{
  "abstract": "This paper presents a near-quadratic-time algorithm that correctly matches almost all nodes of two correlated Erdős-Rényi graphs without any incorrect matches. Each graph has average degree $λ$ and its edges are subsampled from a common parent Erdős-Rényi graph with $n$ nodes, with subsampling probability $s$. The nodes of one graph are then relabeled by an unknown permutation. The algorithm is built on a test for correlated versus independent Galton-Watson trees with approximated likelihood ratios. For every constant $s>\\sqrt{C_{\\mathrm{Otter}}}$, where $C_{\\mathrm{Otter}}\\approx0.338$ is Otter's tree-counting constant, and every $λ=ω(1)$ with $λ=(\\log n)^{O(1)}$, the algorithm outputs a partial matching of size $n-o(n)$ that contains no incorrect matches with high probability. If, in addition, $λs\\ge(1+ε)\\log n$ for a constant $ε>0$, a seeded completion step recovers the permutation exactly. In both cases, the time complexity of the algorithm is $n^{2+o(1)}$ with high probability, whereas previous polynomial-time algorithms with the same guarantees either have a time-complexity bound whose exponent goes to $\\infty$ as $s$ approaches $\\sqrt{C_{\\mathrm{Otter}}}$ from above, or apply only when $s$ is close to $1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02281",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiale Cheng"
    },
    {
      "name": "Ziao Wang"
    },
    {
      "name": "Lei Ying"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vx50fmtme30x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02281",
  "fulltext_url": null,
  "id": "7vx50fmtme30x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02281",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02281",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vx50fmtme30x.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02281",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02281"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Near-Quadratic Error-Free Graph Matching above Otter's Threshold via Approximate Local Tree Correlation Testing",
  "title_text": "Near-Quadratic Error-Free Graph Matching above Otter's Threshold via Approximate Local Tree Correlation Testing",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/7vx50fmtme30x",
  "venue": "arXiv",
  "versions": []
}