{"paper":{"title":"Minimum Opaque Covers for Polygonal Regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Doreen Thomas, Jia F. Weng, J. Scott Provan, Marcus Brazil","submitted_at":"2012-10-30T19:52:37Z","abstract_excerpt":"The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is the problem of finding, for a set S in Euclidean space, the minimum-length set F which intersects every straight line passing through S. In spite of its simplicity, the problem remains remarkably intractable. The aim of this paper is to establish a framework and fundamental results for minimum opaque covers where S is a polygonal region in two-dimensional space. We begin by giving some general results about opaque covers, and describe the close connection that the OCP has with the Point Goalie Problem. We then consider"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8139","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"}