{"paper":{"title":"Optimal Query Time for Encoding Range Majority","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Patrick K. Nicholson, Pawel Gawrychowski","submitted_at":"2017-04-20T14:03:31Z","abstract_excerpt":"We revisit the range $\\tau$-majority problem, which asks us to preprocess an array $A[1..n]$ for a fixed value of $\\tau \\in (0,1/2]$, such that for any query range $[i,j]$ we can return a position in $A$ of each distinct $\\tau$-majority element. A $\\tau$-majority element is one that has relative frequency at least $\\tau$ in the range $[i,j]$: i.e., frequency at least $\\tau (j-i+1)$. Belazzougui et al. [WADS 2013] presented a data structure that can answer such queries in $O(1/\\tau)$ time, which is optimal, but the space can be as much as $\\Theta(n \\lg n)$ bits. Recently, Navarro and Thankachan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06149","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"}