{"paper":{"title":"Truly Perfect Samplers for Data Streams and Sliding Windows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Rajesh Jayaram, Samson Zhou","submitted_at":"2021-08-26T19:58:33Z","abstract_excerpt":"In the $G$-sampling problem, the goal is to output an index $i$ of a vector $f \\in\\mathbb{R}^n$, such that for all coordinates $j \\in [n]$, \\[\\textbf{Pr}[i=j] = (1 \\pm \\epsilon) \\frac{G(f_j)}{\\sum_{k\\in[n]} G(f_k)} + \\gamma,\\] where $G:\\mathbb{R} \\to \\mathbb{R}_{\\geq 0}$ is some non-negative function. If $\\epsilon = 0$ and $\\gamma = 1/\\text{poly}(n)$, the sampler is called perfect. In the data stream model, $f$ is defined implicitly by a sequence of updates to its coordinates, and the goal is to design such a sampler in small space. Jayaram and Woodruff (FOCS 2018) gave the first perfect $L_p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.12017","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.12017/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"}