{
  "abstract": "Every link in the \\(3\\)-sphere admits a generalised \\(T\\)-link presentation. In this paper, we give an explicit polynomial-time algorithm which, given a signed Artin braid word and the number of strands, computes such a presentation. Combining this construction with Yamada--Vogel braiding gives a polynomial-time conversion from arbitrary oriented combinatorial link diagrams to generalised \\(T\\)-link parameters. We prove polynomial bounds on the number of strands and crossings in the resulting braid. As an application, we prove that a link property or a link invariant is computable in polynomial time from diagrams if and only if the corresponding problem is solvable in polynomial time from generalised \\(T\\)-link parameters, with parameter input measured by the total number of strands and crossings in the corresponding braid diagram. Whenever a classification criterion or an explicit invariant formula is available in these parameters, it can be applied to the original link by substituting the parameters obtained from the diagram. A polynomial-time test or evaluation then gives a polynomial-time procedure on diagrams. We also establish the corresponding transfer for approximating real-valued invariants to prescribed accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42077",
  "author_total": 2,
  "authors": [
    {
      "name": "Thiago de Paiva"
    },
    {
      "name": "Yi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/btyc4bcswbxsq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42077",
  "fulltext_url": null,
  "id": "btyc4bcswbxsq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42077",
  "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.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/btyc4bcswbxsq.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Polynomial-Time Algorithms for Links",
  "title_text": "Polynomial-Time Algorithms for Links",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/btyc4bcswbxsq",
  "venue": "arXiv",
  "versions": []
}