{"paper":{"title":"Arboricity and Random Edge Queries Matter for Triangle Counting using Sublinear Queries","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arijit Bishnu, Debarshi Chanda, Gopinath Mishra","submitted_at":"2025-02-21T11:04:43Z","abstract_excerpt":"Given a simple, unweighted, undirected graph $G=(V,E)$ with $|V|=n$ and $|E|=m$, and parameters $0 < \\varepsilon, \\delta <1$, along with \\texttt{Degree}, \\texttt{Neighbour}, \\texttt{Edge} and \\texttt{RandomEdge} query access to $G$, we provide a query based randomized algorithm to generate an estimate $\\widehat{T}$ of the number of triangles $T$ in $G$, such that $\\widehat{T} \\in [(1-\\varepsilon)T , (1+\\varepsilon)T]$ with probability at least $1-\\delta$. The query complexity of our algorithm is $\\widetilde{O}\\left({m \\alpha \\log(1/\\delta)}/{\\varepsilon^3 T}\\right)$, where $\\alpha$ is the arbo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.15379","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.15379/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}