{"paper":{"title":"Art gallery problem with rook and queen vision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"\\'Erika Rold\\'an, Hannah Alpert","submitted_at":"2018-10-25T16:31:09Z","abstract_excerpt":"How many chess rooks or queens does it take to guard all the squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art gallery problem in which the guards can \"see\" whichever squares the rook or queen attacks. We show that floor(n/2) rooks or floor(n/3) queens are sufficient and sometimes necessary to guard a polyomino with n tiles. We also prove that finding the minimum number of rooks or the minimum number of queens needed to guard a polyomino is NP-hard. These results also apply to d-dimensional rooks and queens on d-dimensional polycu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10961","kind":"arxiv","version":2},"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"}