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Notes on the Distributed Computation of Merge Trees on CW-Complexes

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Topological Methods in Data Analysis and Visualization IV (TopoInVis 2015)

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Abstract

Merge trees are topological structures that record changes in super-level set topology of a scalar function. They encapsulate a wide range of threshold based features which can be extracted for analysis and visualization. Several distributed and parallel algorithms for computing merge trees have been proposed in the past, but they are restricted to simplicial complexes or regular grids. In this paper, we present an algorithm for the distributed computation of merge trees on CW-complexes. The conditions on the CW-complex required for the computation of the merge tree are discussed alongside a proof of correctness.

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Acknowledgements

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-CONF-681469).

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Authors and Affiliations

  1. Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, UT, USA

    Aaditya G. Landge, Attila Gyulassy & Valerio Pascucci

  2. Lawrence Livermore National Laboratory, Livermore, CA, USA

    Peer-Timo Bremer

Authors
  1. Aaditya G. Landge
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  2. Peer-Timo Bremer
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  3. Attila Gyulassy
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  4. Valerio Pascucci
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Corresponding author

Correspondence to Aaditya G. Landge .

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Editors and Affiliations

  1. University of Leeds, Leeds, United Kingdom

    Hamish Carr

  2. Department of Computer Science, Technical University of Kaiserslautern, Kaiserslautern, Germany

    Christoph Garth

  3. School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden

    Tino Weinkauf

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Landge, A.G., Bremer, PT., Gyulassy, A., Pascucci, V. (2017). Notes on the Distributed Computation of Merge Trees on CW-Complexes. In: Carr, H., Garth, C., Weinkauf, T. (eds) Topological Methods in Data Analysis and Visualization IV. TopoInVis 2015. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-44684-4_20

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