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This article is cited in 15 scientific papers (total in 15 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
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.
DOI:
https://doi.org/10.4213/sm7835
 Full text:
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English version:
Sbornik: Mathematics, 2013, 204:9, 1285–1306
Bibliographic databases:
     
UDC:
515.124.4+519.176
MSC: Primary 05C35; Secondary 05C05, 05C22, 51K05
Received: 21.12.2010 and 07.05.2013
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
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Linking options:
http://mi.mathnet.ru/eng/msb7835https://doi.org/10.4213/sm7835 http://mi.mathnet.ru/eng/msb/v204/i9/p51
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
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This publication is cited in the following articles:
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Z. N. Ovsyannikov, “An open family of sets that have several minimal fillings”, J. Math. Sci., 203:6 (2014), 855–857
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Z. N. Ovsyannikov, “The Steiner subratio of five points on a plane and four points in three-dimensional space”, J. Math. Sci., 203:6 (2014), 864–872
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V. N. Salnikov, “Probabilistic properties of topologies of finite metric spaces' minimal fillings”, J. Math. Sci., 203:6 (2014), 873–883
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Ivanov A.O., Tuzhilin A.A., “Gromov minimal fillings for finite metric spaces”, Publ. Inst. Math. (Beograd) (N.S.), 94:108 (2013), 3–15
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B. B. Bednov, P. A. Borodin, “Banach spaces that realize minimal fillings”, Sb. Math., 205:4 (2014), 459–475
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A. O. Ivanov, A. A. Tuzhilin, “Minimal fillings of finite metric spaces: The state of the art”, Discrete geometry and algebraic combinatorics, Contemporary Mathematics, 625, eds. A. Barg, O. Musin, 2014, 9–35
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A. C. Pahkomova, “Estimates of Steiner subratio and Steiner–Gromov ratio”, Moscow University Mathematics Bulletin, 69:1 (2014), 16–23
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E. I. Stepanova, “Directional derivative of the weight of a minimal filling in Riemannian manifolds”, Moscow University Mathematics Bulletin, 70:1 (2015), 14–18
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S. Yu. Lipatov, “The functions that do not change types of minimal fillings”, Moscow University Mathematics Bulletin, 70:6 (2015), 267–269
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B. B. Bednov, “The length of a minimal filling of star type”, Sb. Math., 207:8 (2016), 1064–1078
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A. O. Ivanov, A. A. Tuzhilin, “Minimal networks: a review”, Advances in dynamical systems and control, Stud. Syst. Decis. Control, 69, ed. V. A. Sadovnichiy, M. Z. Zgurovsky, Springer, [Cham], 2016, 43–80
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A. O. Ivanov, A. A. Tuzhilin, “Analiticheskie deformatsii minimalnykh setei”, Fundament. i prikl. matem., 21:5 (2016), 159–180
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B. B. Bednov, “The length of minimal filling for a five-point metric space”, Moscow University Mathematics Bulletin, 72:6 (2017), 221–225
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L. Sh. Burusheva, “Banach spaces with shortest network length depending only on pairwise distances between points”, Sb. Math., 210:3 (2019), 297–309
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E. I. Stepanova, “Bifurkatsii minimalnykh zapolnenii dlya chetyrëkh tochek evklidovoi ploskosti”, Fundament. i prikl. matem., 22:6 (2019), 253–261
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