{
  "abstract": "GPU-accelerated first-order methods are increasingly effective for solving large-scale linear programs (LPs), yet LP preprocessing remains predominantly CPU-based and can become costly. A key challenge is that dependencies among presolve reductions and frequent modifications to sparse LP data make efficient GPU parallelization difficult. To address this challenge, we develop GPU-Preprocessor, a GPU-native LP preprocessing framework that integrates folding and presolve. To efficiently implement folding on GPUs, we adapt a randomized partition refinement algorithm to LP folding, using sparse matrix-vector products and parallel sorting to construct stable row and column partitions. For presolve, we introduce a new piecewise-linear reformulation rule that exploits underlying convex piecewise-linear structure to obtain sparser LP representations. We also develop a framework that combines phase scheduling with a Scan-Plan-Apply design to coordinate presolve rules and reduce sparse-matrix reconstruction overhead through batched updates. Numerical experiments on three LP benchmark sets show that GPU-Preprocessor achieves greater average problem-size reductions than PSLP and Gurobi Presolve, with SGM10 preprocessing-time speedups of up to $43.9\\times$ and $677.7\\times$, respectively. Here, SGM10 denotes the shifted geometric mean with a 10-second shift. On the largest tested quadratic assignment problem LP relaxation, these speedups reach $126.3\\times$ and $2{,}207.9\\times$. When integrated with the GPU-accelerated LP solver HPR-LP, GPU-Preprocessor achieves SGM10 speedups of $2.5\\times$ to $5.0\\times$ in combined preprocessing and solving time over HPR-LP without preprocessing. The code is available at https://github.com/PolyU-IOR/GPU-Preprocessor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19840",
  "author_total": 7,
  "authors": [
    {
      "name": "Kaihuang Chen"
    },
    {
      "name": "Jiawei Lu"
    },
    {
      "name": "Defeng Sun"
    },
    {
      "name": "Yancheng Yuan"
    },
    {
      "name": "Guojun Zhang"
    },
    {
      "name": "Xiangyu Zhang"
    },
    {
      "name": "Xinyuan Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nqw3wg2w49tn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19840",
  "fulltext_url": null,
  "id": "7nqw3wg2w49tn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19840",
  "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.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7222025700",
  "pdf_url": "https://arxiv.org/pdf/2610.19840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nqw3wg2w49tn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "GPU-Accelerated Preprocessing for Large-Scale Linear Programming",
  "title_text": "GPU-Accelerated Preprocessing for Large-Scale Linear Programming",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/7nqw3wg2w49tn",
  "venue": "arXiv",
  "versions": []
}