{
  "abstract": "The weighted $k$-matroid intersection problem asks for a maximum-weight set that is independent in each of $k$ matroids on a common ground set. The natural LP relaxation optimizes over the intersection of the $k$ matroid independent set polytopes. It is conjectured that this LP has integrality gap at most $k-1$. The conjecture is known for $k\\le3$, but for $k\\ge4$ the best general upper bound was $k$. We improve this bound to $k-1+1/k$. More generally, we prove that the natural LP of a $p$-matchoid has integrality gap at most $p-1+1/p$, with a deterministic LP-relative algorithm attaining the same factor. The matchoid extension resolves the $p$-matchoid part of a conjecture of Lee, Sviridenko, and Vondrák; projective planes give explicit tight instances whenever one of order $p-1$ exists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21477",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu Cong"
    },
    {
      "name": "Yajie Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2whefzyjp8fhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21477",
  "fulltext_url": null,
  "id": "2whefzyjp8fhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21477",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7213882236",
  "pdf_url": "https://arxiv.org/pdf/2609.21477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2whefzyjp8fhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Integrality-Gap Bounds for Weighted Matchoids and Matroid Intersection",
  "title_text": "Integrality-Gap Bounds for Weighted Matchoids and Matroid Intersection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/2whefzyjp8fhz",
  "venue": "arXiv",
  "versions": []
}