{
  "abstract": "Over the past decade, a growing body of research has shown that $γ$-weak submodularity broadly arises in numerous subset selection tasks, including feature selection, neural network pruning, and video summarization. Despite its prevalence, maximizing a $γ$-weakly submodular function subject to a general matroid constraint remains challenging. To date, the only known approximation guarantee is the conservative $(1+1/γ)^{-2}$ factor established by \\citet{chen2018weakly}. To improve upon this result, this paper proposes a novel algorithm called \\MGPE, which repeatedly performs maximum-gain local exchanges through careful control of a non-homogeneous Poisson clock, and proves that this \\MGPE\\ can attain an approximation ratio arbitrarily close to $ρ_γ=1-\\left(γ/(2-γ)\\right)^{ \\frac{γ^2}{2(1-γ)} }$. In sharp contrast to the previous guarantee, our obtained factor $ρ_γ$ not only strictly improves upon $(1+1/γ)^{-2}$ for every $γ\\in(0,1]$, but also can asymptotically approach the optimal $(1-1/e)$-approximation for submodular maximization as $γ\\to1$. Furthermore, we surprisingly find that when the matroid constraint reduces to a cardinality or the objective satisfies the stronger notion of $α$-weak DR-submodularity, \\MGPE\\ can automatically recover the tight approximation ratios of $1-e^{-γ}$ and $1-e^{-α}$, respectively. Here, $α\\in(0,1]$ denotes the DR ratio.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24569",
  "author_total": 5,
  "authors": [
    {
      "name": "Shi Fu"
    },
    {
      "name": "Youming Qiao"
    },
    {
      "name": "Dacheng Tao"
    },
    {
      "name": "Zongqi Wan"
    },
    {
      "name": "Qixin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/81zndnq0wbqvg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24569",
  "fulltext_url": null,
  "id": "81zndnq0wbqvg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24569",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7214008901",
  "pdf_url": "https://arxiv.org/pdf/2609.24569",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81zndnq0wbqvg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.24569",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24569"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Poisson Exchange Beyond Submodularity: Effective Approximation Algorithms for Offline and Online Subset Selection over Matroids",
  "title_text": "Poisson Exchange Beyond Submodularity: Effective Approximation Algorithms for Offline and Online Subset Selection over Matroids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/81zndnq0wbqvg",
  "venue": "arXiv",
  "versions": []
}