{"paper":{"title":"New results on stabbing segments with a polygon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Alexander Pilz, Carlos Seara, Jos\\'e Miguel D\\'iaz-B\\'a\\~nez, Matias Korman, Pablo P\\'erez-Lantero, Rodrigo I. Silveira","submitted_at":"2012-11-07T09:22:51Z","abstract_excerpt":"We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon $\\mathcal{P}$ if at least one of its two endpoints is contained in $\\mathcal{P}$. A segment set $S$ is stabbed by $\\mathcal{P}$ if every segment of $S$ is stabbed by $\\mathcal{P}$. We show that if $S$ is a set of pairwise disjoint segments, the problem of computing the minimum perimeter polygon stabbing $S$ can be solved in polynomial time. We also prove that for general segments the problem is NP-hard. Further, an adaptation of our polynomial-time algorithm solves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1490","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"}