{"paper":{"title":"Anchored Rectangle and Square Packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth, Kevin Balas","submitted_at":"2016-02-29T21:44:01Z","abstract_excerpt":"For points $p_1,\\ldots , p_n$ in the unit square $[0,1]^2$, an \\emph{anchored rectangle packing} consists of interior-disjoint axis-aligned empty rectangles $r_1,\\ldots , r_n\\subseteq [0,1]^2$ such that point $p_i$ is a corner of the rectangle $r_i$ (that is, $r_i$ is \\emph{anchored} at $p_i$) for $i=1,\\ldots, n$. We show that for every set of $n$ points in $[0,1]^2$, there is an anchored rectangle packing of area at least $7/12-O(1/n)$, and for every $n\\in \\mathbf{N}$, there are point sets for which the area of every anchored rectangle packing is at most $2/3$. The maximum area of an anchored"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00060","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"}