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Gromov-Hausdorff (GH) distance is a natural way to measure the distortion between two metric spaces.
Some max snp-hard results concerning unordered labeled trees
K. Zhang and T. Jiang · 1994
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Alignment of trees - an alternative to tree edit
T. Jiang, L. Wang, and K. Zhang · 1995
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On the approximability of numerical taxonomy (fitting distances by tree metrics)
R. Agarwala, V. Bafna, M. Farach, M. Paterson, and M. Thorup · 1998
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Topological quadrangulations of closed triangulated surfaces using the Reeb graph
F. Hétroy and D. Attali · 2003
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Fitting tree metrics: Hierarchical clustering and phylogeny
N. Ailon and M. Charikar · 2005
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A survey on tree edit distance and related problems
P. Bille · 2005
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Approximating the distortion
A. Hall and C. Papadimitriou · 2005
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A theoretical and computational framework for isometry invariant recognition of point cloud data
F. Mémoli and G. Sapiro · 2005
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Efficient computation of isometry-invariant distances between surfaces
A. M. Bronstein, M. M. Bronstein, and R. Kimmel · 2006
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Approximation algorithms for embedding general metrics into trees
M. Bădoiu, P. Indyk, and A. Sidiropoulos · 2007
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Metric Structures for Riemannian and Non-Riemannian Spaces
M. Gromov · 2007
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Ordinal embeddings of minimum relaxation: general properties, trees, and ultrametrics
N. Alon, M. Bădoiu, E. D. Demaine, M. Farach-Colton, M. Hajiaghayi, and A. Sidiropoulos · 2008
Cited alongside, same era.
Reeb graphs for shape analysis and applications
S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno · 2008
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Parameterized low-distortion embeddings-graph metrics into lines and trees
M. Fellows, F. Fomin, D. Lokshtanov, E. Losievskaja, F. A. Rosamond, and S. Saurabh · 2008
Cited alongside, same era.
Reeb graph based 3D shape modeling and applications
Some properties of gromov–hausdorff distances
F. Mémoli · 2012
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Interleaving distance between merge trees
D. Morozov, K. Beketayev, and G. H. Weber · 2013
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Measuring distance between reeb graphs
U. Bauer, X. Ge, and Y. Wang · 2014
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Categorified reeb graphs
V. de Silva, E. Munch, and A. Patel · 2016
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Computational aspects of the gromov–hausdorff distance and its application in non-rigid shape matching
F. Schmiedl · 2017
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Metric embeddings with outliers
A. Sidiropoulos, D. Wang, and Y. Wang · 2017
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J. Tierny · 2008
Cited alongside, same era.
Data skeletonization via Reeb graphs
X. Ge, I. Safa, M. Belkin, and Y. Wang · 2011
Cited alongside, same era.
Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
V. Chepoi, F. F. Dragan, I. Newman, Y. Rabinovich, and Y. Vaxes · 2012
Cited alongside, same era.
P. K. Agarwal, K. Fox, A. Nath, A. Sidiropoulos, and Y. Wang · 2018
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The reeb graph edit distance is universal
U. Bauer, C. Landi, and F. Mémoli · 2018
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