{"paper":{"title":"Near-Optimal and Efficient Encoding for Two-Dimensional Range Minimum Queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adam G\\'orkiewicz, Pawe{\\l} Gawrychowski, Srinivasa Rao Satti","submitted_at":"2026-07-05T21:19:21Z","abstract_excerpt":"We consider the 2D RMQ encoding problem: given an $m\\times n$ array of $mn$ elements over a total order, encode it such that, for any query rectangle, the position of its maximum element can be reported without accessing the original array. For $m \\le n$, it is known how to encode the array in $O(mn \\min\\{m, \\log n\\})$ bits with $O(1)$-time queries [Brodal et al., Algorithmica 2012], and also how to obtain an asymptotically optimal encoding consisting of $O(mn \\log m)$ bits [Brodal et al., ESA 2013]. However, the latter approach does not prove any guarantee on the query time, and it appears to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04509","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}