{"paper":{"title":"Lower Bound for Succinct Range Minimum Query","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Huacheng Yu, Mingmou Liu","submitted_at":"2020-04-13T01:20:51Z","abstract_excerpt":"Given an integer array $A[1..n]$, the Range Minimum Query problem (RMQ) asks to preprocess $A$ into a data structure, supporting RMQ queries: given $a,b\\in [1,n]$, return the index $i\\in[a,b]$ that minimizes $A[i]$, i.e., $\\mathrm{argmin}_{i\\in[a,b]} A[i]$. This problem has a classic solution using $O(n)$ space and $O(1)$ query time by Gabow, Bentley, Tarjan (STOC, 1984) and Harel, Tarjan (SICOMP, 1984). The best known data structure by Fischer, Heun (SICOMP, 2011) and Navarro, Sadakane (TALG, 2014) uses $2n+n/(\\frac{\\log n}{t})^t+\\tilde{O}(n^{3/4})$ bits and answers queries in $O(t)$ time, as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.05738","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/2004.05738/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"}