{"paper":{"title":"Convex partial transversals of planar regions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Frank Staals, Irina Kostitsyna, J\\'er\\^ome Urhausen, Jordi L. Vermeulen, Lionov Wiratma, Maarten L\\\"offler, Marc van Kreveld, Mees van de Kerkhof, Vahideh Keikha","submitted_at":"2018-09-26T15:50:00Z","abstract_excerpt":"We consider the problem of testing, for a given set of planar regions $\\cal R$ and an integer $k$, whether there exists a convex shape whose boundary intersects at least $k$ regions of $\\cal R$. We provide a polynomial time algorithm for the case where the regions are disjoint line segments with a constant number of orientations. On the other hand, we show that the problem is NP-hard when the regions are intersecting axis-aligned rectangles or 3-oriented line segments. For several natural intermediate classes of shapes (arbitrary disjoint segments, intersecting 2-oriented segments) the problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10078","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"}