research-article

A deterministic o(m log m) time algorithm for the reeb graph

Author:

Salman ParsaAuthors Info & Claims

SoCG '12: Proceedings of the twenty-eighth annual symposium on Computational geometry

Pages 269 - 276

https://doi.org/10.1145/2261250.2261289

Published: 17 June 2012 Publication History

Abstract

We present a deterministic algorithm to compute the Reeb graph of a PL real-valued function on a simplicial complex in O(m log m) time, where m is the size of the 2-skeleton. The problem reduces to dynamic graph connectivity. We obtain the running time by using offline graph connectivity which assumes that the sequence of operations is known in advance. The algorithm is implemented and experimental results are given. In addition, we reduce the offline graph connectivity problem to computing the Reeb graph.

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https://doi.org/10.1109/TVCG.2023.3334755
Sisouk KDelon JTierny J(2024)Wasserstein Dictionaries of Persistence DiagramsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.333026230:2(1638-1651)Online publication date: Feb-2024
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Guillou PVidal JTierny J(2024)Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data – An Algorithm and a BenchmarkIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.323800830:4(1897-1915)Online publication date: Apr-2024
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Index Terms

A deterministic o(m log m) time algorithm for the reeb graph
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SoCG '12: Proceedings of the twenty-eighth annual symposium on Computational geometry

June 2012

436 pages

ISBN:9781450312998

DOI:10.1145/2261250

Program Chairs:
Tamal Dey
The Ohio State University, USA
,
Sue Whitesides
University of Victoria, Canada

Copyright © 2012 ACM.

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Published: 17 June 2012

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SoCG '12

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SoCG '12: Symposium on Computational Geometry 2012

June 17 - 20, 2012

North Carolina, Chapel Hill, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Pont MTierny J(2024)Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)IEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.333475530:9(6390-6406)Online publication date: Sep-2024
https://doi.org/10.1109/TVCG.2023.3334755
Sisouk KDelon JTierny J(2024)Wasserstein Dictionaries of Persistence DiagramsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.333026230:2(1638-1651)Online publication date: Feb-2024
https://doi.org/10.1109/TVCG.2023.3330262
Guillou PVidal JTierny J(2024)Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data – An Algorithm and a BenchmarkIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.323800830:4(1897-1915)Online publication date: Apr-2024
https://doi.org/10.1109/TVCG.2023.3238008
Pareja-Corcho JMontoya-Zapata DMoreno ACadavid CPosada JArenas-Tobon KRuiz-Salguero O(2024)On the shape description of general solids using Morse theoryComputers & Graphics10.1016/j.cag.2024.103994(103994)Online publication date: Jun-2024
https://doi.org/10.1016/j.cag.2024.103994
Pont MVidal JTierny J(2023)Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)IEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.321500129:2(1573-1589)Online publication date: 1-Feb-2023
https://doi.org/10.1109/TVCG.2022.3215001
Shailja SBhagavatula VCieslak MVettel JGrafton SManjunath B(2023)ReeBundle: A Method for Topological Modeling of White Matter Pathways Using Diffusion MRIIEEE Transactions on Medical Imaging10.1109/TMI.2023.330604942:12(3725-3737)Online publication date: Dec-2023
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Pont MVidal JDelon JTierny J(2022)Wasserstein Distances, Geodesics and Barycenters of Merge TreesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.311483928:1(291-301)Online publication date: Jan-2022
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Nauleau FVivodtzev FBridel-Bertomeu TBeaugendre HTierny J(2022)Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows An Experimental Study2022 IEEE 12th Symposium on Large Data Analysis and Visualization (LDAV)10.1109/LDAV57265.2022.9966403(1-11)Online publication date: 16-Oct-2022
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Kim WMémoli F(2021)Generalized persistence diagrams for persistence modules over posetsJournal of Applied and Computational Topology10.1007/s41468-021-00075-1Online publication date: 5-Aug-2021
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Tu JHajij MRosen P(2019)Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb GraphsAdvances in Visual Computing10.1007/978-3-030-33720-9_8(99-113)Online publication date: 21-Oct-2019
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