{
  "abstract": "The branch-and-cut paradigm has led to effective solvers for a wide range of mathematical optimization problems. Despite significant theoretical work on pure branching and pure cutting, less is known about their interaction. We study an extended abstract branch-and-cut model to investigate tradeoffs between branching and cutting, including the time to generate cuts. We prove that, under symmetric branching, some minimal-time tree has all cuts at the root, before the first branching node, and that there is an asymmetric setting where some minimal-time tree has no internal cuts, i.e., cuts both preceded and followed by branching. For other settings, although a root-cut tree may be suboptimal and differ substantially in structure from a minimal-time tree, it nevertheless provides a reliable approximation whose tree time does not deviate arbitrarily from the optimum. For constant cut strength and bounded time functions, we show that the best root-cut tree is asymptotically optimal as the target bound grows. In addition, under a single-cut-per-path restriction, we characterize when some minimal-time tree has an internal cut. Lastly, simulations indicate that the best root-cut tree is much closer to a minimal-time tree than our worst-case approximation guarantee suggests.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31774",
  "author_total": 2,
  "authors": [
    {
      "name": "Boyang Han"
    },
    {
      "name": "Aleksandr M. Kazachkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/13mxcywybhdft.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31774",
  "fulltext_url": null,
  "id": "13mxcywybhdft",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31774",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.31774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/13mxcywybhdft.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Strength of Root Cuts in an Extended Abstract Branch-and-Cut Model",
  "title_text": "The Strength of Root Cuts in an Extended Abstract Branch-and-Cut Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/13mxcywybhdft",
  "venue": "arXiv",
  "versions": []
}