{"paper":{"title":"Optimal Quantile Approximation in Streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Edo Liberty, Kevin Lang, Zohar Karnin","submitted_at":"2016-03-17T03:14:24Z","abstract_excerpt":"This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\\ldots,x_n$ and allows one to approximate the rank of any query up to additive error $\\varepsilon n$ with probability at least $1-\\delta$. The rank of a query $x$ is the number of stream items such that $x_i \\le x$. The minimal sketch size required for this task is trivially at least $1/\\varepsilon$. Felber and Ostrovsky obtain a $O((1/\\varepsilon)\\log(1/\\varepsilon))$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05346","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"}