{
  "abstract": "Kellerhals, Krebs, Nichterlein, and Schmid introduced the optimization problem Tree in Binary Tree (TBT), where, given a tree $T$, the task is to find a binary tree $S^*$ with $V(T)=V(S^*)$ that minimizes $\\sum_{uv\\in E(T)} \\operatorname{dist}_{S^*}(u,v)$. They also introduced the variant Tree in Binary Tree With Steiner Nodes (TBT-SN), where the condition $V(T)=V(S^*)$ is relaxed to $V(T)\\subseteq V(S^*)$. We give a simple linear-time $\\frac{8}{3}$-approximation algorithm for TBT and a polynomial-time approximation scheme (PTAS) for TBT-SN. Our main building idea in both algorithms is to iteratively consider subtrees of the tree $T$ which contain all vertices below some vertex $v$ and construct a solution where $v$ has degree 1. For the PTAS, we cut $T$ into smaller trees, solve these instances, modify the obtained solutions, and combine them to achieve a solution for the original instance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39863",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabian Weisbrodt"
    },
    {
      "name": "Florian Werner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70ke4mde3j0f7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39863",
  "fulltext_url": null,
  "id": "70ke4mde3j0f7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39863",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39863",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70ke4mde3j0f7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39863",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39863"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "From Trees to Binary Trees: Approximation Algorithms and a PTAS",
  "title_text": "From Trees to Binary Trees: Approximation Algorithms and a PTAS",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/70ke4mde3j0f7",
  "venue": "arXiv",
  "versions": []
}