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Chebyshevskii Sbornik, 2020, Volume 21, Issue 2, Pages 169–189
DOI: https://doi.org/10.22405/2226-8383-2018-21-2-169-189 (Mi cheb903) 		 
Gromov–Hausdorff distances to simplexes and some applications to discrete optimisation

A. O. Ivanovab, A. A. Tuzhilina

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (Moscow)
b Bauman Moscow State Technical University (Moscow)
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DOI: https://doi.org/10.22405/2226-8383-2018-21-2-169-189
Abstract: Relations between Gromov–Hausdorff distance and Discrete Optimisation problems are discussed. We use the Gromov–Hausdorff distances to single-distance metric space for solving the following problems: calculation of lengths of minimum spanning tree edges of a finite metric space; generalised Borsuk problem; chromatic number and clique cover number of a simple graph calculation problems.
Keywords: Gromov–Hausdorff distance, minimum spanning tree, Borsuk problem, chromatic number, clique covering, metric geometry, discrete optimisation.
Received: 08.12.2019
Accepted: 11.03.2020
Document Type: Article
UDC: 514.7+519.17+519.8
Language: English
Citation: A. O. Ivanov, A. A. Tuzhilin, “Gromov–Hausdorff distances to simplexes and some applications to discrete optimisation”, Chebyshevskii Sb., 21:2 (2020), 169–189
Citation in format AMSBIB
\Bibitem{IvaTuz20}
\by A.~O.~Ivanov, A.~A.~Tuzhilin
\paper Gromov--Hausdorff distances to simplexes and some applications to discrete optimisation
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 2
\pages 169--189
\mathnet{http://mi.mathnet.ru/cheb903}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-2-169-189}
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