{
  "abstract": "A fault-tolerant (FT) connectivity oracle for an $n$-vertex graph $G=(V,E)$ determines whether $G- F$ is connected for any query set $F\\subseteq E$. When the number of failures is unrestricted, prior constructions exhibited a sharp contrast between randomization and determinism: randomized oracles use only $\\widetilde{O}(n)$ space [Duan and Pettie, SICOMP 2020], whereas no deterministic construction was known to improve upon storing $G$ explicitly, requiring $Θ(n^2)$ bits in the worst case. The promise that $F\\subseteq E$ is essential for subquadratic space: allowing arbitrary queries $F\\subseteq V\\times V$ forces quadratic space. For queries containing at most $f$ failures, Khanna, Konrad, and Putterman [SODA 2027] recently constructed deterministic oracles using $\\widetilde{O}(\\sqrt{f}n)$ space that also report approximate distances with polylogarithmic stretch. Their result improves upon the classical $O(fn)$ space bound for deterministic connectivity oracles [Pătraşcu and Thorup, FOCS 2007], but offers no space savings over storing $G$ when $f=Θ(n^2)$. We present the first deterministic connectivity oracles with subquadratic space for failure sets of unrestricted size, using $\\widetilde{O}(n^{7/4})$ space. We also establish the first polynomial separation between deterministic and randomized connectivity oracles, proving that every deterministic oracle requires $\\widetildeΩ(n^{3/2})$ bits in the worst case. For queries containing at most $f$ failures, we obtain deterministic connectivity oracles using $\\widetilde{O}(f^{2/5}n)$ space, improving the dependence on $f$ in the bound of Khanna et al., and prove a lower bound of $\\widetildeΩ(f^{1/4}n)$ bits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06857",
  "author_total": 2,
  "authors": [
    {
      "name": "Merav Parter"
    },
    {
      "name": "Elad Tzalik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/babh26m235rgz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06857",
  "fulltext_url": null,
  "id": "babh26m235rgz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06857",
  "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.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/babh26m235rgz.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Deterministic Fault-Tolerant Connectivity Oracles with Subquadratic Space",
  "title_text": "Deterministic Fault-Tolerant Connectivity Oracles with Subquadratic Space",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:31Z",
  "url": "https://research.draconitic.com/paper/babh26m235rgz",
  "venue": "arXiv",
  "versions": []
}