{"paper":{"title":"Tree Path Majority Data Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Gonzalo Navarro, Meng He, Travis Gagie","submitted_at":"2018-06-05T16:53:02Z","abstract_excerpt":"We present the first solution to $\\tau$-majorities on tree paths. Given a tree of $n$ nodes, each with a label from $[1..\\sigma]$, and a fixed threshold $0<\\tau<1$, such a query gives two nodes $u$ and $v$ and asks for all the labels that appear more than $\\tau \\cdot |P_{uv}|$ times in the path $P_{uv}$ from $u$ to $v$, where $|P_{uv}|$ denotes the number of nodes in $P_{uv}$. Note that the answer to any query is of size up to $1/\\tau$. On a $w$-bit RAM, we obtain a linear-space data structure with $O((1/\\tau)\\log^* n \\log\\log_w \\sigma)$ query time. For any $\\kappa > 1$, we can also build a st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01804","kind":"arxiv","version":2},"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"}