{"paper":{"title":"On the approximability of covering points by lines and related problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Adrian Dumitrescu, Minghui Jiang","submitted_at":"2013-12-09T19:14:05Z","abstract_excerpt":"Given a set $P$ of $n$ points in the plane, {\\sc Covering Points by Lines} is the problem of finding a minimum-cardinality set $\\L$ of lines such that every point $p \\in P$ is incident to some line $\\ell \\in \\L$. As a geometric variant of {\\sc Set Cover}, {\\sc Covering Points by Lines} is still NP-hard. Moreover, it has been proved to be APX-hard, and hence does not admit any polynomial-time approximation scheme unless P $=$ NP\\@. In contrast to the small constant approximation lower bound implied by APX-hardness, the current best approximation ratio for {\\sc Covering Points by Lines} is still"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2549","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"}