{"paper":{"title":"Approximating Non-Uniform Sparsest Cut via Generalized Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ali Kemal Sinop, Venkatesan Guruswami","submitted_at":"2011-12-18T02:41:12Z","abstract_excerpt":"We give an approximation algorithm for non-uniform sparsest cut with the following guarantee: For any $\\epsilon,\\delta \\in (0,1)$, given cost and demand graphs with edge weights $C, D$ respectively, we can find a set $T\\subseteq V$ with $\\frac{C(T,V\\setminus T)}{D(T,V\\setminus T)}$ at most $\\frac{1+\\epsilon}{\\delta}$ times the optimal non-uniform sparsest cut value, in time $2^{r/(\\delta\\epsilon)}\\poly(n)$ provided $\\lambda_r \\ge \\Phi^*/(1-\\delta)$. Here $\\lambda_r$ is the $r$'th smallest generalized eigenvalue of the Laplacian matrices of cost and demand graphs; $C(T,V\\setminus T)$ (resp. $D("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4109","kind":"arxiv","version":4},"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"}