{"paper":{"title":"Nonuniform Graph Partitioning with Unrelated Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Konstantin Makarychev, Yury Makarychev","submitted_at":"2014-01-03T19:10:51Z","abstract_excerpt":"We give a bi-criteria approximation algorithm for the Minimum Nonuniform Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar (2014). In this problem, we are given a graph $G=(V,E)$ on $n$ vertices and $k$ numbers $\\rho_1,\\dots, \\rho_k$. The goal is to partition the graph into $k$ disjoint sets $P_1,\\dots, P_k$ satisfying $|P_i|\\leq \\rho_i n$ so as to minimize the number of edges cut by the partition. Our algorithm has an approximation ratio of $O(\\sqrt{\\log n \\log k})$ for general graphs, and an $O(1)$ approximation for graphs with excluded minors. This is an im"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0699","kind":"arxiv","version":3},"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"}