{"paper":{"title":"Universal sketches for the frequency negative moments and other decreasing streaming sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Stephen R. Chestnut, Vladimir Braverman","submitted_at":"2014-08-21T18:24:10Z","abstract_excerpt":"Given a stream with frequencies $f_d$, for $d\\in[n]$, we characterize the space necessary for approximating the frequency negative moments $F_p=\\sum |f_d|^p$, where $p<0$ and the sum is taken over all items $d\\in[n]$ with nonzero frequency, in terms of $n$, $\\epsilon$, and $m=\\sum |f_d|$. To accomplish this, we actually prove a much more general result. Given any nonnegative and nonincreasing function $g$, we characterize the space necessary for any streaming algorithm that outputs a $(1\\pm\\epsilon)$-approximation to $\\sum g(|f_d|)$, where again the sum is over items with nonzero frequency. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5096","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"}