{
  "abstract": "We give an FPRAS for the permanent of an $n\\times n$ $0/1$ matrix with running time $\\widetilde O(n^3)$. Our algorithm extends to a strongly polynomial FPRAS for arbitrary nonnegative matrices with the same running-time bound (but in the unit-cost arithmetic model). Jerrum, Sinclair, and Vigoda (2004) gave the first FPRAS for the permanent of a nonnegative matrix. The running time was subsequently improved to $\\widetilde{O}(n^7)$ by Bezáková, Štefankovič, Vazirani, and Vigoda (2008), and recently to $\\widetilde{O}(n^6)$ by Chen, Vigoda, and Yang (2026). We introduce a multicommodity-flow bound inspired by electrical flows, replacing the usual path-length factor by routing energy. For the classical JSV chain with perfect-matching weights multiplied by $n^2$, we prove a relaxation-time bound of $O(n^3\\log n)$ and obtain comparable bounds for estimating the stationary probabilities of having a specified pair of unmatched vertices. We use a separate chain on assignments to generate a warm start at any given temperature, avoiding the long initialization of the JSV chain. Finally, we replace the JSV chain with a new chain that uses only $n$ hole weights and speeds up hole-weight learning by a factor of $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20717",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiaoyu Chen"
    },
    {
      "name": "Heng Guo"
    },
    {
      "name": "Eric Vigoda"
    },
    {
      "name": "Xiongxin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6zdpwrdtvnzej.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20717",
  "fulltext_url": null,
  "id": "6zdpwrdtvnzej",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20717",
  "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.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7213585801",
  "pdf_url": "https://arxiv.org/pdf/2609.20717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6zdpwrdtvnzej.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.20717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "An $\\widetilde{O}(n^3)$-time FPRAS for the Permanent",
  "title_text": "An Õ(n^3)-time FPRAS for the Permanent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/6zdpwrdtvnzej",
  "venue": "arXiv",
  "versions": []
}