{
  "abstract": "We study a hierarchical clustering problem formulated as a sum of k-medoids objectives. This problem is related to the multi-period p-median problem, but instead of having nested facilities, we consider a hierarchy of nested assignments. We present two Benders formulations from the p-median literature and show how the obtained nested p-median solutions can be converted into hierarchical k-medoids solutions. We validate our methods on various instances. First, we show on small-scale instances that a standard Benders decomposition approach achieves speedups of up to three orders of magnitude over an existing branch-and-price method, while producing hierarchical k-medoids solutions that are at most 5% away from optimality. Second, we present an aggregated Benders heuristic that can handle instances with more than 13,000 observations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25757",
  "author_total": 1,
  "authors": [
    {
      "name": "Rick S. H. Willemsen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erjkvjvzqbjpb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25757",
  "fulltext_url": null,
  "id": "erjkvjvzqbjpb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25757",
  "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",
      "1702|Advanced Clustering Algorithms Research"
    ]
  ],
  "openalex": "W7223012761",
  "pdf_url": "https://arxiv.org/pdf/2610.25757",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/erjkvjvzqbjpb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25757",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25757"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Benders decomposition approach for hierarchical k-medoids",
  "title_text": "A Benders decomposition approach for hierarchical k-medoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/erjkvjvzqbjpb",
  "venue": "arXiv",
  "versions": []
}