{"paper":{"title":"Approximating Large Frequency Moments with Pick-and-Drop Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Rafail Ostrovsky, Vladimir Braverman","submitted_at":"2012-12-02T11:32:47Z","abstract_excerpt":"Given data stream $D = \\{p_1,p_2,...,p_m\\}$ of size $m$ of numbers from $\\{1,..., n\\}$, the frequency of $i$ is defined as $f_i = |\\{j: p_j = i\\}|$. The $k$-th \\emph{frequency moment} of $D$ is defined as $F_k = \\sum_{i=1}^n f_i^k$. We consider the problem of approximating frequency moments in insertion-only streams for $k\\ge 3$. For any constant $c$ we show an $O(n^{1-2/k}\\log(n)\\log^{(c)}(n))$ upper bound on the space complexity of the problem. Here $\\log^{(c)}(n)$ is the iterative $\\log$ function. To simplify the presentation, we make the following assumptions: $n$ and $m$ are polynomially "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0202","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"}