{
  "abstract": "We give a randomized polynomial-time $0.48$-approximation for maximizing a nonnegative non-monotone $k$-submodular function under a matroid constraint, for every $k\\ge2$. The algorithm combines a top-two label rule with a nested-chain potential and maximum-weight matroid bases. Its analysis reduces the approximation guarantee to a one-dimensional time allocation: a uniform local lower bound leads to a linear differential equation, concavity closes the remaining interval, and two elementary budgets complete the proof. A strict saving in the time budget absorbs sampling and discretization errors, yielding the exact $0.48$ guarantee in the value-oracle model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20140",
  "author_total": 3,
  "authors": [
    {
      "name": "Zizong Wang"
    },
    {
      "name": "Yibo Wang"
    },
    {
      "name": "Wenguo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/epjf0pjp0n5sx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20140",
  "fulltext_url": null,
  "id": "epjf0pjp0n5sx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20140",
  "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|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7222234715",
  "pdf_url": "https://arxiv.org/pdf/2610.20140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/epjf0pjp0n5sx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.20140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20140"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "An Analytic 0.48-Approximation for Non-Monotone k-Submodular Maximization under a Matroid Constraint",
  "title_text": "An Analytic 0.48-Approximation for Non-Monotone k-Submodular Maximization under a Matroid Constraint",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/epjf0pjp0n5sx",
  "venue": "arXiv",
  "versions": []
}