{"paper":{"title":"A New Upper Bound for the VC-Dimension of Visibility Regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexander Gilbers, Rolf Klein","submitted_at":"2012-06-25T14:12:52Z","abstract_excerpt":"In this paper we are proving the following fact. Let P be an arbitrary simple polygon, and let S be an arbitrary set of 15 points inside P. Then there exists a subset T of S that is not \"visually discernible\", that is, T is not equal to the intersection of S with the visibility region vis(v) of any point v in P. In other words, the VC-dimension d of visibility regions in a simple polygon cannot exceed 14. Since Valtr proved in 1998 that d \\in [6,23] holds, no progress has been made on this bound. By epsilon-net theorems our reduction immediately implies a smaller upper bound to the number of g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5689","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"}