08.2015

Citation: Sh. I. Galiev, A. V. Khorkov, “Multiple circle coverings of an equilateral triangle, square, and circle”, Diskretn. Anal. Issled. Oper., 22:6 (2015), 5–28

Citation in format AMSBIB
\Bibitem{GalKho15}
\by Sh.~I.~Galiev, A.~V.~Khorkov
\paper Multiple circle coverings of an equilateral triangle, square, and circle
\jour Diskretn. Anal. Issled. Oper.
\yr 2015
\vol 22
\issue 6
\pages 5--28
\mathnet{http://mi.mathnet.ru/da830}
\crossref{https://doi.org/10.17377/daio.2015.22.482}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3497820}
\elib{http://elibrary.ru/item.asp?id=25124387}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Lempert, Q. M. Le, “Multiple covering of a closed set on a plane with non-Euclidean metrics”, IFAC-PapersOnLine, 51:32 (2018), 850–854  crossref  isi  scopus
    2. Sh. I. Galiev, A. V. Khorkov, “On the number and arrangement of sensors for the multiple covering of bounded plane domains”, J. Appl. Industr. Math., 13:1 (2019), 43–53  mathnet  crossref  crossref
    3. A. L. Kazakov, A. A. Lempert, K. M. Le, “O zadachakh postroeniya mnogokratnykh pokrytii i upakovok v dvumernom neevklidovom prostranstve”, UBS, 81 (2019), 6–25  mathnet  crossref
  • Дискретный анализ и исследование операций
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