{"paper":{"title":"On Approximate Range Mode and Range Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bryce Sandlund, Hicham El-Zein, J. Ian Munro, Meng He, Yakov Nekrich","submitted_at":"2019-07-19T17:17:44Z","abstract_excerpt":"For any $\\epsilon \\in (0,1)$, a $(1+\\epsilon)$-approximate range mode query asks for the position of an element whose frequency in the query range is at most a factor $(1+\\epsilon)$ smaller than the true mode. For this problem, we design an $O(n/\\epsilon)$ bit data structure supporting queries in $O(\\lg(1/\\epsilon))$ time. This is an encoding data structure which does not require access to the input sequence; we prove the space cost is asymptotically optimal for constant $\\epsilon$. Our solution improves the previous best result of Greve et al. (Cell Probe Lower Bounds and Approximations for R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08579","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"}