{
  "abstract": "We show that any $n$-point Euclidean metric admits a non-expansive embedding into the line with average distortion at most $O\\left(\\sqrt{\\frac{\\log n}{\\log\\log n}}\\right)$, matching a known lower bound. We also present two applications of this result. First, we give a cut-player strategy with an optimal spectral guarantee for the undirected cut-matching game. Second, we give an improved spectral approximation for vertex expansion in high-degree graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41945",
  "author_total": 1,
  "authors": [
    {
      "name": "Jack Spalding-Jamieson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cva69901gftmr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41945",
  "fulltext_url": null,
  "id": "cva69901gftmr",
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  "landing_url": "https://arxiv.org/abs/2610.41945",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CG"
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      "arxiv",
      "math.MG"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cva69901gftmr.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion",
  "title_text": "Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/cva69901gftmr",
  "venue": "arXiv",
  "versions": []
}