{"paper":{"title":"Spectral Clustering Oracles in Sublinear Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aida Mousavifar, Christian Sohler, Grzegorz Gluch, Michael Kapralov, Silvio Lattanzi","submitted_at":"2021-01-14T11:09:26Z","abstract_excerpt":"Given a graph $G$ that can be partitioned into $k$ disjoint expanders with outer conductance upper bounded by $\\epsilon\\ll 1$, can we efficiently construct a small space data structure that allows quickly classifying vertices of $G$ according to the expander (cluster) they belong to? Formally, we would like an efficient local computation algorithm that misclassifies at most an $O(\\epsilon)$ fraction of vertices in every expander. We refer to such a data structure as a \\textit{spectral clustering oracle}. Our main result is a spectral clustering oracle with query time $O^*(n^{1/2+O(\\epsilon)})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.05549","kind":"arxiv","version":2},"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/2101.05549/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"}