{
  "abstract": "We prove that every water transport problem on an $n$-vertex graph has an optimal strategy of length at most $n^{(2+o(1))n}$. More strongly, the convex hull of all strategy operators stabilizes within the same bound. We also give a five-vertex instance in which every optimal strategy repeats a nontrivial connected averaging set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30932",
  "author_total": 2,
  "authors": [
    {
      "name": "Tianyi Tao"
    },
    {
      "name": "Bohan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dw2g238m8bm5y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30932",
  "fulltext_url": null,
  "id": "dw2g238m8bm5y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30932",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7214588014",
  "pdf_url": "https://arxiv.org/pdf/2609.30932",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dw2g238m8bm5y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30932",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30932"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Uniform Bound on Optimal Strategy Length in Water Transport Problem",
  "title_text": "A Uniform Bound on Optimal Strategy Length in Water Transport Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/dw2g238m8bm5y",
  "venue": "arXiv",
  "versions": []
}