{
  "abstract": "The Beardwood-Halton-Hammersley theorem characterizes the asymptotic length of the optimal Euclidean traveling salesman tour through independent and uniformly distributed random points $X_1,\\ldots,X_n$ in the unit square. It states that there exists a universal constant $β$ such that the length of the shortest tour is asymptotic to $β\\sqrt{n}$ almost surely. The best bounds established to date are $0.6277\\leq β\\leq 0.90367$. In this paper, we improve these bounds to $0.6421\\leqβ\\leq0.8810$. Using importance sampling, we further show that $0.6536\\leq β\\leq 0.8749$ holds with probability at least $1-2\\times 10^{-4}$. Here the probability is taken with respect to the randomness of the sampling procedure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02809",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhuolun Dong"
    },
    {
      "name": "Junyu Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9z96sats3hfn5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02809",
  "fulltext_url": null,
  "id": "9z96sats3hfn5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02809",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "1704|Computational Geometry and Mesh Generation"
    ]
  ],
  "openalex": "W7220378645",
  "pdf_url": "https://arxiv.org/pdf/2610.02809",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9z96sats3hfn5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02809",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02809"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "New Bounds for the Euclidean TSP Constant",
  "title_text": "New Bounds for the Euclidean TSP Constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/9z96sats3hfn5",
  "venue": "arXiv",
  "versions": []
}