{"paper":{"title":"Continuous monitoring of $\\ell_p$ norms in data streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jaros{\\l}aw B{\\l}asiok, Jelani Nelson, Jian Ding","submitted_at":"2017-04-21T20:41:43Z","abstract_excerpt":"In insertion-only streaming, one sees a sequence of indices $a_1, a_2, \\ldots, a_m\\in [n]$. The stream defines a sequence of $m$ frequency vectors $x^{(1)},\\ldots,x^{(m)}\\in\\mathbb{R}^n$ with $(x^{(t)})_i = |\\{j : j\\in[t], a_j = i\\}|$. That is, $x^{(t)}$ is the frequency vector after seeing the first $t$ items in the stream. Much work in the streaming literature focuses on estimating some function $f(x^{(m)})$. Many applications though require obtaining estimates at time $t$ of $f(x^{(t)})$, for every $t\\in[m]$. Naively this guarantee is obtained by devising an algorithm with failure probabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06710","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":""},"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"}