{
  "abstract": "We give a fast algorithm for solving min-cost $k$-commodity flow. The basic idea is to construct an auxiliary linear program that has low rank and whose minimum value is at most $1/k$ times the minimum value of the original problem (thus, solving this auxiliary linear program will make at least $1/k$ fraction of progress in the original problem). Low-rank linear programs can be solved quickly using black-box techniques. Thus, our algorithm runs in time $\\tilde{O}(\\operatorname{poly}(k)(n^{2.5}+m\\sqrt{n}))$ on a directed graph with $n$ vertices and $m$ edges. We do not rely on any fast matrix multiplication.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06665",
  "author_total": 3,
  "authors": [
    {
      "name": "Chenxin Dai"
    },
    {
      "name": "Alicia Stepin"
    },
    {
      "name": "Colin Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7r607z5vhmkvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06665",
  "fulltext_url": null,
  "id": "7r607z5vhmkvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06665",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7220723483",
  "pdf_url": "https://arxiv.org/pdf/2610.06665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7r607z5vhmkvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Faster high-accuracy multicommodity flow in dense graphs",
  "title_text": "Faster high-accuracy multicommodity flow in dense graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7r607z5vhmkvs",
  "venue": "arXiv",
  "versions": []
}