{"paper":{"title":"An Improved Approximation for $k$-median, and Positive Correlation in Budgeted Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aravind Srinivasan, Bartosz Rybicki, Jaros{\\l}aw Byrka, Khoa Trinh, Thomas Pensyl","submitted_at":"2014-06-11T16:14:27Z","abstract_excerpt":"Dependent rounding is a useful technique for optimization problems with hard budget constraints. This framework naturally leads to \\emph{negative correlation} properties. However, what if an application naturally calls for dependent rounding on the one hand, and desires \\emph{positive} correlation on the other? More generally, we develop algorithms that guarantee the known properties of dependent rounding, but also have nearly best-possible behavior - near-independence, which generalizes positive correlation - on \"small\" subsets of the variables. The recent breakthrough of Li & Svensson for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2951","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"}