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Intrinsic Interleaving Distance for Merge Trees

https://doi.org/10.1007/s44007-024-00143-9

Gasparovic, Ellen ; Munch, Elizabeth ; Oudot, Steve ; Turner, Katharine ; Wang, Bei ; Wang, Yusu ( December 2024 , La Matematica)

Free, publicly-accessible full text available December 16, 2025
Distances Between Immersed Graphs: Metric Properties

https://doi.org/10.1007/s44007-022-00037-8

Buchin, Maike ; Chambers, Erin ; Fang, Pan ; Fasy, Brittany Terese ; Gasparovic, Ellen ; Munch, Elizabeth ; Wenk, Carola ( January 2023 , La Matematica)

Abstract
Graphs in metric spaces appear in a wide range of data sets, and there is a large body of work focused on comparing, matching, or analyzing collections of graphs in different ambient spaces. In this survey, we provide an overview of a diverse collection of distance measures that can be defined on the set of finite graphs immersed (and in some cases, embedded) in a metric space. For each of the distance measures, we recall their definitions and investigate which of the properties of a metric they satisfy. Furthermore we compare the distance measures based on these properties and discuss their computational complexity.

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On homotopy types of Vietoris–Rips complexes of metric gluings

https://doi.org/10.1007/s41468-020-00054-y

Adamaszek, Michał ; Adams, Henry ; Gasparovic, Ellen ; Gommel, Maria ; Purvine, Emilie ; Sazdanovic, Radmila ; Wang, Bei ; Wang, Yusu ; Ziegelmeier, Lori ( September 2020 , Journal of Applied and Computational Topology)

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A Structural Average of Labeled Merge Trees for Uncertainty Visualization

https://doi.org/10.1109/TVCG.2019.2934242

Yan, Lin ; Wang, Yusu ; Munch, Elizabeth ; Gasparovic, Ellen ; Wang, Bei ( January 2020 , IEEE Transactions on Visualization and Computer Graphics)

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The relationship between the intrinsic Cech and persistence distortion distances for metric graphs

https://doi.org/10.20382/jocg.v10i1a16

Gasparovic, Ellen ; Gommel, Maria ; Purvine, Emilie ; Sazdanovic, Radmila ; Wang, Bei ; Wang, Yusu ; Ziegelmeier, Lori ( January 2019 , Journal of computational geometry)

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Vietoris-Rips and Cech Complexes of Metric Gluings

https://doi.org/10.4230/LIPIcs.SoCG.2018.3

Adamaszek, Michal ; Adams, Henry ; Gasparovic, Ellen ; Gommel, Maria ; Purvine, Emilie ; Sazdanovic, Radmila ; Wang, Bei ; Wang, Yusu ; Ziegelmeier, Lori ( January 2018 , 34th International Symposium on Computational Geometry (SoCG 2018))

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