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Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions.
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D. F. Robinson and L. R. Foulds · 1979
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G. De Soete · 1983
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Jean-Francois Le Gall · 1991
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The median procedure for partitions
J.-P. Barthélemy and B. Leclerc · 1993
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On distances between phylogenetic trees
B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp, and L. Zhang · 1997
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The average consensus procedure: combination of weighted trees containing identical or overlapping sets of taxa
F.-J. Lapointe and G. Cucumel · 1997
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P. W. Diaconis and S. P. Holmes · 1998
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B. Leclerc · 1998
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On the linear-cost subtree-transfer distance between phylogenetic trees
B. DasGupta, X. He, T. Jiang, M. Li, and J. Tromp · 1999
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l ∞ l_{\infty} -approximation via subdominants
V. Chepoi and B. Fichet · 2000
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Geometry of the space of phylogenetic trees
L. J. Billera, S. P. Holmes, and K. Vogtmann · 2001
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A Course in Metric Geometry
D. Burago, Y. Burago, and S. Ivanov · 2001
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Topological persistence and simplification
H. Edelsbrunner, D. Letscher, and A. Zomorodian · 2002
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Barrier trees of degenerate landscapes
C. Flamm, I. L. Hofacker, P. F. Stadler, and M. T. Wolfinger · 2002
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Computing contour trees in all dimensions
H. Carr, J. Snoeyink, and U. Axen · 2003
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The category of ultrametric spaces is isomorphic to the category of complete, atomic, tree-like, and real graduated lattices L A T ∗ {LAT}^{\ast}
A. J. Lemin · 2003
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Phylogenetics
C. Semple, M. Steel, and R. A. Caplan · 2003
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Trees and ultrametric spaces: A categorical equivalence
B. Hughes · 2004
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Probability and Real Trees
S. N. Evans · 2006
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Topological methods for the analysis of high dimensional data sets and 3D object recognition
G. Singh, F. Mémoli, and G. Carlsson · 2007
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G. Weber, P.-T. Bremer, and V. Pascucci · 2007
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Persistent homology - a survey
H. Edelsbrunner and J. Harer · 2008
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Barcodes: the persistent topology of data
R. Ghrist · 2008
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Nodal distances for rooted phylogenetic trees
The Structure and Stability of Persistence Modules
F. Chazal, V. de Silva, M. Glisse, and S. Oudot · 2016
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Categorified Reeb graphs
V. de Silva, E. Munch, and A. Patel · 2016
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The edit distance for Reeb graphs of surfaces
B. Di Fabio and C. Landi · 2016
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How rigid the finite ultrametric spaces can be?
O. Dovgoshey, E. Petrov, and H.-M. Teichert · 2016
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The space of ultrametric phylogenetic trees
A. Gavryushkin and A. J. Drummond · 2016
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Convergence between categorical representations of Reeb space and Mapper
E. Munch and B. Wang · 2016
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G. Cardona, M. Llabrés, F. Rosselló, and G. Valiente · 2009
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Proximity of persistence modules and their diagrams
F. Chazal, D. Cohen-Steiner, M. Glisse, L. J. Guibas, and S. Y. Oudot · 2009
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Comparison of phylogenetic trees through alignment of embedded evolutionary distances
K. Choi and S. M. Gomez · 2009
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Characterization, stability and convergence of hierarchical clustering methods
G. Carlsson and F. Mémoli · 2010
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Visualization of high-dimensional point clouds using their density distribution’s topology
P. Oesterling, C. Heine, H. Jaenicke, G. Scheuermann, and G. Heyer · 2011
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Matching split distance for unrooted binary phylogenetic trees
D. Bogdanowicz and K. Giaro · 2012
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Hierarchical representations of network data with optimal distortion bounds
Z. Smith, S. Chowdhury, and F. Mémoli · 2016
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Local equivalence and intrinsic metrics between Reeb graphs
M. Carrière and S. Oudot · 2017
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Cophenetic median trees under the manhattan distance
A. Markin and O. Eulenstein · 2017
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Exploring the evolution of pressure-perturbations to understand atmospheric phenomena
W. Widanagamaachchi, A. Jacques, B. Wang, E. Crosman, P.-T. Bremer, V. Pascucci, and J. Horel · 2017
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Statistical analysis and parameter selection for mapper
M. Carrière, B. Michel, and S. Oudot · 2018
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Structure and stability of the one-dimensional mapper
M. Carrière and S. Oudot · 2018
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Theory of interleavings on categories with a flow
V. de Silva, E. Munch, and A. Stefanou · 2018
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From isomorphic rooted trees to isometric ultrametric spaces
O. Dovgoshey and E. Petrov · 2018
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The complexity of comparing multiply-labelled trees by extending phylogenetic-tree metrics
M. Lafond, N. El-Mabrouk, K. Huber, and V. Moulton · 2019
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The ℓ ∞ \ell^{\infty} -cophenetic metric for phylogenetic trees as an interleaving distance
E. Munch and A. Stefanou · 2019
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FPT-algorithms for computing Gromov-Hausdorff and interleaving distances between trees
E. F. Touli and Y. Wang · 2019
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Edit distance between merge trees
R. Sridharamurthy, T. B. Masood, A. Kamakshidasan, and V. Natarajan · 2020
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A structural average of labeled merge trees for uncertainty visualization
L. Yan, Y. Wang, E. Munch, E. Gasparovic, and B. Wang · 2020
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The Reeb graph edit distance is universal
U. Bauer, C. Landi, and F. Memoli · 2021
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Reeb graph metrics from the ground up
B. Bollen, E. Chambers, J. A. Levine, and E. Munch · 2021
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Decorated merge trees for persistent topology
J. Curry, H. Hang, W. Mio, T. Needham, and O. B. Okutan · 2021
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Scalar field comparison with topological descriptors: Properties and applications for scientific visualization
L. Yan, T. B. Masood, R. Sridharamurthy, F. Rasheed, V. Natarajan, I. Hotz, and B. Wang · 2021
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Wasserstein distances, geodesics and barycenters of merge trees
M. Pont, J. Vidal, J. Delon, and J. Tierny · 2022
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