{
  "abstract": "We study the classical problem of scheduling jobs with random processing times on $m$ identical machines to minimize the expected sum of completion times, for Bernoulli jobs: job $j$ takes time $p_j$ with probability $q_j$ and time $0$ otherwise, and its outcome is revealed when it starts. The benchmark is an optimal adaptive policy. We give a quasi-polynomial-time approximation scheme for every number of machines. Previously, quasi-polynomial time was known to give an $O(\\log N)$-approximation, and approximation schemes were known only for a constant number of distinct sizes. The scheme rests on a simple observation: it suffices to round the times at which machines become free, rather than the times at which jobs start, to a grid whose width is proportional to the job size, and an optimal policy stretched by a factor close to one already respects such grids. We also show that every policy that fixes the order of the jobs in advance loses a factor $Ω(\\log N)$, already on two machines, so a constant factor requires adapting the order to the observed outcomes. Further results include a polynomial-time adaptive rule with ratio $\\min\\{m,1+\\sum_j q_j\\}$, a simpler approximation scheme for a constant number of sizes, and #P-hardness of computing the optimal expected cost on two machines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11481",
  "author_total": 1,
  "authors": [
    {
      "name": "Junho Hwang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/317scz80g6tyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11481",
  "fulltext_url": null,
  "id": "317scz80g6tyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11481",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2209|Scheduling and Optimization Algorithms"
    ]
  ],
  "openalex": "W7221159855",
  "pdf_url": "https://arxiv.org/pdf/2610.11481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/317scz80g6tyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A QPTAS for Stochastic Scheduling of Bernoulli Jobs",
  "title_text": "A QPTAS for Stochastic Scheduling of Bernoulli Jobs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/317scz80g6tyk",
  "venue": "arXiv",
  "versions": []
}