{
  "abstract": "In communication networks, network coding allows intermediate nodes to combine messages, achieving transmission rates unattainable by routing alone in many multicast settings. In multiple unicast, where each source sends a message only to its prescribed destination, a central question is under what conditions fractional routing suffices to attain the transmission rates supported by network coding. We prove that, for any given collection of multiple-unicast demands in an undirected network, if the maximum flow between every pair of distinct destinations is at least the total demand rate, then the following are equivalent in feasibility: multiple-unicast coding, multiple-unicast fractional routing, and simultaneous fractional routing of all source rates to any fixed destination. Verifying this pairwise maximum-flow condition and, when it holds, deciding feasibility of the given multiple-unicast demands require at most as many maximum-flow computations as there are destinations. As a direct corollary, we prove the Langberg--Médard conjecture: if a directed network supports coded multicast of independent source messages at a common rate to every destination, then removing arc directions without changing capacities permits simultaneous fractional routing at that rate for all prescribed source--destination pairs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33655",
  "author_total": 3,
  "authors": [
    {
      "name": "Sirui Liu"
    },
    {
      "name": "Zongpeng Li"
    },
    {
      "name": "Baochun Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mvjz4hk02wqw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33655",
  "fulltext_url": null,
  "id": "0mvjz4hk02wqw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33655",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1705|Cooperative Communication and Network Coding"
    ]
  ],
  "openalex": "W7223996388",
  "pdf_url": "https://arxiv.org/pdf/2610.33655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mvjz4hk02wqw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.33655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33655"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "When Multiple-Unicast Feasibility Is Equivalent to Single-Sink Routability",
  "title_text": "When Multiple-Unicast Feasibility Is Equivalent to Single-Sink Routability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/0mvjz4hk02wqw",
  "venue": "arXiv",
  "versions": []
}