{"paper":{"title":"Approximation Algorithm for Sparsest k-Partitioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anand Louis, Konstantin Makarychev","submitted_at":"2013-06-18T23:00:35Z","abstract_excerpt":"Given a graph $G$, the sparsest-cut problem asks to find the set of vertices $S$ which has the least expansion defined as $$\\phi_G(S) := \\frac{w(E(S,\\bar{S}))}{\\min \\set{w(S), w(\\bar{S})}}, $$ where $w$ is the total edge weight of a subset. Here we study the natural generalization of this problem: given an integer $k$, compute a $k$-partition $\\set{P_1, \\ldots, P_k}$ of the vertex set so as to minimize $$ \\phi_k(\\set{P_1, \\ldots, P_k}) := \\max_i \\phi_G(P_i). $$ Our main result is a polynomial time bi-criteria approximation algorithm which outputs a $(1 - \\e)k$-partition of the vertex set such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4384","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"}