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    Area of Science:

    • Computational topology
    • Data analysis

    Background:

    • Edit distance calculations on merge trees are crucial for data analysis but computationally challenging (NP-complete).
    • Existing methods struggle with specific data perturbations like saddle swaps, limiting their practical application.

    Purpose of the Study:

    • To introduce a novel heuristic algorithm for deformation-based edit distance on merge trees.
    • To enable a trade-off between accuracy and computational cost using a user-controlled look-ahead parameter.

    Main Methods:

    • Developed a heuristic algorithm for deformation-based edit distance.
    • Incorporated a user-controlled look-ahead parameter to manage accuracy and computational complexity.
    • Achieved a fixed parameter tractable running time, polynomial in input size and exponential in the look-ahead value.

    Main Results:

    • The algorithm efficiently handles saddle swaps, a common challenge in merge tree analysis.
    • Demonstrated computational efficiency and effectiveness in experimental results.
    • Maintained feasible computation times despite increased complexity.

    Conclusions:

    • The novel heuristic algorithm enhances the applicability of deformation-based edit distance for merge trees.
    • The look-ahead parameter provides practical control over computational resources.
    • This method effectively addresses specific data perturbations, improving data analysis capabilities.