{
  "abstract": "We introduce Lehmer branch-and-price, an exact algorithm for bin packing and cutting stock problems built on the Lehmer transform, the ratio of Mellin transforms of item weights at consecutive orders. The transform maps each bin, a finite multiset of item weights, to a smooth increasing curve, and so gives the discrete problem a continuous representation on which the tools of analysis, such as convexity, exponential families and smoothing, can act. Read along this curve, the problem yields an explicit dual solution, a monotone representation of the dominance order, a family of constructive heuristics with first fit decreasing as its limit, and an integer identity that tells when the linear relaxation can decide an instance and when only a perfect packing can improve the best solution known. Lifted from items to patterns, the transform gives entropic column generation, a new form of column generation that bounds the relaxation from both sides at every iteration without solving the pricing problem exactly, maximizes a smoothed dual at an explicit rate, and measures by an entropy how much the relaxation leaves undecided. We show that the proposed algorithm outperforms the state-of-the-art methods on the standard benchmark in both the number of instances solved and the computational time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01251",
  "author_total": 1,
  "authors": [
    {
      "name": "Masoud Ataei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03ttmse2hj6sp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01251",
  "fulltext_url": null,
  "id": "03ttmse2hj6sp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01251",
  "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.DM"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01251",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03ttmse2hj6sp.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01251",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01251"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Entropic Column Generation and Lehmer Branch-and-Price for Bin Packing Problem",
  "title_text": "Entropic Column Generation and Lehmer Branch-and-Price for Bin Packing Problem",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/03ttmse2hj6sp",
  "venue": "arXiv",
  "versions": []
}