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    The ExTreeM-Algorithm efficiently computes merge trees using extremum graphs, significantly accelerating data analysis. This scalable approach offers up to a tenfold speedup and reduced memory usage compared to existing methods.

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    Area of Science:

    • Scientific visualization
    • Data analysis
    • Computational geometry

    Background:

    • Merge trees are crucial for abstracting complex datasets in visualization and analysis.
    • Existing methods for merge tree computation can be computationally intensive and memory-demanding.

    Purpose of the Study:

    • To introduce the ExTreeM-Algorithm, a novel and scalable method for computing merge trees.
    • To demonstrate the efficiency and effectiveness of ExTreeM compared to state-of-the-art algorithms.

    Main Methods:

    • Deriving an extremum graph G from a scalar field f on a cell complex K.
    • Computing the merge tree on the derived extremum graph G, which is equivalent to computing it on K.
    • Utilizing a tailored procedure for merge tree computation on extremum graphs.
    • Implementing parallelizable procedures for all computational steps.

    Main Results:

    • ExTreeM achieves a speedup of up to one order of magnitude over existing algorithms.
    • The algorithm requires significantly less memory compared to state-of-the-art methods.
    • Experiments show excellent scaling behavior on publicly available datasets.
    • Formal proof of correctness for the ExTreeM-Algorithm is provided.

    Conclusions:

    • ExTreeM offers a computationally efficient and scalable solution for merge tree generation.
    • The algorithm's performance improvements make complex data analysis more accessible.
    • ExTreeM represents a significant advancement in the field of scientific visualization and data analysis.