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Sbornik: Mathematics, 2013, Volume 204, Issue 9, Pages 1285–1306
DOI: https://doi.org/10.1070/SM2013v204n09ABEH004340 (Mi sm7835) 		 
This article is cited in 19 scientific papers (total in 19 papers)

A formula for the weight of a minimal filling of a finite metric space

A. Yu. Ereminab

a M. V. Lomonosov Moscow State University
b Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University
English version PDF (558 kB) Citations (19)
References:
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DOI: https://doi.org/10.1070/SM2013v204n09ABEH004340
Abstract: We consider the problem of finding a minimal filling for a finite metric space, that is, a weighted graph of minimal weight joining a given finite metric space. We obtain a minimax formula for the weight of the minimal filling, which we use to prove various properties of minimal fillings.
Bibliography: 10 titles.
Keywords: minimal filling, finite metric spaces, graph, Gromov's problem, perimeter of a metric space.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00664а
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1
11.G34.31.0053
Received: 21.12.2010 and 07.05.2013
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 9, Pages 51–72
DOI: https://doi.org/10.4213/sm7835
Bibliographic databases:
Document Type: Article
UDC: 515.124.4+519.176
MSC: Primary 05C35; Secondary 05C05, 05C22, 51K05
Language: English
Original paper language: Russian
Citation: A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space”, Mat. Sb., 204:9 (2013), 51–72; Sb. Math., 204:9 (2013), 1285–1306
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v204/i9/p51
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:232
    English version PDF:10
    References:51
    First page:25
     
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