Results 71 to 80 of about 7,327 (139)
Metric Space Recognition by Gromov–Hausdorff Distances to Simplexes
Lobachevskii Journal of Mathematics14 pages, 2 ...
Ivanov, A. O. +2 more
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Computing the Gromov--Hausdorff distance using gradient methods
, 2023 The Gromov--Hausdorff distance measures the difference in shape between metric spaces and poses a notoriously difficult problem in combinatorial optimization. We introduce its quadratic relaxation over a convex polytope whose solutions provably deliver the Gromov--Hausdorff distance. The optimality guarantee is enabled by the fact that the search space
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Gromov-Hausdorff Distance for Directed Spaces
Changes have been made in the last part of Section 3.
Fajstrup, Lisbeth +6 more
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Who Invented the Gromov-Hausdorff Distance?
, 2016 One of the most beautiful notions of metric geometry is the Gromov-Hausdorff distance which measures the difference between two metric spaces. To define the distance, let us isometrically embed these spaces into various metric spaces and measure the Hausdorff distance between their images.
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The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces
, 2019 In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called $2$-distance spaces). As a corollary, a complete solution to generalized Borsuk problem for the $2$-distance spaces
Ivanov, A. O., Tuzhilin, A. A.
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Potential and challenges of high-speed (4D) body scanning for mobility analysis of firefighter clothing: a methodical case study. [PDF]
EXCLI J, 2023 Muenks D, Kyosev Y, Kunzelmann F.
europepmc +1 more source
Null Distance and Convergence of Lorentzian Length Spaces. [PDF]
Ann Henri Poincare, 2022 Kunzinger M, Steinbauer R.
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Lectures on Hausdorff and Gromov-Hausdorff Distance Geometry
, 2020 The course was given at Peking University, Fall 2019. We discuss the following subjects: (1) Introduction to general topology, hyperspaces, metric and pseudometric spaces, graph theory. (2) Graphs in metric spaces, minimum spanning tree, Steiner minimal tree, Gromov minimal filling.
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Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]
Calc Var Partial Differ Equ, 2023 Don S, Magnani V.
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