{
  "abstract": "We revisit the online submodular welfare maximization problem (OSW), a vast generalization of numerous well-studied online allocation problems, including online bipartite matching, display ads and AdWords. A natural greedy OSW algorithm achieves a competitive ratio of $1/2$ [LLN06], and $1-1/e$ under i.i.d. arrivals [KPV13]. Both bounds are tight for polynomial-time algorithms unless NP=RP [KPV13]. The information-theoretic limits for OSW, in contrast, remained open. This prompted researchers to ask for tighter upper bounds [Mehta13] or conjecture the existence of better-competitive (slow) algorithms [Huang23, LTX+23, CHS24, Huang2024, HTW24}. We resolve Mehta's question and refute the subsequent conjectures, proving that the greedy algorithm is in fact tight for both adversarial and i.i.d. arrivals, regardless of computation time. Seemingly contradicting recent $(1-1/e)$-competitive fractional algorithms for OSW [HJP+24,Patton26], we show that this impossibility even holds for fractional algorithms, provided their outputs correspond to marginals that are roundable in hindsight. Conceptually, our proofs can be seen as identifying that a bottleneck for OSW, even under (deterministic) adversarial arrivals, is the inherently random notion of correlation gap [ADSY12].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16060",
  "author_total": 2,
  "authors": [
    {
      "name": "Rajan Udwani"
    },
    {
      "name": "David Wajc"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6td47cvt78qrh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16060",
  "fulltext_url": null,
  "id": "6td47cvt78qrh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16060",
  "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.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7221790276",
  "pdf_url": "https://arxiv.org/pdf/2610.16060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6td47cvt78qrh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Online Submodular Welfare Maximization: Computation is not the Bottleneck",
  "title_text": "Online Submodular Welfare Maximization: Computation is not the Bottleneck",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6td47cvt78qrh",
  "venue": "arXiv",
  "versions": []
}