{"paper":{"title":"Restricted Parameter Range Promise Set Cover Problems Are Easy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hao Chen","submitted_at":"2011-10-10T00:40:28Z","abstract_excerpt":"Let $({\\bf U},{\\bf S},d)$ be an instance of Set Cover Problem, where ${\\bf U}=\\{u_1,...,u_n\\}$ is a $n$ element ground set, ${\\bf S}=\\{S_1,...,S_m\\}$ is a set of $m$ subsets of ${\\bf U}$ satisfying $\\bigcup_{i=1}^m S_i={\\bf U}$ and $d$ is a positive integer. In STOC 1993 M. Bellare, S. Goldwasser, C. Lund and A. Russell proved the NP-hardness to distinguish the following two cases of ${\\bf GapSetCover_{\\eta}}$ for any constant $\\eta > 1$. The Yes case is the instance for which there is an exact cover of size $d$ and the No case is the instance for which any cover of ${\\bf U}$ from ${\\bf S}$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1896","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"}