English

Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics

Computational Geometry 2025-01-13 v1

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.

Keywords

Cite

@article{arxiv.2501.05529,
  title  = {Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics},
  author = {Florian Wetzels and Heike Leitte and Christoph Garth},
  journal= {arXiv preprint arXiv:2501.05529},
  year   = {2025}
}
R2 v1 2026-06-28T21:01:52.927Z