{"paper":{"title":"Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DB"],"primary_cat":"cs.DS","authors_text":"G\\'abor Tardos, Hossein Jowhari, Mert Sa\\u{g}lam","submitted_at":"2010-12-22T06:55:58Z","abstract_excerpt":"In this paper, we present near-optimal space bounds for Lp-samplers. Given a stream of updates (additions and subtraction) to the coordinates of an underlying vector x \\in R^n, a perfect Lp sampler outputs the i-th coordinate with probability |x_i|^p/||x||_p^p. In SODA 2010, Monemizadeh and Woodruff showed polylog space upper bounds for approximate Lp-samplers and demonstrated various applications of them. Very recently, Andoni, Krauthgamer and Onak improved the upper bounds and gave a O(\\epsilon^{-p} log^3 n) space \\epsilon relative error and constant failure rate Lp-sampler for p \\in [1,2]. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4889","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"}