{
  "abstract": "The problem of Private Information Retrieval (PIR) across graph-based replicated systems has seen a surge of interest in recent literature. In such systems, servers are modeled as the vertices of a graph, and each file is represented by an edge connecting the pair of servers that store it. While previous research on Graph-PIR (G-PIR) has focused mostly on perfect information-theoretic privacy, relaxing this constraint has the potential for significantly higher retrieval rates. In this work, we consider the setting of Graph-based Weak Private Information Retrieval (G-WPIR), under an $ε$-privacy metric. We adapt an existing G-WPIR scheme for arbitrary graphs to analyze its performance under the $ε$-privacy metric. Additionally, we establish a lower bound on the expected download cost for arbitrary graphs under the $ε$-privacy metric and derive from it an explicit rate upper bound for complete graphs. Finally, we show the achievable rate-privacy trade-offs for two specific graph classes---complete graphs and complete bipartite graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19456",
  "author_total": 2,
  "authors": [
    {
      "name": "Jayesh Seshadri"
    },
    {
      "name": "Prasad Krishnan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6xqbdcv137n8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19456",
  "fulltext_url": null,
  "id": "f6xqbdcv137n8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19456",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Cryptography and Data Security"
    ]
  ],
  "openalex": "W7221981238",
  "pdf_url": "https://arxiv.org/pdf/2610.19456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6xqbdcv137n8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19456"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Weak Private Information Retrieval for Graph-based Storage under $ε$-privacy",
  "title_text": "Weak Private Information Retrieval for Graph-based Storage under ε-privacy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/f6xqbdcv137n8",
  "venue": "arXiv",
  "versions": []
}