Accelerating Computation of Stable Merge Tree Edit Distances using Parameterized Heuristics

TL;DR

This paper introduces a heuristic algorithm with a user-controlled look-ahead parameter for faster computation of stable merge tree edit distances, balancing accuracy and efficiency.

Contribution

It presents a novel fixed parameter tractable heuristic that improves computation times for deformation-based merge tree edit distances with saddle swaps.

Findings

Achieves polynomial runtime in input size with exponential dependence on look-ahead.

Effectively handles saddle swaps in merge trees.

Demonstrates computational efficiency in experiments.

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.