{
  "abstract": "Submodular maximization arises in a wide range of combinatorial optimization problems and has been extensively studied from the perspective of approximation algorithms. For maximizing nonnegative, non-monotone submodular functions subject to a matroid constraint, randomized algorithms achieve a $0.401$-approximation, whereas obtaining comparable deterministic guarantees remains challenging. In this paper, we present a deterministic $0.401$-approximation algorithm in the exact value and independence oracle model, improving upon the previous deterministic guarantee of $(0.385-\\varepsilon)$ \\cite{ChenGLSZ2026}. Our algorithm builds on the extended multilinear extension and provides a deterministic implementation of the recursive guided framework underlying the randomized $0.401$-approximation algorithm. The main technical ingredient is a direction oracle supported on at most two partitioned matroid bases. This oracle simultaneously satisfies the growth condition required by the extended-multilinear update and an approximate stationarity condition needed to construct the recursive guides. The resulting finite-support representation enables exact evaluation of the relevant expectations and marginal values without random sampling. The algorithm uses polynomially many value- and independence-oracle queries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16785",
  "author_total": 4,
  "authors": [
    {
      "name": "Shengminjie Chen"
    },
    {
      "name": "Kaifeng Lin"
    },
    {
      "name": "Xiaoming Sun"
    },
    {
      "name": "Jialin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1q66ake477yr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16785",
  "fulltext_url": null,
  "id": "d1q66ake477yr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16785",
  "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.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7221792218",
  "pdf_url": "https://arxiv.org/pdf/2610.16785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1q66ake477yr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16785"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Deterministic $0.401$-Approximation for Non-monotone Submodular Maximization under Matroid Constraints",
  "title_text": "A Deterministic $0.401$-Approximation for Non-monotone Submodular Maximization under Matroid Constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/d1q66ake477yr",
  "venue": "arXiv",
  "versions": []
}