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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 3, Pages 64–75 (Mi da776)  

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

An exact algorithm for solving the discrete Weber problem for a $k$-tree

A. V. Panyukov, R. E. Shangin

South Ural State University, 76 Lenin Ave., 454080 Chelyabinsk, Russia

Abstract: We consider the discrete Weber problem. A consistent deterministic algorithm for finding an exact solution to the problem for a $k$-tree and a finite set of placement positions is suggested. The algorithm is based on the idea of dynamic programming with a decomposition tree. A numerical experiment was performed to examine the effectiveness of the proposed algorithm in comparison with IBM ILOG CPLEX. Ill. 2, bibliogr. 23.

Keywords: Weber problem, $k$-tree, dynamic programming, decomposition tree, exact algorithm.

Full text: PDF file (285 kB)
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Bibliographic databases:
UDC: 519.863
Received: 03.09.2013
Revised: 31.01.2014

Citation: A. V. Panyukov, R. E. Shangin, “An exact algorithm for solving the discrete Weber problem for a $k$-tree”, Diskretn. Anal. Issled. Oper., 21:3 (2014), 64–75

Citation in format AMSBIB
\Bibitem{PanSha14}
\by A.~V.~Panyukov, R.~E.~Shangin
\paper An exact algorithm for solving the discrete Weber problem for a~$k$-tree
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 3
\pages 64--75
\mathnet{http://mi.mathnet.ru/da776}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242102}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. E. Shangin, “Tochnyi i evristicheskii algoritmy resheniya diskretnoi zadachi Vebera dlya prostogo tsikla”, Vestn. NGU. Ser. matem., mekh., inform., 14:2 (2014), 98–107  mathnet
    2. A. V. Panyukov, R. E. Shangin, “Algorithm for the discrete Weber's problem with an accuracy estimate”, Autom. Remote Control, 77:7 (2016), 1208–1215  mathnet  crossref  isi  elib  elib
    3. G. G. Zabudskii, T. I. Keiner, “Optimal placement of rectangles on a plane with fixed objects”, Autom. Remote Control, 78:9 (2017), 1651–1661  mathnet  crossref  isi  elib
  • Дискретный анализ и исследование операций
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