{
  "abstract": "In the online carpooling problem, edges on $n$ vertices arrive one at a time and must be oriented immediately, so as to keep the difference between the indegree and the outdegree of every vertex small. We give a randomized online algorithm which bounds the largest absolute difference over the first $T$ edges by $O((\\log T)^{1/3})$ with high probability on every input sequence fixed in advance. This proves a conjecture of Kulkarni, Reis and Rothvoss and matches the known worst case lower bound. The algorithm keeps the law of the discrepancy vector dominated in the convex order by a Gaussian measure, and forces the endpoint with the smaller discrepancy to receive the edge whenever the two discrepancies are far apart. In the analysis we show that a vertex of discrepancy $D$ is preceded by a set of $O(D)$ vertices with total discrepancy $Ω(D^2)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00388",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuhao Lei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zqys0hrwqv30.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00388",
  "fulltext_url": null,
  "id": "8zqys0hrwqv30",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00388",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zqys0hrwqv30.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Online carpooling against an oblivious adversary",
  "title_text": "Online carpooling against an oblivious adversary",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8zqys0hrwqv30",
  "venue": "arXiv",
  "versions": []
}