{
  "abstract": "Tree-based networks are a broad graph class in phylogenetics which posit a model of evolution composed of tree-like processes and hybridization events. Hence, for any non-tree-based phylogenetic network, it is meaningful to study the magnitude of violation of the tree-based model assumptions. For rooted networks, we introduce the proximity measure delta_rNNI, defined by the minimum number of rooted nearest neighbor interchanges (NNIs) required to transform a network into a tree-based network. For binary networks, we prove that delta_rNNI is pairwise distinct from all previously known proximity measures in the literature and that no approximation guarantees between delta_rNNI and other known proximity measures holds. In addition, we characterize a family of networks for which a linear time lower bound on delta_rNNI is tight. Moreover, we analyze upper bounds and give an exact solution algorithm to compute delta_rNNI.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23426",
  "author_total": 2,
  "authors": [
    {
      "name": "Martin Frohn"
    },
    {
      "name": "Takatora Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33y8sgd5g7scf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23426",
  "fulltext_url": null,
  "id": "33y8sgd5g7scf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23426",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "1312|Genomics and Phylogenetic Studies"
    ]
  ],
  "openalex": "W7222954092",
  "pdf_url": "https://arxiv.org/pdf/2610.23426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33y8sgd5g7scf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23426"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The nearest neighbor interchange proximity measure for the tree-basedness of rooted binary phylogenetic networks",
  "title_text": "The nearest neighbor interchange proximity measure for the tree-basedness of rooted binary phylogenetic networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:34Z",
  "url": "https://research.draconitic.com/paper/33y8sgd5g7scf",
  "venue": "arXiv",
  "versions": []
}