Towards Computing Average Merge Tree Based on the Interleaving Distance
Computational Geometry
2026-03-03 v1
Abstract
The interleaving distance is a key tool for comparing merge trees, which provide topological summaries of scalar functions. In this work, we define an average merge tree for a pair of merge trees using the interleaving distance. Since such an average is not unique, we propose a method to construct a representative average merge tree. We further prove that the resulting merge tree indeed satisfies a natural notion of averaging for the two given merge trees. To demonstrate the structure of the average merge tree, we include illustrative examples.
Cite
@article{arxiv.2603.00783,
title = {Towards Computing Average Merge Tree Based on the Interleaving Distance},
author = {Elena Farahbakhsh Touli and Ingrid Hotz and Talha Bin Masood},
journal= {arXiv preprint arXiv:2603.00783},
year = {2026}
}