{"paper":{"title":"Improved Submatrix Maximum Queries in Monge Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oren Weimann, Pawel Gawrychowski, Shay Mozes","submitted_at":"2013-07-09T01:14:48Z","abstract_excerpt":"We present efficient data structures for submatrix maximum queries in Monge matrices and Monge partial matrices. For $n\\times n$ Monge matrices, we give a data structure that requires O(n) space and answers submatrix maximum queries in $O(\\log n)$ time. The best previous data structure [Kaplan et al., SODA`12] required $O(n \\log n)$ space and $O(\\log^2 n)$ query time. We also give an alternative data structure with constant query-time and $ O(n^{1+\\varepsilon})$ construction time and space for any fixed $\\varepsilon<1$. For $n\\times n$ {\\em partial} Monge matrices we obtain a data structure wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2313","kind":"arxiv","version":4},"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"}