Geodesic
Gromov--Hausdorff distances to simplexes and some applications to discrete optimisation
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 169-189

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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. 
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     author = {A. O. Ivanov and A. A. Tuzhilin},
     title = {Gromov--Hausdorff distances to simplexes and some applications to discrete optimisation},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     publisher = {mathdoc},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a13/}
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A. O. Ivanov; A. A. Tuzhilin. Gromov--Hausdorff distances to simplexes and some applications to discrete optimisation. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 169-189. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a13/