{"paper":{"title":"Fast Similarity Sketching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jakob B{\\ae}k Tejs Houen, Mathias B{\\ae}k Tejs Langhede, Mikkel Thorup, S{\\o}ren Dahlgaard","submitted_at":"2017-04-14T09:24:04Z","abstract_excerpt":"We consider the $\\textit{Similarity Sketching}$ problem: Given a universe $[u] = \\{0,\\ldots, u-1\\}$ we want a random function $S$ mapping subsets $A\\subseteq [u]$ into vectors $S(A)$ of size $t$, such that the Jaccard similarity $J(A,B) = |A\\cap B|/|A\\cup B|$ between sets $A$ and $B$ is preserved. More precisely, define $X_i = [S(A)[i] =\n  S(B)[i]]$ and $X = \\sum_{i\\in [t]} X_i$. We want $E[X_i]=J(A,B)$, and we want $X$ to be strongly concentrated around $E[X] = t \\cdot J(A,B)$ (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, lar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04370","kind":"arxiv","version":4},"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/1704.04370/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"}