{
  "abstract": "We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17146",
  "author_total": 3,
  "authors": [
    {
      "name": "Giacomo Como"
    },
    {
      "name": "Fabio Fagnani"
    },
    {
      "name": "Stephane Durand"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tz3dh3zzqhhd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17146",
  "fulltext_url": null,
  "id": "9tz3dh3zzqhhd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17146",
  "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.GT"
    ],
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      "arxiv",
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      "arxiv",
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      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
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  "openalex": "W7213397742",
  "pdf_url": "https://arxiv.org/pdf/2609.17146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tz3dh3zzqhhd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Intervention problems in the Linear Threshold Model: A general formulation and new results",
  "title_text": "Intervention problems in the Linear Threshold Model: A general formulation and new results",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/9tz3dh3zzqhhd",
  "venue": "arXiv",
  "versions": []
}