{
  "abstract": "Parallel AI agents can produce useful local edits yet degrade a shared solution when their edits are combined. We model this coordination problem as discrete block optimization with an exactly evaluable objective and a known dependency graph. Independent sets certify compatible edits whose verified gains, measured against the same current solution, add exactly. A coordinator constructs a safe compatible candidate and can also evaluate interacting edits to capture favorable interactions. We prove that an optimal fractional coloring yields a merger that preserves a $1/χ_f(G)$ fraction of the total verified local improvement, where $χ_f(G)$ is the graph's fractional chromatic number. This guarantee is tight among mergers that select a subset of the same proposals. Under conditional local-improvement guarantees and a block error-bound condition, repeated collaboration converges geometrically in the objective gap. The rate separates task structure, agent allocation, and computation cost, yielding a linear program for agent assignment and an explicit time-cost trade-off. Code-repair experiments show that verified merging resolves conflicts between individually useful edits that cause naive merging to fail. On larger conflict-free tasks, parallel agents reduce modeled completion time at higher input-token-equivalent cost. On three public road networks, fractional integration retains 922 units of verified graph-cut improvement across 90 paired runs. For route-search agents sharing exclusive access to vehicle routes, fractional scheduling reduces measured wall time by a median of 15% across twelve paired runs, with route-cost changes varying across runs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30074",
  "author_total": 3,
  "authors": [
    {
      "name": "Hanmin Li"
    },
    {
      "name": "Yury Demidovich"
    },
    {
      "name": "Peter Richtárik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ama2cvr8z88v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30074",
  "fulltext_url": null,
  "id": "2ama2cvr8z88v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30074",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.MA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1705|Distributed Control Multi-Agent Systems"
    ]
  ],
  "openalex": "W7223218906",
  "pdf_url": "https://arxiv.org/pdf/2610.30074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ama2cvr8z88v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.30074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30074"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Parallel AI Agent Collaboration as Graph-Structured Distributed Block Optimization",
  "title_text": "Parallel AI Agent Collaboration as Graph-Structured Distributed Block Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2ama2cvr8z88v",
  "venue": "arXiv",
  "versions": []
}