{"paper":{"title":"Near Optimal LP Rounding Algorithm for Correlation Clustering on Complete and Complete k-partite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Grigory Yaroslavtsev, Konstantin Makarychev, Shuchi Chawla, Tselil Schramm","submitted_at":"2014-12-01T21:11:40Z","abstract_excerpt":"We give new rounding schemes for the standard linear programming relaxation of the correlation clustering problem, achieving approximation factors almost matching the integrality gaps:\n  - For complete graphs our appoximation is $2.06 - \\varepsilon$ for a fixed constant $\\varepsilon$, which almost matches the previously known integrality gap of $2$.\n  - For complete $k$-partite graphs our approximation is $3$. We also show a matching integrality gap.\n  - For complete graphs with edge weights satisfying triangle inequalities and probability constraints, our approximation is $1.5$, and we show a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0681","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"}