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arXiv · 2501.05529

Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics

Florian Wetzels·Heike Leitte·Christoph Garth
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Abstract

In this paper, we present a novel heuristic algorithm for the stable but NP-complete deformation-based edit distance on merge trees. Our key contribution is the introduction of a user-controlled look-ahead parameter that allows to trade off accuracy and computational cost. We achieve a fixed parameter tractable running time that is polynomial in the size of the input but exponential in the look-ahead value. This extension unlocks the potential of the deformation-based edit distance in handling saddle swaps, while maintaining feasible computation times. Experimental results demonstrate the computational efficiency and effectiveness of this approach in handling specific perturbations.

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Florian Wetzels, Heike Leitte, Christoph Garth. 2025-01-09. Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics. https://arxiv.org/abs/2501.05529

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