Work

Accelerating Computation of Stable Merge Tree Edit Distances Using Parameterized Heuristics

Year: 2025

Type: article

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.

Source: IEEE Transactions on Visualization and Computer Graphics

DOI: 10.1109/tvcg.2025.3567120

Authors: Florian Wetzels, Heike Leitte, Christoph Garth

Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,645

Funder: Deutsche Forschungsgemeinschaft