{"paper":{"title":"Local Graph Clustering Beyond Cheeger's Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Silvio Lattanzi, Vahab Mirrokni, Zeyuan Allen Zhu","submitted_at":"2013-04-30T19:57:36Z","abstract_excerpt":"Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms guarantee an output conductance of $\\tilde{O}(\\sqrt{\\phi(A)})$ when the target set $A$ has conductance $\\phi(A)\\in[0,1]$. In this paper, we improve it to $$\\tilde{O}\\bigg( \\min\\Big\\{\\sqrt{\\phi(A)}, \\frac{\\phi(A)}{\\sqrt{\\mathsf{Conn}(A)}} \\Big\\} \\bigg)\\enspace, $$ where the internal connectivity parameter $\\mathsf{Conn}(A) \\in [0,1]$ is defined as the reciprocal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8132","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":""},"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"}