{
  "abstract": "In this paper we consider the problem of computing a positive diagonal scaling of a $d \\times d$ symmetric $M$-matrix so that all row and column sums are $1$. We provide a poly-logarithmic iteration algorithm that solves this problem to high accuracy, where the cost of each iteration is dominated by the cost of solving a Laplacian system. This improves upon the recent $\\tilde{O}(d^{1/3})$ iteration bound of [Vladu STOC 2025] and yields a randomized algorithm for the problem that runs in near-linear time and poly-logarithmic parallel depth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22302",
  "author_total": 3,
  "authors": [
    {
      "name": "Chih-Hung Liu"
    },
    {
      "name": "Aaron Sidford"
    },
    {
      "name": "Ta-Wei Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cs7ej3sa7fapz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22302",
  "fulltext_url": null,
  "id": "cs7ej3sa7fapz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22302",
  "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.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7222611316",
  "pdf_url": "https://arxiv.org/pdf/2610.22302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cs7ej3sa7fapz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Near-Optimal Parallel $M$-Matrix Scaling",
  "title_text": "Near-Optimal Parallel M-Matrix Scaling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/cs7ej3sa7fapz",
  "venue": "arXiv",
  "versions": []
}