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  "path": "/abs/2603.00783v1",
  "publishedAt": "2026-03-03T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Elena Farahbakhsh Touli",
    "Ingrid Hotz",
    "Talha Bin Masood"
  ],
  "textContent": "**Authors:** Elena Farahbakhsh Touli, Ingrid Hotz, Talha Bin Masood\n\nThe 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"
}