{
  "abstract": "We give the first deterministic polynomial time algorithm that approximates the permanent of arbitrary nonnegative rational matrices within a subexponential factor. For a matrix of order $n$, the approximation factor is \\[ \\exp\\!\\left(O\\!\\left(\\frac{n(\\log\\log n)^2}{\\log n}\\right)\\right)=\\exp(o(n)). \\] All previously known deterministic polynomial time guarantees for unrestricted inputs had approximation factors $\\exp(Ω(n))$. Our proof uses convex optimization to tighten an upper bound on the permanent. The bound is based on weighted sums over all matchings in a bipartite graph representing the matrix, and correlations between unmatched vertices control its error. We approximate these sums deterministically using correlation decay and a bound on the effect of vertex deletion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10516",
  "author_total": 3,
  "authors": [
    {
      "name": "Sergei Kudria"
    },
    {
      "name": "Jason Luo"
    },
    {
      "name": "Mahbod Majid"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0k6d8we9azbms.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10516",
  "fulltext_url": null,
  "id": "0k6d8we9azbms",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10516",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7212171764",
  "pdf_url": "https://arxiv.org/pdf/2609.10516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0k6d8we9azbms.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Subexponential Approximation of the Permanent in Deterministic Polynomial Time",
  "title_text": "Subexponential Approximation of the Permanent in Deterministic Polynomial Time",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/0k6d8we9azbms",
  "venue": "arXiv",
  "versions": []
}