Towards Computing Average Merge Tree Based on the Interleaving Distance
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914361341116416 |
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| author | Touli, Elena Farahbakhsh Hotz, Ingrid Masood, Talha Bin |
| author_facet | Touli, Elena Farahbakhsh Hotz, Ingrid Masood, Talha Bin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00783 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Computing Average Merge Tree Based on the Interleaving Distance Touli, Elena Farahbakhsh Hotz, Ingrid Masood, Talha Bin Computational Geometry 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. |
| title | Towards Computing Average Merge Tree Based on the Interleaving Distance |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2603.00783 |