{"paper":{"title":"Edge covering with budget constrains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"G. Kortsarz, Rajiv Gandhi","submitted_at":"2013-11-04T14:36:54Z","abstract_excerpt":"We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms).\n  Goldschmidt and Hochbaum \\cite{GH97} show that the mvms problem is NP-hard and they give a 3-approximation algorithm for the problem. We improve \\cite{GH97} by giving a ratio of 2. A 2(1+\\epsilon)-approximation for the problem follows from the work of Carnes and Shmoys \\cite{CS08}. We improve the approximation ratio to 2. algorithm for the problem. We show that the natural LP for \\kmin has an integrality gap of 2-o(1)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0713","kind":"arxiv","version":1},"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"}