{"paper":{"title":"Adaptive Techniques to find Optimal Planar Boxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"G. Navarro, J. Barbay, P. P\\'erez-Lantero","submitted_at":"2012-04-10T02:58:52Z","abstract_excerpt":"Given a set $P$ of $n$ planar points, two axes and a real-valued score function $f()$ on subsets of $P$, the Optimal Planar Box problem consists in finding a box (i.e. axis-aligned rectangle) $H$ maximizing $f(H\\cap P)$. We consider the case where $f()$ is monotone decomposable, i.e. there exists a composition function $g()$ monotone in its two arguments such that $f(A)=g(f(A_1),f(A_2))$ for every subset $A\\subseteq P$ and every partition $\\{A_1,A_2\\}$ of $A$. In this context we propose a solution for the Optimal Planar Box problem which performs in the worst case $O(n^2\\lg n)$ score compositi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2034","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"}