{"paper":{"title":"Approximating Large Frequency Moments with $O(n^{1-2/k})$ Bits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Charles Seidell, Gregory Vorsanger, Jonathan Katzman, Vladimir Braverman","submitted_at":"2014-01-08T18:05:26Z","abstract_excerpt":"In this paper we consider the problem of approximating frequency moments in the streaming model. Given a stream $D = \\{p_1,p_2,\\dots,p_m\\}$ of numbers from $\\{1,\\dots, n\\}$, a frequency of $i$ is defined as $f_i = |\\{j: p_j = i\\}|$. The $k$-th \\emph{frequency moment} of $D$ is defined as $F_k = \\sum_{i=1}^n f_i^k$.\n  In this paper we give an upper bound on the space required to find a $k$-th frequency moment of $O(n^{1-2/k})$ bits that matches, up to a constant factor, the lower bound of Woodruff and Zhang (STOC 12) for constant $\\epsilon$ and constant $k$. Our algorithm makes a single pass ov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1763","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"}