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Diskr. Mat., 1993, Volume 5, Issue 2, Pages 3–28 (Mi dm674)  

This article is cited in 7 scientific papers (total in 7 papers)

The Steiner problem: A survey

E. N. Gordeev, O. G. Tarastsov


Abstract: In the last decade the Steiner problem has attracted considerable attention from investigators in the field of discrete optimization. Here we give a brief survey of the fundamental results concerning the properties and algorithms for solving the Steiner problem on a Euclidean plane, the Steiner problem on a plane with a rectangular metric, and the Steiner problem on graphs, and in the latter problem we focus on results obtained after 1985. We consider both exact and heuristic algorithms, their efficiency and the results of numerical experiments. We give examples of probabilistic approaches to the solution of the problem. The final section of the paper is devoted to the Gilbert – Pollak conjecture.

Full text: PDF file (3541 kB)

English version:
Discrete Mathematics and Applications, 1993, 3:4, 339–364

Bibliographic databases:
UDC: 519.854
Received: 19.03.1992

Citation: E. N. Gordeev, O. G. Tarastsov, “The Steiner problem: A survey”, Diskr. Mat., 5:2 (1993), 3–28; Discrete Math. Appl., 3:4 (1993), 339–364

Citation in format AMSBIB
\Bibitem{GorTar93}
\by E.~N.~Gordeev, O.~G.~Tarastsov
\paper The Steiner problem: A~survey
\jour Diskr. Mat.
\yr 1993
\vol 5
\issue 2
\pages 3--28
\mathnet{http://mi.mathnet.ru/dm674}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1250953}
\zmath{https://zbmath.org/?q=an:0805.05018}
\transl
\jour Discrete Math. Appl.
\yr 1993
\vol 3
\issue 4
\pages 339--364


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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. A. V. Panyukov, “The steiner problem in graphs: topological methods of solution”, Autom. Remote Control, 65:3 (2004), 439–448  mathnet  crossref  mathscinet  zmath  isi
    2. D. T. Lotarev, A. V. Suprun, A. P. Uzdemir, “Local optimization in the steiner problem on the euclidean plane”, Autom. Remote Control, 65:7 (2004), 1089–1098  mathnet  crossref  mathscinet  zmath  isi
    3. D. T. Lotarev, A. P. Uzdemir, “Conversion of the Steiner problem on the euclidean plane to the steiner problem on graph”, Autom. Remote Control, 66:10 (2005), 1603–1613  mathnet  crossref  mathscinet  zmath
    4. A. L. Kazakov, A. A. Lempert, D. S. Bukharov, “On segmenting logistical zones for servicing continuously developed consumers”, Autom. Remote Control, 74:6 (2013), 968–977  mathnet  crossref  mathscinet  isi
    5. M. A. Bagov, “Zadachi proektirovaniya truboprovodnoi seti Shteinera”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2016, no. 4-1(16), 80–84  mathnet  crossref  mathscinet  elib
    6. M. A. Bagov, V. Ch. Kudaev, “Setevaya zadacha Shteinera s uchetom energeticheskikh zatrat”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2016, no. 4-1(16), 85–92  mathnet  crossref  elib
    7. M. A. Bagov, “Nelokalnoe reshenie setevoi zadachi Shteinera”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 4(24), 148–157  mathnet  crossref  elib
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