{"paper":{"title":"Perfect $L_p$ Sampling in a Data Stream","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Rajesh Jayaram","submitted_at":"2018-08-16T14:00:44Z","abstract_excerpt":"In this paper, we resolve the one-pass space complexity of $L_p$ sampling for $p \\in (0,2)$. Given a stream of updates (insertions and deletions) to the coordinates of an underlying vector $f \\in \\mathbb{R}^n$, a perfect $L_p$ sampler must output an index $i$ with probability $|f_i|^p/\\|f\\|_p^p$, and is allowed to fail with some probability $\\delta$. So far, for $p > 0$ no algorithm has been shown to solve the problem exactly using $\\text{poly}( \\log n)$-bits of space. In 2010, Monemizadeh and Woodruff introduced an approximate $L_p$ sampler, which outputs $i$ with probability $(1 \\pm \\nu)|f_i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05497","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.05497/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}