{
  "abstract": "In spatial matching markets, a supply unit's flexibility is measured by its service radius, the maximum distance at which it can serve demand. In dimensions $k \\geq 2$, we study how a platform should allocate service radii among the supply nodes subject to a budget on their sum. The platform makes this choice before observing supply and demand locations, with the objective of maximizing the expected fulfilled demand. We show that the shape of a preferred allocation depends on the total budget: under suitable conditions, large budgets favor allocations that are more uniform in the sense of majorization, while small budgets favor concentration. We also characterize a non-uniform allocation that is asymptotically optimal for a very-sparse regime, and show that the uniform allocation is suboptimal in this regime. Our results provide theoretical explanations for the radius allocation questions raised by the numerical experiments in [ASY26b].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36361",
  "author_total": 2,
  "authors": [
    {
      "name": "Taha Ameen"
    },
    {
      "name": "Sophie H. Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aver7jd87rbdq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36361",
  "fulltext_url": null,
  "id": "aver7jd87rbdq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36361",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7214994840",
  "pdf_url": "https://arxiv.org/pdf/2609.36361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aver7jd87rbdq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36361"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Distance flexibility in spatial matching: the value of concentration",
  "title_text": "Distance flexibility in spatial matching: the value of concentration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/aver7jd87rbdq",
  "venue": "arXiv",
  "versions": []
}