{
  "abstract": "We study Multi-Level Aggregation with Maximum Delay (MLA-MD) on finite weighted rooted trees. Each service pays for a rooted subtree and for the maximum waiting time among the requests it clears. For the offline problem, we give an exact polynomial-time algorithm that computes both the optimum and an optimal service schedule. For the online problem, we give a deterministic $2$-competitive algorithm and, against an oblivious adversary, a randomized $e/(e-1)$-competitive algorithm. Both competitive ratios are optimal, even on rooted paths. We also extend the offline result and both online guarantees to service systems with submodular costs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06796",
  "author_total": 4,
  "authors": [
    {
      "name": "Tianhang Lu"
    },
    {
      "name": "Runtian Ren"
    },
    {
      "name": "Shengcai Liu"
    },
    {
      "name": "Ke Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71qhqv7hmkjad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06796",
  "fulltext_url": null,
  "id": "71qhqv7hmkjad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06796",
  "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.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7202130368",
  "pdf_url": "https://arxiv.org/pdf/2608.06796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71qhqv7hmkjad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.06796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Online Multi-Level Aggregation with Maximum Delay",
  "title_text": "Online Multi-Level Aggregation with Maximum Delay",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/71qhqv7hmkjad",
  "venue": "arXiv",
  "versions": []
}