{"paper":{"title":"An Approximation Algorithm for the Art Gallery Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CG","authors_text":"\\'Edouard Bonnet, Tillmann Miltzow","submitted_at":"2016-07-19T11:32:54Z","abstract_excerpt":"Given a simple polygon $\\mathcal{P}$ on $n$ vertices, two points $x,y$ in $\\mathcal{P}$ are said to be visible to each other if the line segment between $x$ and $y$ is contained in $\\mathcal{P}$. The Point Guard Art Gallery problem asks for a minimum set $S$ such that every point in $\\mathcal{P}$ is visible from a point in $S$. The set $S$ is referred to as guards. Assuming integer coordinates and a specific general position assumption, we present the first $O(\\log \\text{OPT})$-approximation algorithm for the point guard problem for simple polygons. This algorithm combines ideas of a paper of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05527","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"}